diff --git a/docs/html/img1.png b/docs/html/img1.png index 0423c177..be2b1fe9 100644 Binary files a/docs/html/img1.png and b/docs/html/img1.png differ diff --git a/docs/html/img100.png b/docs/html/img100.png index edebeaa4..837fdfa2 100644 Binary files a/docs/html/img100.png and b/docs/html/img100.png differ diff --git a/docs/html/img101.png b/docs/html/img101.png index 9113ab47..edebeaa4 100644 Binary files a/docs/html/img101.png and b/docs/html/img101.png differ diff --git a/docs/html/img32.png b/docs/html/img32.png index 8f2424d5..5ec9d53a 100644 Binary files a/docs/html/img32.png and b/docs/html/img32.png differ diff --git a/docs/html/img58.png b/docs/html/img58.png index f220846e..48a1cba2 100644 Binary files a/docs/html/img58.png and b/docs/html/img58.png differ diff --git a/docs/html/img71.png b/docs/html/img71.png index b7d510e1..7bbd8b98 100644 Binary files a/docs/html/img71.png and b/docs/html/img71.png differ diff --git a/docs/html/img83.png b/docs/html/img83.png index e2052d1f..f2edec00 100644 Binary files a/docs/html/img83.png and b/docs/html/img83.png differ diff --git a/docs/html/img92.png b/docs/html/img92.png index 809810bb..fdb8db9f 100644 Binary files a/docs/html/img92.png and b/docs/html/img92.png differ diff --git a/docs/html/img93.png b/docs/html/img93.png index 37d84a8e..5f7f2e98 100644 Binary files a/docs/html/img93.png and b/docs/html/img93.png differ diff --git a/docs/html/img94.png b/docs/html/img94.png index faea0ef9..5db96932 100644 Binary files a/docs/html/img94.png and b/docs/html/img94.png differ diff --git a/docs/html/img95.png b/docs/html/img95.png index fa8de263..faea0ef9 100644 Binary files a/docs/html/img95.png and b/docs/html/img95.png differ diff --git a/docs/html/img96.png b/docs/html/img96.png index 105a324f..fa8de263 100644 Binary files a/docs/html/img96.png and b/docs/html/img96.png differ diff --git a/docs/html/img97.png b/docs/html/img97.png index 17e3679d..105a324f 100644 Binary files a/docs/html/img97.png and b/docs/html/img97.png differ diff --git a/docs/html/img98.png b/docs/html/img98.png index dcac3db4..17e3679d 100644 Binary files a/docs/html/img98.png and b/docs/html/img98.png differ diff --git a/docs/html/img99.png b/docs/html/img99.png index 837fdfa2..dcac3db4 100644 Binary files a/docs/html/img99.png and b/docs/html/img99.png differ diff --git a/docs/html/index.html b/docs/html/index.html index fb8df33b..03db67c7 100644 --- a/docs/html/index.html +++ b/docs/html/index.html @@ -67,7 +67,7 @@ University of Rome ``Tor Vergata'', Italy
Software version: 1.0
-July 24, 2008 +Sept. 9th, 2008
diff --git a/docs/html/node12.html b/docs/html/node12.html index 2fc7ee8f..b718718e 100644 --- a/docs/html/node12.html +++ b/docs/html/node12.html @@ -276,7 +276,7 @@ three steps: ALT="$i=1,\ldots,m$">;
  • prolongation and sum of the $w_i$'s, i.e. diff --git a/docs/html/node26.html b/docs/html/node26.html index f36d1f08..65ac3daa 100644 --- a/docs/html/node26.html +++ b/docs/html/node26.html @@ -67,7 +67,7 @@ Mathematics Department, Macquarie University, Sydney. The command line arguments were:
    latex2html-noaddress -dir ../../html userhtml.tex

    -The translation was initiated by Salvatore Filippone on 2008-09-04 +The translation was initiated by Salvatore Filippone on 2008-09-09

    diff --git a/docs/html/node3.html b/docs/html/node3.html index 123339e8..641f4ce7 100644 --- a/docs/html/node3.html +++ b/docs/html/node3.html @@ -75,7 +75,7 @@ Ax=b, -->
    \begin{displaymath} S = I - \omega D^{-1} A , diff --git a/docs/html/node18.html b/docs/html/node18.html index 8b76a6d5..6dd010ad 100644 --- a/docs/html/node18.html +++ b/docs/html/node18.html @@ -439,7 +439,7 @@ level.</CAPTION> <TR><TD ALIGN=mld_coarse_sweeps_ integer Any int. num. $> 0$ 4
    \begin{displaymath} Ax=b, diff --git a/docs/html/userhtml.html b/docs/html/userhtml.html index fb8df33b..03db67c7 100644 --- a/docs/html/userhtml.html +++ b/docs/html/userhtml.html @@ -67,7 +67,7 @@ University of Rome ``Tor Vergata'', Italy <BR> Software version: 1.0 <BR> -July 24, 2008 +Sept. 9th, 2008 <BR> diff --git a/docs/mld2p4-1.0-guide.pdf b/docs/mld2p4-1.0-guide.pdf index 484a2ff4..6a1d2e3c 100644 --- a/docs/mld2p4-1.0-guide.pdf +++ b/docs/mld2p4-1.0-guide.pdf @@ -1,5 +1,4 @@ %PDF-1.4 -% 5 0 obj << /S /GoTo /D (title.0) >> endobj @@ -139,7 +138,7 @@ endobj (7 Error Handling) endobj 97 0 obj -<< /S /GoTo /D (appendix.A) >> +<< /S /GoTo /D (section.A) >> endobj 100 0 obj (A License) @@ -154,5397 +153,8704 @@ endobj << /S /GoTo /D [106 0 R /Fit ] >> endobj 108 0 obj << -/Length 1164 +/Length 1832 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G +1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G +1 g 1 G 0 g 0 G +1 g 1 G 0 g 0 G +0 g 0 G +0 g 0 G +1 g 1 G +0 g 0 G +0 g 0 G +0 g 0 G +0 g 0 G +0 g 0 G +0 g 0 G +0 g 0 G +0.25 g 0.25 G +0 g 0 G +0.5 g 0.5 G +0 g 0 G +1 0 0 1 295.4835 -96.2627 cm +0 g 0 G +0 g 0 G +1 0 0 1 -389.0837 -618.8325 cm BT -/F17 24.7871 Tf 394.538 618.833 Td [(MLD2P4)]TJ -229.059 -27.023 Td [(User's)-375(and)-375(Reference)-375(Guide)]TJ +/F19 24.7871 Tf 394.5382 618.8325 Td[(MLD2)-1(P)1(4)]TJ -229.0594 -27.0226 Td[(Us)1(e)-1(r')-1(s)-374(and)-375(Re)-1(f)1(e)-1(re)-1(nce)-375(Gui)-1(de)]TJ ET -q -1 0 0 1 93.6 573.564 cm -0 0 412.451 4.981 re f -Q +1 0 0 1 93.6002 573.5637 cm +0 0 412.4511 4.9813 re f +1 0 0 1 -93.6002 -573.5637 cm BT -/F19 14.3462 Tf 192.132 548.586 Td [(A)-350(guide)-350(for)-350(the)-350(Multi-L)50(evel)-350(Domain)-350(De)50(c)50(omp)50(osition)]TJ -5.512 -17.256 Td [(Par)50(al)-50(lel)-350(Pr)50(e)50(c)50(onditioners)-350(Package)-350(b)50(ase)50(d)-350(on)-350(PSBLAS)]TJ +/F21 14.3462 Tf 192.1325 548.5855 Td[(A)-350(guide)-350(for)-349(the)-350(Multi-L)49(evel)-350(Domain)-350(D)-1(e)50(c)50(omp)50(osition)]TJ -5.5128 -17.2553 Td[(Par)50(al)-50(lel)-350(Pr)50(e)50(c)50(onditioner)1(s)-350(P)-1(ackage)-350(b)50(ase)50(d)-350(on)-350(PSB)-1(LAS)]TJ +ET +1 0 0 1 399.8094 451.9414 cm 0 g 0 G 0 g 0 G -/F17 11.9552 Tf 218.644 -79.389 Td [(P)31(asqua)-375(D'Am)31(bra)]TJ/F37 11.9552 Tf -31.595 -13.947 Td [(ICAR-CNR,)-326(Naples,)-327(Italy)]TJ/F17 11.9552 Tf 20.434 -29.39 Td [(Daniela)-375(di)-375(Sera\014no)]TJ/F37 11.9552 Tf -62.784 -13.948 Td [(Second)-326(Univ)27(ersit)27(y)-326(of)-327(Na)1(ples,)-327(Italy)]TJ/F17 11.9552 Tf 60.715 -29.39 Td [(Salv)62(atore)-375(Filipp)-31(one)]TJ/F37 11.9552 Tf -93.327 -13.947 Td [(Univ)27(ersit)27(y)-326(of)-326(Rome)-327(\134T)82(or)-326(V)81(ergata> endobj 109 0 obj << -/D [106 0 R /XYZ 93.6 740.002 null] +/D [106 0 R /XYZ 93.6002 740.0018 null] >> endobj 110 0 obj << -/D [106 0 R /XYZ 93.6 715.095 null] +/D [106 0 R /XYZ 93.6002 715.0952 null] >> endobj 6 0 obj << -/D [106 0 R /XYZ 93.6 715.095 null] +/D [106 0 R /XYZ 93.6002 715.0952 null] >> endobj 107 0 obj << -/Font << /F17 111 0 R /F19 112 0 R /F37 113 0 R >> +/Font << /F19 113 0 R /F21 116 0 R /F39 119 0 R >> /ProcSet [ /PDF /Text ] >> endobj -117 0 obj << -/Length 32 +123 0 obj << +/Length 135 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G +1 0 0 1 -412.4511 -648.3688 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -116 0 obj << +122 0 obj << /Type /Page -/Contents 117 0 R -/Resources 115 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 114 0 R +/Contents 123 0 R +/Resources 121 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 120 0 R >> endobj -118 0 obj << -/D [116 0 R /XYZ 86.4 740.002 null] +124 0 obj << +/D [122 0 R /XYZ 86.3998 740.0018 null] >> endobj -115 0 obj << +121 0 obj << /ProcSet [ /PDF ] >> endobj -121 0 obj << -/Length 3755 +127 0 obj << +/Length 4830 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G +1 0 0 1 -93.6002 -740.0018 cm BT -/F15 10.9091 Tf 503.021 740.002 Td [(i)]TJ +/F15 10.9091 Tf 503.021 740.0018 Td[(i)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -409.421 -35.866 Td [(Abstract)]TJ/F41 10.9091 Tf 0 -24.352 Td [(MLD2P4)-514(\050Mul)66(ti-Level)-514(Domain)-515(Decomposition)-514(P)87(arallel)-514(Preconditioners)]TJ 0 -13.549 Td [(P)88(a)22(cka)22(ge)-370(based)-370(on)-370(PSBLAS)]TJ/F15 10.9091 Tf 149.304 0 Td [(\051)-326(is)-326(a)-326(pac)28(k)55(age)-326(of)-326(parallel)-326(al)1(ge)-1(b)1(raic)-326(m)27(ulti-lev)28(el)-326(precondi-)]TJ -149.304 -13.549 Td [(tioners.)-442(It)-328(implemen)28(ts)-327(v)55(arious)-327(v)28(ers)-1(i)1(ons)-328(of)-327(one-lev)28(e)-1(l)-327(additiv)28(e)-327(and)-328(of)-327(m)28(ulti-lev)28(el)-328(additiv)28(e)]TJ 0 -13.549 Td [(and)-339(h)28(ybrid)-339(Sc)28(h)28(w)27(ar)1(z)-339(algorithms.)-462(In)-339(the)-339(m)28(ulti-lev)28(el)-339(case,)-341(a)-338(purely)-339(algebraic)-339(approac)28(h)-339(is)]TJ 0 -13.55 Td [(applied)-307(to)-306(ge)-1(n)1(e)-1(rat)1(e)-307(coarse-le)-1(v)28(el)-307(corrections,)-312(so)-307(th)1(at)-307(no)-307(geometric)-307(bac)28(kground)-307(is)-307(needed)]TJ 0 -13.549 Td [(concerning)-348(the)-347(matrix)-348(to)-348(b)-27(e)-348(preconditioned.)-488(The)-347(matrix)-348(is)-348(required)-347(to)-348(b)-28(e)-347(square,)-352(real)]TJ 0 -13.549 Td [(or)-333(complex,)-334(with)-333(a)-333(symmetric)-334(sparsit)28(y)-333(pattern.)]TJ 16.937 -13.549 Td [(MLD2P4)-362(has)-361(b)-28(een)-362(designed)-361(to)-362(pro)28(vide)-362(scalable)-361(and)-362(easy-to-use)-362(preconditioners)-361(in)]TJ -16.937 -13.549 Td [(the)-346(con)28(text)-346(of)-345(the)-346(PSBLAS)-345(\050P)27(arallel)-345(Sparse)-346(Basic)-346(Linear)-345(Algebra)-346(Subprograms\051)-345(com)-1(-)]TJ 0 -13.55 Td [(putational)-357(f)1(rame)-1(w)28(ork)-356(and)-357(can)-357(b)-27(e)-357(used)-357(in)-356(conjuction)-357(with)-357(the)-356(Krylo)28(v)-357(solv)28(ers)-357(a)28(v)55(ailable)]TJ 0 -13.549 Td [(in)-424(this)-423(framew)27(or)1(k.)-716(MLD2P4)-424(enab)1(le)-1(s)-423(the)-424(user)-424(to)-423(easily)-424(sp)-28(ecify)-423(di\013eren)27(t)-423(asp)-28(ects)-424(of)-424(a)]TJ 0 -13.549 Td [(generic)-485(algebraic)-485(m)28(ultilev)27(el)-485(Sc)28(h)28(w)28(arz)-485(preconditioner,)-523(th)28(us)-485(allo)27(wing)-485(to)-485(searc)28(h)-485(for)-485(the)]TJ 0 -13.549 Td [(\134b)-28(est")-333(preconditioner)-333(for)-334(the)-333(problem)-333(at)-334(h)1(and.)]TJ 16.937 -13.549 Td [(The)-278(pac)27(k)56(age)-278(has)-279(b)-28(een)-278(designed)-278(em)-1(p)1(lo)27(ying)-278(ob)-56(j)1(e)-1(ct-orien)28(ted)-278(tec)28(hniques,)-290(using)-278(F)83(ortran)]TJ -16.937 -13.55 Td [(95,)-485(with)-455(in)28(terfaces)-455(to)-455(addition)1(al)-455(third)-455(part)28(y)-455(libraries)-454(s)-1(u)1(c)27(h)-455(as)-454(UMFP)83(A)28(CK,)-455(Sup)-28(erLU)]TJ 0 -13.549 Td [(and)-366(Sup)-28(erLU)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 14.3462 Tf 93.6002 704.1363 Td[(Abs)1(t)-1(ract)]TJ/F43 10.9091 Tf 0 -24.3522 Td[(MLD2P4)-514(\050Mul)66(ti-L)-1(e)1(v)-1(e)1(l)-515(Domain)-515(Decom)1(pos)1(i)-1(tion)-514(P)87(aral)-1(lel)-515(P)1(r)-1(e)1(cond)-1(itioners)]TJ 0 -13.5492 Td[(P)88(a)22(cka)22(ge)-370(based)-370(on)-370(PSBLAS)]TJ/F15 10.9091 Tf 149.304 0 Td[(\051)-326(is)-326(a)-326(pac)28(k)55(age)-326(of)-326(p)1(arall)1(e)-1(l)-326(al)1(ge)-1(b)1(raic)-326(m)27(u)1(lti-lev)28(e)-1(l)-325(prec)-1(on)1(di)1(-)]TJ -149.304 -13.5492 Td[(tion)1(e)-1(r)1(s)-1(.)-442(It)-327(im)-1(p)1(lem)-1(en)28(ts)-328(v)56(ar)1(ious)-328(v)28(ersions)-327(of)-327(one-)-1(l)1(e)-1(v)28(el)-327(addi)1(tiv)28(e)-328(an)1(d)-327(of)-327(m)27(u)1(lti-lev)28(e)-1(l)-327(add)1(itiv)28(e)]TJ 0 -13.5492 Td[(and)-338(h)28(yb)1(rid)-338(Sc)28(h)28(w)27(ar)1(z)-340(al)1(gorith)1(m)-1(s.)-461(In)-339(th)1(e)-340(m)28(ult)1(i-)-1(l)1(e)-1(v)28(el)-339(cas)-1(e,)-340(a)-339(pur)1(e)-1(l)1(y)-339(algebrai)1(c)-340(ap)1(proac)28(h)-339(is)]TJ 0 -13.5492 Td[(app)1(lied)-306(to)-307(ge)-1(n)1(e)-1(r)1(ate)-307(c)-1(oarse-)-1(lev)28(el)-307(correc)-1(ti)1(ons,)-312(s)-1(o)-307(t)1(hat)-307(n)1(o)-307(geom)-1(etric)-307(b)1(ac)27(kgrou)1(nd)-306(is)-307(needed)]TJ 0 -13.5492 Td[(conce)-1(rn)1(in)1(g)-348(the)-348(matri)1(x)-348(to)-347(b)-28(e)-348(pr)1(e)-1(cond)1(ition)1(e)-1(d)1(.)-488(Th)1(e)-348(m)-1(atr)1(ix)-348(i)1(s)-349(r)1(e)-1(q)1(uir)1(e)-1(d)-347(to)-348(b)-27(e)-348(s)-1(q)1(uare,)-351(real)]TJ 0 -13.5492 Td[(or)-333(com)-1(p)1(le)-1(x)1(,)-333(w)-1(i)1(th)-333(a)-334(symme)-1(tr)1(ic)-334(sparsit)28(y)-333(patt)1(e)-1(rn)1(.)]TJ 16.9365 -13.5492 Td[(MLD2P)1(4)-362(h)1(as)-362(b)-28(ee)-1(n)-361(d)1(e)-1(signed)-361(to)-362(p)1(ro)28(vid)1(e)-363(scalable)-362(an)1(d)-361(e)-1(asy-to-)-1(u)1(s)-1(e)-362(p)1(rec)-1(on)1(diti)1(oners)-362(in)]TJ -16.9365 -13.5492 Td[(th)1(e)-347(con)28(text)-345(of)-346(th)1(e)-346(PS)1(B)-1(LAS)-345(\050P)28(ar)1(allel)-346(S)1(parse)-346(Bas)-1(ic)-346(Lin)1(e)-1(ar)-345(Algebr)1(a)-346(Su)1(bp)1(rograms\051)-346(com)-1(-)]TJ 0 -13.5492 Td[(pu)1(tation)1(al)-357(f)1(rame)-1(w)28(ork)-356(and)-356(c)-1(an)-356(b)-27(e)-357(use)-1(d)-356(in)-356(conj)1(uction)-356(w)-1(i)1(th)-357(t)1(he)-357(Kry)1(lo)28(v)-357(solv)28(ers)-357(a)28(v)55(ai)1(lable)]TJ 0 -13.5492 Td[(in)-423(th)1(is)-424(framew)27(or)1(k.)-716(M)1(LD2P4)-423(e)-1(n)1(ables)-424(the)-424(u)1(s)-1(er)-424(t)1(o)-424(e)-1(asily)-423(s)-1(p)-27(ec)-1(if)1(y)-424(d)1(i\013e)-1(r)1(e)-1(n)28(t)-423(as)-1(p)-27(ec)-1(ts)-424(of)-423(a)]TJ 0 -13.5492 Td[(generic)-485(alge)-1(b)1(raic)-485(m)27(u)1(ltil)1(e)-1(v)28(el)-485(Sc)28(h)28(w)27(ar)1(z)-486(p)1(rec)-1(on)1(diti)1(oner,)-523(th)28(u)1(s)-486(al)1(lo)28(w)-1(i)1(ng)-485(to)-485(se)-1(arc)28(h)-485(f)1(or)-485(the)]TJ 0 -13.5492 Td[(\134b)-27(e)-1(st")-333(prec)-1(on)1(di)1(tioner)-333(for)-333(th)1(e)-334(p)1(robl)1(e)-1(m)-334(at)-333(h)1(and)1(.)]TJ 16.9365 -13.5492 Td[(The)-279(p)1(ac)27(k)56(age)-279(h)1(as)-279(b)-28(ee)-1(n)-277(des)-1(ign)1(e)-1(d)-278(emplo)28(yin)1(g)-279(ob)-55(j)1(e)-1(ct-orien)28(ted)-278(te)-1(c)28(hn)1(iqu)1(e)-1(s,)-290(u)1(s)-1(i)1(ng)-278(F)83(or)1(tran)]TJ -16.9365 -13.5492 Td[(95,)-485(with)-454(in)28(terf)1(ac)-1(es)-455(to)-455(add)1(ition)1(al)-455(th)1(ird)-454(par)1(t)28(y)-455(li)1(brar)1(ie)-1(s)-455(suc)28(h)-455(as)-455(UMF)1(P)83(A)28(CK,)-454(Sup)-27(erLU)]TJ 0 -13.5492 Td[(and)-365(Su)1(p)-28(erLU)]TJ ET +1 0 0 1 158.4299 476.5462 cm q -1 0 0 1 158.43 476.745 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.2728 0.1992 l +S Q +1 0 0 1 -158.4299 -476.5462 cm BT -/F15 10.9091 Tf 161.703 476.546 Td [(Dist,)-374(that)-366(can)-366(b)-28(e)-366(exploited)-366(in)-366(building)-366(m)28(ulti-lev)28(el)-366(preconditioners.)-543(The)]TJ -68.103 -13.549 Td [(parallel)-276(implemen)28(tation)-276(is)-276(based)-276(on)-276(a)-276(Single)-276(Program)-276(Multiple)-276(Data)-276(\050SP)1(MD\051)-276(paradigm)]TJ 0 -13.549 Td [(for)-267(distri)1(buted-me)-1(mory)-266(arc)28(hitectures;)-289(the)-267(in)28(ter-pro)-28(cess)-267(d)1(ata)-267(comm)28(unication)-267(is)-267(based)-266(on)]TJ 0 -13.549 Td [(MPI)-333(and)-334(is)-333(managed)-333(mainly)-333(through)-334(PSBLAS.)]TJ 16.937 -13.55 Td [(This)-353(guide)-354(pro)28(vides)-353(a)-354(brief)-353(description)-354(of)-353(the)-354(fu)1(nctionalities)-354(and)-353(the)-354(user)-353(in)28(terface)]TJ -16.937 -13.549 Td [(of)-333(MLD2P4.)]TJ +/F15 10.9091 Tf 161.7027 476.5462 Td[(Dist,)-374(th)1(at)-366(c)-1(an)-365(b)-28(e)-366(e)-1(x)1(ploit)1(e)-1(d)-366(i)1(n)-366(b)1(uild)1(in)1(g)-367(m)28(ul)1(ti-le)-1(v)28(el)-366(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-1(.)-542(The)]TJ -68.1025 -13.5492 Td[(par)1(allel)-276(impl)1(e)-1(me)-1(n)29(tation)-276(i)1(s)-277(b)1(as)-1(ed)-276(on)-275(a)-276(Sin)1(gle)-276(Progr)1(am)-277(M)1(ult)1(iple)-276(Data)-276(\050S)1(PM)1(D\051)-276(par)1(adigm)]TJ 0 -13.5492 Td[(for)-266(d)1(is)-1(tr)1(ibu)1(ted-m)-1(emory)-266(arc)27(h)1(ite)-1(ctu)1(re)-1(s;)-289(t)1(he)-267(in)28(ter-pr)1(o)-28(ce)-1(ss)-267(data)-266(c)-1(omm)27(u)1(nication)-266(is)-267(b)1(as)-1(ed)-266(on)]TJ 0 -13.5492 Td[(MP)1(I)-334(an)1(d)-333(is)-334(managed)-333(mainl)1(y)-333(throu)1(gh)-333(PS)1(BLAS.)]TJ 16.9365 -13.5492 Td[(This)-353(guid)1(e)-354(pr)1(o)27(v)1(ides)-354(a)-354(b)1(rief)-353(des)-1(cri)1(ption)-353(of)-353(th)1(e)-354(fu)1(nction)1(alities)-354(and)-353(t)1(he)-354(u)1(s)-1(er)-354(i)1(n)28(terface)]TJ -16.9365 -13.5492 Td[(of)-333(MLD)1(2P4.)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -120 0 obj << +126 0 obj << /Type /Page -/Contents 121 0 R -/Resources 119 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 114 0 R +/Contents 127 0 R +/Resources 125 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 120 0 R >> endobj -122 0 obj << -/D [120 0 R /XYZ 93.6 740.002 null] +128 0 obj << +/D [126 0 R /XYZ 93.6002 740.0018 null] >> endobj 10 0 obj << -/D [120 0 R /XYZ 93.6 693.333 null] +/D [126 0 R /XYZ 93.6002 693.3333 null] >> endobj -119 0 obj << -/Font << /F15 123 0 R /F17 111 0 R /F41 124 0 R >> +125 0 obj << +/Font << /F15 131 0 R /F19 113 0 R /F43 134 0 R >> /ProcSet [ /PDF /Text ] >> endobj -127 0 obj << -/Length 79 +137 0 obj << +/Length 222 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(ii)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(ii)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -648.3688 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -126 0 obj << +136 0 obj << /Type /Page -/Contents 127 0 R -/Resources 125 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 114 0 R +/Contents 137 0 R +/Resources 135 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 120 0 R >> endobj -128 0 obj << -/D [126 0 R /XYZ 86.4 740.002 null] +138 0 obj << +/D [136 0 R /XYZ 86.3998 740.0018 null] >> endobj -125 0 obj << -/Font << /F15 123 0 R >> +135 0 obj << +/Font << /F15 131 0 R >> /ProcSet [ /PDF /Text ] >> endobj -155 0 obj << -/Length 6438 +141 0 obj << +/Length 13097 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G +1 0 0 1 -93.6002 -740.0018 cm BT -/F15 10.9091 Tf 496.96 740.002 Td [(iii)]TJ +/F15 10.9091 Tf 496.9604 740.0018 Td[(iii)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -403.36 -35.866 Td [(Con)31(ten)31(ts)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 14.3462 Tf 93.6002 704.1363 Td[(Co)-1(n)31(te)-1(n)32(t)-1(s)]TJ +ET +1 0 0 1 93.6002 679.678 cm 0 0 1 rg 0 0 1 RG -/F43 10.9091 Tf 0 -24.458 Td [(Abstract)]TJ +1 0 0 1 -93.6002 -679.678 cm +BT +/F45 10.9091 Tf 93.6002 679.678 Td[(Abstract)]TJ +ET +1 0 0 1 141.6014 679.678 cm 0 g 0 G - 408.966 0 Td [(i)]TJ +1 0 0 1 -141.6014 -679.678 cm +BT +/F45 10.9091 Tf 502.5665 679.678 Td[(i)]TJ +ET +1 0 0 1 93.6002 655.2197 cm 0 0 1 rg 0 0 1 RG - -408.966 -24.458 Td [(1)-925(General)-383(Ov)32(erview)]TJ +1 0 0 1 -93.6002 -655.2197 cm +BT +/F45 10.9091 Tf 93.6002 655.2197 Td[(1)-925(General)-384(Ov)33(e)-1(r)1(vi)-1(ew)]TJ +ET +1 0 0 1 208.7587 655.2197 cm 0 g 0 G - [-26677(1)]TJ +1 0 0 1 -208.7587 -655.2197 cm +BT +/F45 10.9091 Tf 499.7786 655.2197 Td[(1)]TJ +ET +1 0 0 1 93.6002 630.7614 cm 0 0 1 rg 0 0 1 RG - 0 -24.459 Td [(2)-925(Co)-32(de)-383(Distribution)]TJ +1 0 0 1 -93.6002 -630.7614 cm +BT +/F45 10.9091 Tf 93.6002 630.7614 Td[(2)-925(Co)-31(de)-384(Distribution)]TJ +ET +1 0 0 1 209.6769 630.7614 cm 0 g 0 G - [-26593(3)]TJ +1 0 0 1 -209.6769 -630.7614 cm +BT +/F45 10.9091 Tf 499.7786 630.7614 Td[(3)]TJ +ET +1 0 0 1 93.6002 606.3031 cm 0 0 1 rg 0 0 1 RG - 0 -24.458 Td [(3)-925(Con\014guring)-383(and)-384(Building)-383(MLD2P4)]TJ +1 0 0 1 -93.6002 -606.3031 cm +BT +/F45 10.9091 Tf 93.6002 606.3031 Td[(3)-925(Con)1(\014guring)-383(and)-384(Buildi)-1(ng)-383(ML)1(D2P4)]TJ +ET +1 0 0 1 303.7126 606.3031 cm 0 g 0 G - [-17973(4)]TJ +1 0 0 1 -303.7126 -606.3031 cm +BT +/F45 10.9091 Tf 499.7786 606.3031 Td[(4)]TJ +ET +1 0 0 1 109.9639 592.7539 cm 0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.549 Td [(3.1)-1022(Prerequisites)]TJ +1 0 0 1 -109.9639 -592.7539 cm +BT +/F15 10.9091 Tf 109.9639 592.7539 Td[(3.1)-1022(Pr)1(e)-1(r)1(e)-1(qu)1(isites)]TJ +ET +1 0 0 1 196.2974 592.7539 cm 0 g 0 G - [-947(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -196.2974 -592.7539 cm +BT +/F15 10.9091 Tf 206.629 592.7539 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.5968 592.7539 cm 0 g 0 G - [-1781(4)]TJ +1 0 0 1 -500.5968 -592.7539 cm +BT +/F15 10.9091 Tf 500.5968 592.7539 Td[(4)]TJ +ET +1 0 0 1 506.0513 592.7539 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(3.2)-1022(Optional)-333(third)-334(par)1(t)27(y)-333(libraries)]TJ +1 0 0 1 -109.9639 -579.2047 cm +BT +/F15 10.9091 Tf 109.9639 579.2047 Td[(3.2)-1022(Op)1(tional)-333(th)1(ird)-332(part)28(y)-333(li)1(brar)1(ie)-1(s)]TJ +ET +1 0 0 1 275.2369 579.2047 cm 0 g 0 G - [-711(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -275.2369 -579.2047 cm +BT +/F15 10.9091 Tf 282.9917 579.2047 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.5968 579.2047 cm 0 g 0 G - [-1781(5)]TJ +1 0 0 1 -500.5968 -579.2047 cm +BT +/F15 10.9091 Tf 500.5968 579.2047 Td[(5)]TJ +ET +1 0 0 1 506.0513 579.2047 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(3.3)-1022(Con\014guration)-333(options)]TJ +1 0 0 1 -109.9639 -565.6555 cm +BT +/F15 10.9091 Tf 109.9639 565.6555 Td[(3.3)-1022(Con\014)1(gurat)1(ion)-333(opti)1(ons)]TJ +ET +1 0 0 1 238.7823 565.6555 cm 0 g 0 G - [-942(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -238.7823 -565.6555 cm +BT +/F15 10.9091 Tf 249.0527 565.6555 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.5968 565.6555 cm 0 g 0 G - [-1781(5)]TJ +1 0 0 1 -500.5968 -565.6555 cm +BT +/F15 10.9091 Tf 500.5968 565.6555 Td[(5)]TJ +ET +1 0 0 1 506.0513 565.6555 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - 0 -13.55 Td [(3.4)-1022(Bug)-334(r)1(e)-1(p)-27(orting)]TJ +1 0 0 1 -109.9639 -552.1063 cm +BT +/F15 10.9091 Tf 109.9639 552.1063 Td[(3.4)-1022(Bug)-333(rep)-28(or)1(ting)]TJ +ET +1 0 0 1 201.9338 552.1063 cm 0 g 0 G - [-431(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -201.9338 -552.1063 cm +BT +/F15 10.9091 Tf 206.629 552.1063 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.5968 552.1063 cm 0 g 0 G - [-1780(8)]TJ +1 0 0 1 -500.5968 -552.1063 cm +BT +/F15 10.9091 Tf 500.5968 552.1063 Td[(8)]TJ +ET +1 0 0 1 506.0513 552.1063 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(3.5)-1022(Example)-333(and)-334(test)-333(programs)]TJ +1 0 0 1 -109.9639 -538.5571 cm +BT +/F15 10.9091 Tf 109.9639 538.5571 Td[(3.5)-1022(Ex)1(am)-1(p)1(le)-334(an)1(d)-333(te)-1(st)-333(pr)1(ograms)]TJ +ET +1 0 0 1 267.2066 538.5571 cm 0 g 0 G - [-669(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -267.2066 -538.5571 cm +BT +/F15 10.9091 Tf 274.5069 538.5571 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +ET +1 0 0 1 500.5968 538.5571 cm 0 g 0 G - [-1780(8)]TJ +1 0 0 1 -500.5968 -538.5571 cm +BT +/F15 10.9091 Tf 500.5968 538.5571 Td[(8)]TJ +ET +1 0 0 1 506.0513 538.5571 cm 0 g 0 G +1 0 0 1 -412.4511 -24.4583 cm 0 0 1 rg 0 0 1 RG -/F43 10.9091 Tf -16.364 -24.458 Td [(4)-925(Multi-lev)32(el)-384(Domain)-383(Decomp)-32(osition)-383(Bac)32(kground)]TJ +1 0 0 1 -93.6002 -514.0988 cm +BT +/F45 10.9091 Tf 93.6002 514.0988 Td[(4)-925(Multi)-1(-le)-1(v)32(el)-383(Dom)-1(ain)-383(Decom)-1(p)-32(os)1(i)-1(tion)-383(B)-1(ac)32(kgr)1(ound)]TJ +ET +1 0 0 1 371.8576 514.0988 cm 0 g 0 G - [-11727(9)]TJ +1 0 0 1 -371.8576 -514.0988 cm +BT +/F45 10.9091 Tf 499.7786 514.0988 Td[(9)]TJ +ET +1 0 0 1 109.9639 500.5496 cm 0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.549 Td [(4.1)-1022(Multi-lev)28(el)-334(Sc)28(h)28(w)28(arz)-334(Preconditioners)]TJ +1 0 0 1 -109.9639 -500.5496 cm +BT +/F15 10.9091 Tf 109.9639 500.5496 Td[(4.1)-1022(Mu)1(lti-lev)28(e)-1(l)-333(S)1(c)27(h)28(w)28(arz)-334(P)1(rec)-1(on)1(diti)1(oners)]TJ +ET +1 0 0 1 306.2671 500.5496 cm 0 g 0 G - [-977(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +1 0 0 1 -306.2671 -500.5496 cm +BT +/F15 10.9091 Tf 316.9306 500.5496 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 495.1422 500.5496 cm 0 g 0 G - [-1281(10)]TJ +1 0 0 1 -495.1422 -500.5496 cm +BT +/F15 10.9091 Tf 495.1422 500.5496 Td[(10)]TJ +ET +1 0 0 1 506.0513 500.5496 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - 0 -13.55 Td [(4.2)-1022(Smo)-28(othed)-333(Aggregation)]TJ +1 0 0 1 -109.9639 -487.0004 cm +BT +/F15 10.9091 Tf 109.9639 487.0004 Td[(4.2)-1022(Smo)-28(oth)1(e)-1(d)-332(Aggre)-1(gat)1(ion)]TJ +ET +1 0 0 1 244.1762 487.0004 cm 0 g 0 G - [-447(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -244.1762 -487.0004 cm +BT +/F15 10.9091 Tf 249.0527 487.0004 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 495.1422 487.0004 cm 0 g 0 G - [-1281(12)]TJ +1 0 0 1 -495.1422 -487.0004 cm +BT +/F15 10.9091 Tf 495.1422 487.0004 Td[(12)]TJ +ET +1 0 0 1 506.0513 487.0004 cm 0 g 0 G +1 0 0 1 -412.4511 -24.4583 cm 0 0 1 rg 0 0 1 RG -/F43 10.9091 Tf -16.364 -24.458 Td [(5)-925(Getting)-383(Started)]TJ +1 0 0 1 -93.6002 -462.5421 cm +BT +/F45 10.9091 Tf 93.6002 462.5421 Td[(5)-925(Gett)-1(ing)-383(Started)]TJ +ET +1 0 0 1 196.9557 462.5421 cm 0 g 0 G - [-27184(15)]TJ +1 0 0 1 -196.9557 -462.5421 cm +BT +/F45 10.9091 Tf 493.506 462.5421 Td[(15)]TJ +ET +1 0 0 1 109.9639 448.9929 cm 0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.549 Td [(5.1)-1022(Examples)]TJ +1 0 0 1 -109.9639 -448.9929 cm +BT +/F15 10.9091 Tf 109.9639 448.9929 Td[(5.1)-1022(Ex)1(am)-1(p)1(les)]TJ +ET +1 0 0 1 181.0246 448.9929 cm 0 g 0 G - [-792(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -181.0246 -448.9929 cm +BT +/F15 10.9091 Tf 189.6596 448.9929 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 495.1422 448.9929 cm 0 g 0 G - [-1280(16)]TJ +1 0 0 1 -495.1422 -448.9929 cm +BT +/F15 10.9091 Tf 495.1422 448.9929 Td[(16)]TJ +ET +1 0 0 1 506.0513 448.9929 cm 0 g 0 G +1 0 0 1 -412.4511 -24.4583 cm 0 0 1 rg 0 0 1 RG -/F43 10.9091 Tf -16.364 -24.458 Td [(6)-925(User)-383(In)32(terface)]TJ +1 0 0 1 -93.6002 -424.5346 cm +BT +/F45 10.9091 Tf 93.6002 424.5346 Td[(6)-925(Us)1(er)-383(In)32(t)-1(er)1(f)-1(ace)]TJ +ET +1 0 0 1 188.0937 424.5346 cm 0 g 0 G - [-27997(20)]TJ +1 0 0 1 -188.0937 -424.5346 cm +BT +/F45 10.9091 Tf 493.506 424.5346 Td[(20)]TJ +ET +1 0 0 1 109.9639 410.9854 cm 0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.55 Td [(6.1)-1022(Subroutine)-333(mld)]TJ +1 0 0 1 -109.9639 -410.9854 cm +BT +/F15 10.9091 Tf 109.9639 410.9854 Td[(6.1)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ ET +1 0 0 1 209.6792 410.9854 cm q -1 0 0 1 209.679 411.185 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.2728 0.1992 l +S Q +1 0 0 1 -209.6792 -410.9854 cm BT -/F15 10.9091 Tf 212.952 410.985 Td [(precinit)]TJ +/F15 10.9091 Tf 212.952 410.9854 Td[(pr)1(e)-1(cin)1(it)]TJ +ET +1 0 0 1 249.346 410.9854 cm 0 g 0 G - [-751(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -249.346 -410.9854 cm +BT +/F15 10.9091 Tf 257.5375 410.9854 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +ET +1 0 0 1 495.1422 410.9854 cm 0 g 0 G - [-1281(21)]TJ +1 0 0 1 -495.1422 -410.9854 cm +BT +/F15 10.9091 Tf 495.1422 410.9854 Td[(21)]TJ +ET +1 0 0 1 506.0513 410.9854 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - -102.988 -13.549 Td [(6.2)-1022(Subroutine)-333(mld)]TJ +1 0 0 1 -109.9639 -397.4362 cm +BT +/F15 10.9091 Tf 109.9639 397.4362 Td[(6.2)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ ET +1 0 0 1 209.6792 397.4362 cm q -1 0 0 1 209.679 397.635 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.2728 0.1992 l +S Q +1 0 0 1 -209.6792 -397.4362 cm BT -/F15 10.9091 Tf 212.952 397.436 Td [(precset)]TJ +/F15 10.9091 Tf 212.952 397.4362 Td[(pr)1(e)-1(cs)-1(et)]TJ +ET +1 0 0 1 246.3762 397.4362 cm 0 g 0 G - [-1023(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -246.3762 -397.4362 cm +BT +/F15 10.9091 Tf 257.5375 397.4362 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +ET +1 0 0 1 495.1422 397.4362 cm 0 g 0 G - [-1281(22)]TJ +1 0 0 1 -495.1422 -397.4362 cm +BT +/F15 10.9091 Tf 495.1422 397.4362 Td[(22)]TJ +ET +1 0 0 1 506.0513 397.4362 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - -102.988 -13.549 Td [(6.3)-1022(Subroutine)-333(mld)]TJ +1 0 0 1 -109.9639 -383.887 cm +BT +/F15 10.9091 Tf 109.9639 383.887 Td[(6.3)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ ET +1 0 0 1 209.6792 383.887 cm q -1 0 0 1 209.679 384.086 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.2728 0.1992 l +S Q +1 0 0 1 -209.6792 -383.887 cm BT -/F15 10.9091 Tf 212.952 383.887 Td [(precbld)]TJ +/F15 10.9091 Tf 212.952 383.887 Td[(pr)1(e)-1(cbl)1(d)]TJ +ET +1 0 0 1 248.1338 383.887 cm 0 g 0 G - [-862(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -248.1338 -383.887 cm +BT +/F15 10.9091 Tf 257.5375 383.887 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +ET +1 0 0 1 495.1422 383.887 cm 0 g 0 G - [-1281(27)]TJ +1 0 0 1 -495.1422 -383.887 cm +BT +/F15 10.9091 Tf 495.1422 383.887 Td[(27)]TJ +ET +1 0 0 1 506.0513 383.887 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - -102.988 -13.549 Td [(6.4)-1022(Subroutine)-333(mld)]TJ +1 0 0 1 -109.9639 -370.3378 cm +BT +/F15 10.9091 Tf 109.9639 370.3378 Td[(6.4)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ ET +1 0 0 1 209.6792 370.3378 cm q -1 0 0 1 209.679 370.537 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.2728 0.1992 l +S Q +1 0 0 1 -209.6792 -370.3378 cm BT -/F15 10.9091 Tf 212.952 370.338 Td [(precaply)]TJ +/F15 10.9091 Tf 212.952 370.3378 Td[(pr)1(e)-1(capl)1(y)]TJ +ET +1 0 0 1 253.2854 370.3378 cm 0 g 0 G - [-390(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -253.2854 -370.3378 cm +BT +/F15 10.9091 Tf 257.5375 370.3378 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +ET +1 0 0 1 495.1422 370.3378 cm 0 g 0 G - [-1281(28)]TJ +1 0 0 1 -495.1422 -370.3378 cm +BT +/F15 10.9091 Tf 495.1422 370.3378 Td[(28)]TJ +ET +1 0 0 1 506.0513 370.3378 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - -102.988 -13.549 Td [(6.5)-1022(Subroutine)-333(mld)]TJ +1 0 0 1 -109.9639 -356.7886 cm +BT +/F15 10.9091 Tf 109.9639 356.7886 Td[(6.5)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ ET +1 0 0 1 209.6792 356.7886 cm q -1 0 0 1 209.679 356.988 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.2728 0.1992 l +S Q +1 0 0 1 -209.6792 -356.7886 cm BT -/F15 10.9091 Tf 212.952 356.789 Td [(precfree)]TJ +/F15 10.9091 Tf 212.952 356.7886 Td[(pr)1(e)-1(cfr)1(e)-1(e)]TJ +ET +1 0 0 1 250.2853 356.7886 cm 0 g 0 G - [-665(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -250.2853 -356.7886 cm +BT +/F15 10.9091 Tf 257.5375 356.7886 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +ET +1 0 0 1 495.1422 356.7886 cm 0 g 0 G - [-1281(29)]TJ +1 0 0 1 -495.1422 -356.7886 cm +BT +/F15 10.9091 Tf 495.1422 356.7886 Td[(29)]TJ +ET +1 0 0 1 506.0513 356.7886 cm 0 g 0 G +1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG - -102.988 -13.55 Td [(6.6)-1022(Subroutine)-333(mld)]TJ +1 0 0 1 -109.9639 -343.2394 cm +BT +/F15 10.9091 Tf 109.9639 343.2394 Td[(6.6)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ ET +1 0 0 1 209.6792 343.2394 cm q -1 0 0 1 209.679 343.439 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.2728 0.1992 l +S Q +1 0 0 1 -209.6792 -343.2394 cm BT -/F15 10.9091 Tf 212.952 343.239 Td [(precdescr)]TJ +/F15 10.9091 Tf 212.952 343.2394 Td[(pr)1(e)-1(cdes)-1(cr)]TJ +ET +1 0 0 1 257.3156 343.2394 cm 0 g 0 G - [-798(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -257.3156 -343.2394 cm +BT +/F15 10.9091 Tf 266.0222 343.2394 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 495.1422 343.2394 cm 0 g 0 G - [-1281(30)]TJ +1 0 0 1 -495.1422 -343.2394 cm +BT +/F15 10.9091 Tf 495.1422 343.2394 Td[(30)]TJ +ET +1 0 0 1 506.0513 343.2394 cm 0 g 0 G +1 0 0 1 -412.4511 -24.4583 cm 0 0 1 rg 0 0 1 RG -/F43 10.9091 Tf -119.352 -24.458 Td [(7)-925(Error)-383(Handling)]TJ +1 0 0 1 -93.6002 -318.7811 cm +BT +/F45 10.9091 Tf 93.6002 318.7811 Td[(7)-925(Er)1(ror)-383(Handling)]TJ +ET +1 0 0 1 194.2285 318.7811 cm 0 g 0 G - [-27434(31)]TJ +1 0 0 1 -194.2285 -318.7811 cm +BT +/F45 10.9091 Tf 493.506 318.7811 Td[(31)]TJ +ET +1 0 0 1 93.6002 294.3228 cm 0 0 1 rg 0 0 1 RG - 0 -24.458 Td [(A)-631(License)]TJ +1 0 0 1 -93.6002 -294.3228 cm +BT +/F45 10.9091 Tf 93.6002 294.3228 Td[(A)-631(License)]TJ +ET +1 0 0 1 149.9879 294.3228 cm 0 g 0 G - [-31489(32)]TJ +1 0 0 1 -149.9879 -294.3228 cm +BT +/F45 10.9091 Tf 493.506 294.3228 Td[(32)]TJ +ET +1 0 0 1 93.6002 269.8645 cm 0 0 1 rg 0 0 1 RG - 0 -24.459 Td [(References)]TJ +1 0 0 1 -93.6002 -269.8645 cm +BT +/F45 10.9091 Tf 93.6002 269.8645 Td[(Re)-1(ferences)]TJ +ET +1 0 0 1 152.5029 269.8645 cm 0 g 0 G - [-31259(33)]TJ +1 0 0 1 -152.5029 -269.8645 cm +BT +/F45 10.9091 Tf 493.506 269.8645 Td[(33)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -154 0 obj << +140 0 obj << /Type /Page -/Contents 155 0 R -/Resources 153 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 114 0 R -/Annots [ 129 0 R 130 0 R 131 0 R 132 0 R 133 0 R 134 0 R 135 0 R 136 0 R 137 0 R 138 0 R 139 0 R 140 0 R 141 0 R 142 0 R 143 0 R 144 0 R 145 0 R 146 0 R 147 0 R 148 0 R 149 0 R 150 0 R 151 0 R 152 0 R ] +/Contents 141 0 R +/Resources 139 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 120 0 R +/Annots [ 144 0 R 148 0 R 149 0 R 150 0 R 151 0 R 152 0 R 153 0 R 154 0 R 155 0 R 156 0 R 157 0 R 158 0 R 159 0 R 160 0 R 161 0 R 162 0 R 163 0 R 164 0 R 165 0 R 166 0 R 167 0 R 168 0 R 169 0 R 170 0 R ] >> endobj -129 0 obj << +144 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 678.682 142.598 688.25] +/Rect [92.604 678.6818 142.5977 688.25] /Subtype /Link /A << /S /GoTo /D (section*.1) >> >> endobj -130 0 obj << +148 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 654.223 209.755 663.792] +/Rect [92.604 654.2234 209.755 663.7917] /Subtype /Link /A << /S /GoTo /D (section.1) >> >> endobj -131 0 obj << +149 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 629.765 210.673 639.333] +/Rect [92.604 629.7651 210.6731 639.3334] /Subtype /Link /A << /S /GoTo /D (section.2) >> >> endobj -132 0 obj << +150 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 603.186 304.709 614.875] +/Rect [92.604 603.1856 304.7089 614.8751] /Subtype /Link /A << /S /GoTo /D (section.3) >> >> endobj -133 0 obj << +151 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 589.636 197.294 601.205] +/Rect [108.9676 589.6364 197.2936 601.2047] /Subtype /Link /A << /S /GoTo /D (subsection.3.1) >> >> endobj -134 0 obj << +152 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 576.087 276.233 587.777] +/Rect [108.9676 576.0872 276.2332 587.7767] /Subtype /Link /A << /S /GoTo /D (subsection.3.2) >> >> endobj -135 0 obj << +153 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 562.538 239.779 574.228] +/Rect [108.9676 562.538 239.7786 574.2275] /Subtype /Link /A << /S /GoTo /D (subsection.3.3) >> >> endobj -136 0 obj << +154 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 548.989 202.93 560.557] +/Rect [108.9676 548.9888 202.93 560.5571] /Subtype /Link /A << /S /GoTo /D (subsection.3.4) >> >> endobj -137 0 obj << +155 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 535.44 268.203 547.129] +/Rect [108.9676 535.4396 268.2028 547.1291] /Subtype /Link /A << /S /GoTo /D (subsection.3.5) >> >> endobj -138 0 obj << +156 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 510.981 372.854 522.671] +/Rect [92.604 510.9813 372.8539 522.6708] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -139 0 obj << +157 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 499.553 307.263 509.122] +/Rect [108.9676 499.5533 307.2634 509.1216] /Subtype /Link /A << /S /GoTo /D (subsection.4.1) >> >> endobj -140 0 obj << +158 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 483.883 245.172 495.572] +/Rect [108.9676 483.8829 245.1725 495.5724] /Subtype /Link /A << /S /GoTo /D (subsection.4.2) >> >> endobj -141 0 obj << +159 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 459.425 197.952 471.114] +/Rect [92.604 459.4246 197.952 471.1141] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -142 0 obj << +160 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 445.875 182.021 457.565] +/Rect [108.9676 445.8754 182.0209 457.5649] /Subtype /Link /A << /S /GoTo /D (subsection.5.1) >> >> endobj -143 0 obj << +161 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 423.538 189.09 433.107] +/Rect [92.604 423.5383 189.09 433.1066] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -144 0 obj << +162 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 407.868 250.342 419.557] +/Rect [108.9676 407.8679 250.3422 419.5574] /Subtype /Link /A << /S /GoTo /D (subsection.6.1) >> >> endobj -145 0 obj << +163 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 394.319 247.372 406.008] +/Rect [108.9676 394.3187 247.3725 406.0082] /Subtype /Link /A << /S /GoTo /D (subsection.6.2) >> >> endobj -146 0 obj << +164 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 380.77 249.13 392.459] +/Rect [108.9676 380.7695 249.1301 392.459] /Subtype /Link /A << /S /GoTo /D (subsection.6.3) >> >> endobj -147 0 obj << +165 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 367.22 254.282 378.91] +/Rect [108.9676 367.2203 254.2816 378.9098] /Subtype /Link /A << /S /GoTo /D (subsection.6.4) >> >> endobj -148 0 obj << +166 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 353.671 251.282 365.361] +/Rect [108.9676 353.6711 251.2816 365.3606] /Subtype /Link /A << /S /GoTo /D (subsection.6.5) >> >> endobj -149 0 obj << +167 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 340.122 258.312 351.811] +/Rect [108.9676 340.1219 258.3119 351.8114] /Subtype /Link /A << /S /GoTo /D (subsection.6.6) >> >> endobj -150 0 obj << +168 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 315.664 195.225 327.353] +/Rect [92.604 315.6636 195.2248 327.3531] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -151 0 obj << +169 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 293.326 150.984 302.895] +/Rect [92.604 293.3265 150.9841 302.8948] /Subtype /Link -/A << /S /GoTo /D (appendix.A) >> +/A << /S /GoTo /D (section.A) >> >> endobj -152 0 obj << +170 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 268.868 153.499 278.436] +/Rect [92.604 268.8682 153.4992 278.4364] /Subtype /Link /A << /S /GoTo /D (section*.3) >> >> endobj -156 0 obj << -/D [154 0 R /XYZ 93.6 740.002 null] +142 0 obj << +/D [140 0 R /XYZ 93.6002 740.0018 null] >> endobj -157 0 obj << -/D [154 0 R /XYZ 93.6 693.333 null] +143 0 obj << +/D [140 0 R /XYZ 93.6002 693.3333 null] >> endobj -153 0 obj << -/Font << /F15 123 0 R /F17 111 0 R /F43 158 0 R >> +139 0 obj << +/Font << /F15 131 0 R /F19 113 0 R /F45 147 0 R >> /ProcSet [ /PDF /Text ] >> endobj -161 0 obj << -/Length 79 +173 0 obj << +/Length 222 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(iv)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(iv)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -648.3688 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -160 0 obj << +172 0 obj << /Type /Page -/Contents 161 0 R -/Resources 159 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 114 0 R +/Contents 173 0 R +/Resources 171 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 120 0 R >> endobj -162 0 obj << -/D [160 0 R /XYZ 86.4 740.002 null] +174 0 obj << +/D [172 0 R /XYZ 86.3998 740.0018 null] >> endobj -159 0 obj << -/Font << /F15 123 0 R >> +171 0 obj << +/Font << /F15 131 0 R >> /ProcSet [ /PDF /Text ] >> endobj -172 0 obj << -/Length 8043 +177 0 obj << +/Length 11572 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(1)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(1)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(General)-378(O)30(ver)88(view)]TJ/F15 10.9091 Tf 406.997 0 Td [(1)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Genera)-1(l)-378(O)29(v)-1(e)1(r)88(view)]TJ/F15 10.9091 Tf 396.8452 0 Td[(1)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -406.997 -35.866 Td [(1)-1125(General)-375(Ov)31(erview)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)]TJ/F41 10.9091 Tf 23.408 0 Td [(Mul)67(ti-Level)-473(Domain)-472(Decomposition)-472(P)87(arallel)-472(Preconditioners)-473(P)88(a)22(ck-)]TJ -23.408 -13.549 Td [(a)22(ge)-278(based)-277(on)-278(PSBLAS)-278(\050MLD2P)1(4)]TJ/F15 10.9091 Tf 174.54 0 Td [(\051)-238(pro)28(vides)]TJ/F18 10.9091 Tf 48.921 0 Td [(multi-level)-270(Schwarz)-270(pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 168.99 0 Td [([)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 14.3462 Tf 93.6002 704.1363 Td[(1)-1125(G)-1(ener)-1(al)-375(Ov)31(ervi)-1(ew)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(The)]TJ/F43 10.9091 Tf 23.4074 0 Td[(Mul)66(ti-Level)-473(Dom)1(a)-1(in)-473(Deco)1(mpo)1(sition)-473(P)88(ara)-1(llel)-473(Preco)1(n)-1(diti)-1(o)1(ners)-473(P)88(a)22(ck-)]TJ -23.4074 -13.5492 Td[(a)22(ge)-278(based)-278(o)1(n)-278(PSBLAS)-278(\050MLD2P4)]TJ/F15 10.9091 Tf 174.5401 0 Td[(\051)-238(p)1(ro)28(vid)1(e)-1(s)]TJ/F20 10.9091 Tf 48.9208 0 Td[(mu)1(lti-l)1(evel)-270(Schw)-1(ar)1(z)-270(pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 168.9902 0 Td[([)]TJ +ET +1 0 0 1 489.0816 666.2349 cm 1 0 0 rg 1 0 0 RG - [(20)]TJ +1 0 0 1 -489.0816 -666.2349 cm +BT +/F15 10.9091 Tf 489.0816 666.2349 Td[(20)]TJ +ET +1 0 0 1 499.9907 666.2349 cm 0 g 0 G - [(],)]TJ -392.451 -13.549 Td [(to)-333(b)-28(e)-333(used)-334(in)-333(the)-333(iterativ)27(e)-333(solutions)-333(of)-333(s)-1(p)1(arse)-334(linear)-333(systems:)]TJ/F22 10.9091 Tf 186.98 -23.153 Td [(Ax)]TJ/F15 10.9091 Tf 17.446 0 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(b;)]TJ +1 0 0 1 -499.9907 -666.2349 cm +BT +/F15 10.9091 Tf 499.9907 666.2349 Td[(],)]TJ -406.3905 -13.5492 Td[(to)-333(b)-28(e)-333(use)-1(d)-333(i)1(n)-333(the)-334(i)1(te)-1(r)1(ativ)28(e)-334(solut)1(ions)-334(of)-332(s)-1(p)1(ars)-1(e)-333(lin)1(e)-1(ar)-333(sys)-1(t)1(e)-1(ms)-1(:)]TJ/F24 10.9091 Tf 186.9794 -23.1523 Td[(Ax)]TJ/F15 10.9091 Tf 17.4469 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(b;)]TJ +ET +1 0 0 1 492.1119 629.5334 cm 0 g 0 G -/F15 10.9091 Tf 182.57 0 Td [(\0501\051)]TJ +1 0 0 1 -492.1119 -629.5334 cm +BT +/F15 10.9091 Tf 492.1119 629.5334 Td[(\0501\051)]TJ +ET +1 0 0 1 506.0513 629.5334 cm 0 g 0 G - -398.512 -23.152 Td [(where)]TJ/F22 10.9091 Tf 31.318 0 Td [(A)]TJ/F15 10.9091 Tf 11.591 0 Td [(is)-312(a)-313(square,)-317(real)-312(or)-312(c)-1(ompl)1(e)-1(x,)-316(sparse)-313(matrix)-312(with)-313(a)-312(symmetric)-313(sparsit)28(y)-312(pattern.)]TJ -42.909 -13.549 Td [(These)-333(preconditioners)-334(ha)28(v)28(e)-333(the)-334(follo)28(wing)-333(general)-334(f)1(e)-1(atu)1(res)-1(:)]TJ +1 0 0 1 -506.0513 -629.5334 cm +BT +/F15 10.9091 Tf 93.6002 606.3811 Td[(where)]TJ/F24 10.9091 Tf 31.3179 0 Td[(A)]TJ/F15 10.9091 Tf 11.5907 0 Td[(is)-313(a)-312(s)-1(q)1(uare,)-316(re)-1(al)-312(or)-312(com)-1(p)1(le)-1(x)1(,)-317(spar)1(s)-1(e)-313(matri)1(x)-313(with)-312(a)-312(s)-1(y)1(m)-1(metric)-313(spar)1(s)-1(it)28(y)-312(pat)1(te)-1(r)1(n.)]TJ -42.9086 -13.5492 Td[(Thes)-1(e)-333(prec)-1(on)1(di)1(tioners)-334(h)1(a)28(v)28(e)-334(the)-333(foll)1(o)27(win)1(g)-334(general)-333(f)1(e)-1(atu)1(res)-1(:)]TJ +ET +1 0 0 1 93.6002 571.4462 cm 0 g 0 G -/F25 10.9091 Tf 16.364 -21.386 Td [(\017)]TJ +1 0 0 1 -93.6002 -571.4462 cm +BT +/F27 10.9091 Tf 109.9639 571.4462 Td[(\017)]TJ +ET +1 0 0 1 115.4185 571.4462 cm 0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(b)-28(oth)]TJ/F18 10.9091 Tf 24.794 0 Td [(additive)-277(and)-276(hybrid)-277(mu)1(ltilevel)]TJ/F15 10.9091 Tf 141.789 0 Td [(v)56(arian)27(ts)-245(are)-245(implemen)28(ted,)-263(i.e.)-245(v)56(arian)28(ts)-245(that)-245(are)]TJ -166.583 -13.549 Td [(additiv)28(e)-226(among)-226(th)1(e)-226(lev)28(e)-1(ls)-225(and)-226(inside)-226(eac)28(h)-226(lev)28(el,)-247(and)-226(v)56(arian)28(ts)-226(that)-226(are)-225(m)27(ultipl)1(ic)-1(ati)1(v)27(e)]TJ 0 -13.549 Td [(among)-334(the)-334(lev)27(els)-334(and)-334(additiv)28(e)-334(inside)-334(eac)27(h)-334(lev)28(el;)-335(the)-334(basic)-334(Additiv)28(e)-334(Sc)27(h)28(w)28(arz)-334(\050AS\051)]TJ 0 -13.549 Td [(preconditioners)-333(are)-334(obtai)1(ned)-334(b)28(y)-333(considering)-334(on)1(ly)-334(one)-333(lev)28(el;)]TJ +1 0 0 1 -115.4185 -571.4462 cm +BT +/F15 10.9091 Tf 120.873 571.4462 Td[(b)-27(oth)]TJ/F20 10.9091 Tf 24.7943 0 Td[(additive)-276(a)-1(nd)-276(hybri)1(d)-277(mu)1(ltil)1(evel)]TJ/F15 10.9091 Tf 141.7891 0 Td[(v)56(arian)29(ts)-246(ar)1(e)-246(impl)1(e)-1(me)-1(n)29(te)-1(d)1(,)-263(i.)1(e)-1(.)-245(v)56(ar)1(ian)28(ts)-245(that)-245(ar)1(e)]TJ -166.5834 -13.5492 Td[(add)1(itiv)28(e)-226(among)-225(the)-226(lev)28(e)-1(l)1(s)-227(an)1(d)-225(inside)-226(eac)27(h)-225(lev)28(e)-1(l,)-247(an)1(d)-225(v)55(ar)1(ian)28(ts)-226(th)1(at)-226(are)-226(m)28(ulti)1(pli)1(c)-1(ativ)28(e)]TJ 0 -13.5492 Td[(among)-334(the)-334(lev)28(e)-1(ls)-334(and)-334(ad)1(di)1(tiv)28(e)-335(in)1(s)-1(i)1(de)-335(eac)27(h)-333(le)-1(v)28(el;)-334(the)-334(basic)-335(Ad)1(diti)1(v)28(e)-335(S)1(c)27(h)28(w)28(arz)-335(\050AS)1(\051)]TJ 0 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-334(are)-334(ob)1(tain)1(e)-1(d)-333(b)29(y)-334(consid)1(e)-1(r)1(ing)-333(onl)1(y)-334(on)1(e)-334(lev)28(e)-1(l)1(;)]TJ +ET +1 0 0 1 93.6002 508.7349 cm 0 g 0 G -/F25 10.9091 Tf -10.909 -22.064 Td [(\017)]TJ +1 0 0 1 -93.6002 -508.7349 cm +BT +/F27 10.9091 Tf 109.9639 508.7349 Td[(\017)]TJ +ET +1 0 0 1 115.4185 508.7349 cm 0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(a)]TJ/F18 10.9091 Tf 10.389 0 Td [(pur)51(ely)-467(algebr)51(aic)]TJ/F15 10.9091 Tf 80.623 0 Td [(approac)28(h)-452(is)-453(used)-452(to)-452(generate)-453(a)-452(sequence)-452(of)-453(coarse-lev)28(el)-452(cor-)]TJ -91.012 -13.549 Td [(rections)-415(to)-415(a)-415(basic)-415(AS)-414(preconditioner,)-435(without)-415(explicitly)-415(using)-415(an)28(y)-415(information)]TJ 0 -13.549 Td [(on)-374(the)-374(geometry)-374(of)-374(the)-373(original)-374(problem)-374(\050e.g.)-374(the)-374(discretization)-374(of)-374(a)-374(P)1(DE\051.)-374(The)]TJ/F18 10.9091 Tf 0 -13.55 Td [(smo)51(othe)51(d)-313(aggr)51(e)52(gation)]TJ/F15 10.9091 Tf 103.953 0 Td [(tec)28(hnique)-285(is)-284(applied)-285(as)-284(algebraic)-285(coarsening)-284(strategy)-285([)]TJ +1 0 0 1 -115.4185 -508.7349 cm +BT +/F15 10.9091 Tf 120.873 508.7349 Td[(a)]TJ/F20 10.9091 Tf 10.3888 0 Td[(pur)52(ely)-467(al)1(gebr)51(aic)]TJ/F15 10.9091 Tf 80.6232 0 Td[(app)1(roac)28(h)-452(is)-453(u)1(s)-1(ed)-452(to)-452(ge)-1(n)1(e)-1(r)1(ate)-453(a)-452(s)-1(equence)-453(of)-452(coarse)-1(-lev)28(e)-1(l)-452(cor-)]TJ -91.012 -13.5492 Td[(rec)-1(t)1(ions)-415(to)-415(a)-415(b)1(as)-1(ic)-415(AS)-414(pr)1(e)-1(cond)1(ition)1(e)-1(r,)-435(wit)1(hout)-414(e)-1(xp)1(licitly)-414(using)-414(an)28(y)-415(in)1(for)1(m)-1(ati)1(on)]TJ 0 -13.5492 Td[(on)-373(the)-374(ge)-1(ometry)-374(of)-373(the)-374(ori)1(ginal)-373(prob)1(lem)-375(\050e.g.)-373(the)-374(disc)-1(r)1(e)-1(ti)1(z)-1(ati)1(on)-374(of)-373(a)-374(PDE)1(\051.)-374(The)]TJ/F20 10.9091 Tf 0 -13.5492 Td[(smo)51(othe)51(d)-313(aggr)51(e)52(ga)-1(ti)1(o)-1(n)]TJ/F15 10.9091 Tf 103.9531 0 Td[(tec)27(hn)1(iqu)1(e)-285(is)-285(ap)1(plied)-284(as)-285(algebrai)1(c)-285(c)-1(oar)1(s)-1(enin)1(g)-285(strategy)-284([)]TJ +ET +1 0 0 1 477.4929 468.0873 cm 1 0 0 rg 1 0 0 RG - [(1)]TJ +1 0 0 1 -477.4929 -468.0873 cm +BT +/F15 10.9091 Tf 477.4929 468.0873 Td[(1)]TJ +ET +1 0 0 1 482.9474 468.0873 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -482.9474 -468.0873 cm +BT +/F15 10.9091 Tf 482.9474 468.0873 Td[(,)]TJ +ET +1 0 0 1 489.0816 468.0873 cm 1 0 0 rg 1 0 0 RG - [-284(24)]TJ +1 0 0 1 -489.0816 -468.0873 cm +BT +/F15 10.9091 Tf 489.0816 468.0873 Td[(24)]TJ +ET +1 0 0 1 499.9907 468.0873 cm 0 g 0 G - [(].)]TJ -114.289 -21.385 Td [(The)-287(pac)28(k)56(age)-287(is)-287(written)-286(in)]TJ/F18 10.9091 Tf 122.396 0 Td [(F)77(ortr)51(an)-315(95)]TJ/F15 10.9091 Tf 50.422 0 Td [(,)-296(follo)28(wing)-287(an)]TJ/F18 10.9091 Tf 66.455 0 Td [(obje)51(ct-oriente)51(d)-315(appr)52(o)51(ach)]TJ/F15 10.9091 Tf 118.635 0 Td [(through)]TJ -374.845 -13.55 Td [(the)-330(e)-1(xp)1(loitation)-331(of)-330(features)-331(suc)28(h)-330(as)-331(abstract)-330(data)-331(t)28(yp)-28(e)-330(creation,)-331(functional)-331(o)28(v)28(erloading)]TJ 0 -13.549 Td [(and)-360(dynamic)-360(memory)-360(managemen)28(t.)-525(The)-360(parallel)-360(implemen)28(tation)-360(is)-360(based)-360(on)-360(a)-360(Single)]TJ 0 -13.549 Td [(Program)-231(Mul)1(tiple)-231(Data)-231(\050SPMD\051)-230(paradigm)-231(for)-230(distributed-memory)-231(arc)28(hitectures.)-410(Single)]TJ 0 -13.549 Td [(and)-377(double)-376(precis)-1(i)1(on)-377(implemen)27(tat)1(ions)-377(of)-377(MLD2P4)-377(are)-377(a)28(v)56(ailable)-377(for)-377(b)-28(oth)-376(the)-377(real)-377(and)]TJ 0 -13.549 Td [(the)-333(complex)-334(case,)-333(that)-333(can)-334(b)-27(e)-334(used)-333(through)-333(a)-334(single)-333(in)28(terface.)]TJ 16.937 -13.549 Td [(MLD2P4)-229(has)-230(b)-27(e)-1(en)-229(designed)-229(to)-230(implemen)28(t)-230(scalable)-229(and)-229(easy-to-use)-230(m)28(ultilev)28(el)-230(precon-)]TJ -16.937 -13.55 Td [(ditioners)-348(in)-348(the)-349(con)28(text)-348(of)-348(the)]TJ/F18 10.9091 Tf 147.432 0 Td [(PSBLAS)-372(\050Par)52(al)-52(l)1(el)-372(Sp)51(arse)-371(BLAS\051)-372(c)51(omputational)-371(fr)51(ame-)]TJ -147.432 -13.549 Td [(work)]TJ/F15 10.9091 Tf 27.287 0 Td [([)]TJ +1 0 0 1 -499.9907 -468.0873 cm +BT +/F15 10.9091 Tf 499.9907 468.0873 Td[(].)]TJ -389.454 -21.3857 Td[(The)-287(p)1(ac)27(k)56(age)-288(i)1(s)-287(w)-1(r)1(itten)-287(i)1(n)]TJ/F20 10.9091 Tf 122.3962 0 Td[(F)77(ortr)51(an)-315(95)]TJ/F15 10.9091 Tf 50.4226 0 Td[(,)-296(f)1(ollo)28(wing)-286(an)]TJ/F20 10.9091 Tf 66.4546 0 Td[(obje)51(ct-or)1(ient)-1(e)52(d)-315(ap)-1(pr)52(o)51(ach)]TJ/F15 10.9091 Tf 118.6351 0 Td[(th)1(rough)]TJ -374.845 -13.5492 Td[(th)1(e)-331(e)-1(xp)1(loitat)1(ion)-330(of)-330(featur)1(e)-1(s)-331(suc)28(h)-330(as)-331(abstract)-331(d)1(ata)-331(t)28(yp)-27(e)-331(creation,)-330(fun)1(c)-1(t)1(ional)-330(o)28(v)28(e)-1(r)1(loadi)1(ng)]TJ 0 -13.5492 Td[(and)-359(dy)1(namic)-361(mem)-1(or)1(y)-360(m)-1(an)1(age)-1(men)28(t.)-524(The)-360(paral)1(le)-1(l)-359(im)-1(p)1(lem)-1(en)28(tati)1(on)-360(is)-360(base)-1(d)-359(on)-360(a)-360(S)1(ingle)]TJ 0 -13.5492 Td[(Pr)1(ogram)-231(Mu)1(ltip)1(le)-231(Data)-230(\050SP)1(MD\051)-230(parad)1(igm)-231(f)1(or)-231(d)1(is)-1(t)1(rib)1(uted-m)-1(emory)-230(arc)27(h)1(itec)-1(tu)1(res)-1(.)-410(S)1(ingle)]TJ 0 -13.5492 Td[(and)-376(d)1(oubl)1(e)-378(p)1(rec)-1(ision)-376(impleme)-1(n)28(t)1(ations)-377(of)-376(MLD2P)1(4)-377(are)-377(a)28(v)55(ai)1(lable)-377(f)1(or)-377(b)-27(oth)-376(the)-377(real)-377(an)1(d)]TJ 0 -13.5492 Td[(th)1(e)-334(c)-1(ompl)1(e)-1(x)-333(cas)-1(e,)-333(that)-333(can)-333(b)-28(e)-333(use)-1(d)-333(th)1(rou)1(gh)-333(a)-334(sin)1(gle)-334(in)28(t)1(e)-1(rf)1(ac)-1(e.)]TJ 16.9365 -13.5492 Td[(MLD2P)1(4)-230(h)1(as)-230(b)-27(e)-1(en)-229(des)-1(i)1(gned)-229(to)-230(imp)1(le)-1(men)28(t)-230(scalable)-229(and)-229(eas)-1(y-to-use)-230(m)27(u)1(ltil)1(e)-1(v)28(el)-230(p)1(rec)-1(on)1(-)]TJ -16.9365 -13.5492 Td[(di)1(tioners)-348(in)-348(th)1(e)-349(c)-1(on)29(te)-1(x)1(t)-349(of)-347(the)]TJ/F20 10.9091 Tf 147.4316 0 Td[(PS)-1(B)1(L)-1(AS)-372(\050Par)51(al)-50(lel)-371(Sp)51(arse)-371(BLA)-1(S\051)-371(c)51(omputationa)-1(l)-371(f)1(r)51(ame-)]TJ -147.4316 -13.5492 Td[(wo)-1(r)1(k)]TJ/F15 10.9091 Tf 27.2865 0 Td[([)]TJ +ET +1 0 0 1 123.917 338.308 cm 1 0 0 rg 1 0 0 RG - [(15)]TJ +1 0 0 1 -123.917 -338.308 cm +BT +/F15 10.9091 Tf 123.917 338.308 Td[(15)]TJ +ET +1 0 0 1 134.8261 338.308 cm 0 g 0 G - [(].)-454(PSBLAS)-336(is)-336(a)-337(library)-336(originally)-336(dev)28(elop)-28(ed)-337(to)-336(address)-336(the)-337(parallel)-336(implemen-)]TJ -27.287 -13.549 Td [(tation)-442(of)-442(iterativ)28(e)-442(solv)28(ers)-442(for)-442(sparse)-442(linear)-442(system,)-469(b)28(y)-442(pro)28(viding)-442(basic)-442(linear)-442(algebra)]TJ 0 -13.549 Td [(op)-28(erators)-442(and)-442(data)-442(managemen)27(t)-442(facilities)-442(for)-442(distributed)-442(sparse)-443(matrices;)-496(it)-443(also)-442(in-)]TJ 0 -13.549 Td [(cludes)-337(parallel)-337(Krylo)28(v)-337(solv)28(ers,)-338(built)-337(on)-336(the)-337(top)-337(of)-337(the)-337(basic)-337(PSBLAS)-337(k)28(ernels.)-455(The)-337(pre-)]TJ 0 -13.55 Td [(conditioners)-379(a)27(v)56(ailable)-380(in)-379(MLD2P4)-380(can)-379(b)-28(e)-379(used)-380(with)-379(these)-380(Krylo)28(v)-380(solv)28(ers.)-583(The)-380(c)28(hoice)]TJ 0 -13.549 Td [(of)-362(PSBLAS)-361(has)-362(b)-28(een)-361(mainly)-362(motiv)56(ated)-362(b)28(y)-362(the)-362(need)-361(of)-362(ha)28(ving)-362(a)-361(p)-28(ortable)-362(and)-361(e\016cien)27(t)]TJ 0 -13.549 Td [(soft)28(w)28(are)-313(infrastructure)-312(implemen)28(ting)-312(\134de)-313(facto")-312(standard)-312(parallel)-312(sparse)-313(linear)-312(algebra)]TJ 0 -13.549 Td [(k)28(ernels,)-304(to)-297(pursue)-297(goals)-296(suc)27(h)-296(as)-297(p)-28(erformance,)-304(p)-28(or)1(tabilit)27(y)84(,)-304(mo)-28(dularit)28(y)-297(ed)-296(e)-1(xt)1(e)-1(nsib)1(ilit)27(y)-296(in)]TJ 0 -13.549 Td [(the)-272(dev)27(elopmen)28(t)-272(of)-273(the)-272(preconditioner)-272(pac)27(k)56(age.)-424(On)-273(the)-272(other)-272(hand,)-285(the)-272(implemen)27(tation)]TJ 0 -13.55 Td [(of)-379(MLD2P4)-378(has)-379(led)-379(to)-379(some)-379(revisions)-379(and)-378(exten)27(tion)1(s)-379(of)-379(the)-379(PSBLAS)-379(k)28(ernels,)-390(leading)]TJ 0 -13.549 Td [(to)-439(the)-439(recen)28(t)-439(PSBLAS)-439(2.0)-438(v)27(ersion)-438([)]TJ +1 0 0 1 -134.8261 -338.308 cm +BT +/F15 10.9091 Tf 134.8261 338.308 Td[(].)-453(PS)1(B)-1(LAS)-336(i)1(s)-337(a)-337(l)1(ibr)1(ary)-336(origin)1(ally)-336(d)1(e)-1(v)28(elop)-27(e)-1(d)-336(to)-336(add)1(res)-1(s)-337(th)1(e)-337(par)1(allel)-336(im)-1(p)1(lem)-1(en-)]TJ -41.2259 -13.5492 Td[(tation)-441(of)-442(i)1(te)-1(r)1(ativ)28(e)-442(s)-1(olv)28(ers)-442(for)-441(s)-1(p)1(arse)-443(l)1(inear)-442(syste)-1(m,)-469(b)28(y)-441(pro)28(vi)1(din)1(g)-442(basic)-442(linear)-442(al)1(ge)-1(b)1(ra)]TJ 0 -13.5492 Td[(op)-27(e)-1(r)1(ators)-443(an)1(d)-442(dat)1(a)-443(manageme)-1(n)28(t)-442(f)1(ac)-1(il)1(ities)-443(f)1(or)-442(distri)1(but)1(e)-1(d)-442(spar)1(s)-1(e)-443(matr)1(ic)-1(es)-1(;)-496(it)-442(also)-442(in-)]TJ 0 -13.5492 Td[(clud)1(e)-1(s)-337(par)1(allel)-337(Kr)1(ylo)28(v)-337(solv)28(e)-1(r)1(s)-1(,)-337(bu)1(ilt)-337(on)-336(the)-337(top)-336(of)-337(th)1(e)-338(b)1(as)-1(i)1(c)-338(P)1(SBLAS)-337(k)28(ern)1(e)-1(ls.)-455(The)-337(pr)1(e)-1(-)]TJ 0 -13.5492 Td[(condi)1(tioners)-380(a)28(v)56(ailab)1(le)-380(in)-379(MLD)1(2P4)-380(can)-379(b)-27(e)-380(use)-1(d)-379(with)-379(th)1(e)-1(se)-380(Kry)1(lo)28(v)-380(solv)28(ers)-1(.)-582(T)-1(h)1(e)-380(c)27(h)1(oic)-1(e)]TJ 0 -13.5492 Td[(of)-361(PS)1(B)-1(LAS)-361(h)1(as)-363(b)-27(ee)-1(n)-361(mainl)1(y)-362(motiv)56(ate)-1(d)-361(b)28(y)-361(th)1(e)-363(n)1(e)-1(ed)-361(of)-362(h)1(a)28(vin)1(g)-362(a)-362(p)-27(ortab)1(le)-362(and)-361(e\016)-1(cien)28(t)]TJ 0 -13.5492 Td[(soft)28(w)27(ar)1(e)-313(in)1(frastru)1(c)-1(t)1(ure)-312(im)-1(p)1(lem)-1(en)28(tin)1(g)-312(\134de)-313(f)1(ac)-1(to")-312(stand)1(ard)-312(p)1(arallel)-312(s)-1(p)1(arse)-313(lin)1(e)-1(ar)-312(al)1(ge)-1(b)1(ra)]TJ 0 -13.5492 Td[(k)28(ernels,)-304(to)-297(p)1(ursue)-297(goal)1(s)-298(suc)28(h)-297(as)-297(p)-27(erfor)1(m)-1(an)1(c)-1(e,)-304(p)-27(ortab)1(ilit)28(y)84(,)-304(mo)-28(du)1(larit)28(y)-296(e)-1(d)-296(extensibil)1(it)28(y)-297(i)1(n)]TJ 0 -13.5492 Td[(th)1(e)-273(dev)28(e)-1(lop)1(me)-1(n)28(t)-272(of)-272(th)1(e)-273(precondi)1(tioner)-272(pac)28(k)55(age.)-424(On)-272(th)1(e)-273(other)-272(han)1(d,)-284(the)-272(im)-1(p)1(lem)-1(en)28(tati)1(on)]TJ 0 -13.5492 Td[(of)-378(MLD2P)1(4)-379(has)-379(led)-379(to)-378(s)-1(ome)-379(revis)-1(i)1(ons)-379(and)-378(exte)-1(n)29(tions)-379(of)-378(the)-379(P)1(SBLAS)-379(k)28(ern)1(e)-1(ls,)-390(leadi)1(ng)]TJ 0 -13.5492 Td[(to)-439(th)1(e)-440(r)1(e)-1(ce)-1(n)29(t)-439(PS)1(B)-1(LAS)-438(2.0)-438(v)28(e)-1(rsion)-438([)]TJ +ET +1 0 0 1 268.6586 202.8161 cm 1 0 0 rg 1 0 0 RG - [(14)]TJ +1 0 0 1 -268.6586 -202.8161 cm +BT +/F15 10.9091 Tf 268.6586 202.8161 Td[(14)]TJ +ET +1 0 0 1 279.5677 202.8161 cm 0 g 0 G - [(].)-761(The)-439(in)27(t)1(e)-1(r-p)1(ro)-28(cess)-439(com)27(uni)1(c)-1(ati)1(on)-439(required)-439(b)28(y)]TJ 0 -13.549 Td [(MLD2P4)-355(is)-354(encapsulated)-355(in)28(to)-355(the)-354(PSBLAS)-355(routines,)-360(except)-354(few)-355(cases)-355(where)-354(MPI)-355([)]TJ +1 0 0 1 -279.5677 -202.8161 cm +BT +/F15 10.9091 Tf 279.5677 202.8161 Td[(].)-761(Th)1(e)-440(i)1(n)28(te)-1(r)1(-)-1(p)1(ro)-28(ces)-1(s)-439(c)-1(om)28(un)1(ic)-1(at)1(ion)-439(r)1(e)-1(qu)1(ired)-438(b)28(y)]TJ -185.9675 -13.5492 Td[(MLD2P)1(4)-355(is)-355(encapsul)1(ate)-1(d)-354(in)29(to)-355(th)1(e)-355(PSBLAS)-354(rou)1(tines,)-360(e)-1(x)1(c)-1(ept)-354(few)-355(c)-1(ases)-356(wh)1(e)-1(r)1(e)-356(M)1(PI)-354([)]TJ +ET +1 0 0 1 492.1119 189.2669 cm 1 0 0 rg 1 0 0 RG - [(21)]TJ +1 0 0 1 -492.1119 -189.2669 cm +BT +/F15 10.9091 Tf 492.1119 189.2669 Td[(21)]TJ +ET +1 0 0 1 503.021 189.2669 cm 0 g 0 G - [(])]TJ 0 -13.549 Td [(is)-458(explicitly)-458(called.)-818(Therefore,)-489(MLD2P4)-458(can)-457(b)-28(e)-458(run)-458(on)-458(an)28(y)-458(parallel)-457(mac)27(hine)-458(where)]TJ 0 -13.549 Td [(PSBLAS)-333(and)-334(M)1(PI)-334(implemen)28(tations)-333(are)-334(a)28(v)56(ailable.)]TJ 16.937 -13.55 Td [(MLD2P4)-342(has)-341(a)-342(la)28(y)28(ered)-342(and)-342(mo)-27(dular)-342(soft)28(w)28(are)-342(arc)28(hitecture)-342(where)-342(th)1(ree)-342(main)-342(la)28(y)28(ers)]TJ -16.937 -13.549 Td [(can)-458(b)-28(e)-458(iden)28(ti\014ed.)-819(The)-458(lo)28(w)28(er)-458(la)27(y)28(er)-458(consists)-458(of)-458(the)-458(PSBLAS)-458(k)28(ernels,)-490(the)-458(middle)-458(one)]TJ 0 -13.549 Td [(implemen)28(ts)-458(the)-457(construction)-457(and)-458(application)-457(phases)-458(of)-457(the)-457(preconditioners,)-489(and)-457(the)]TJ +1 0 0 1 -503.021 -189.2669 cm +BT +/F15 10.9091 Tf 503.021 189.2669 Td[(])]TJ -409.4208 -13.5492 Td[(is)-458(e)-1(x)1(pli)1(c)-1(itl)1(y)-458(called.)-818(Therefor)1(e)-1(,)-489(M)1(LD2P4)-458(can)-457(b)-28(e)-458(ru)1(n)-458(on)-457(an)28(y)-458(p)1(arall)1(e)-1(l)-457(m)-1(ac)28(hin)1(e)-459(wh)1(e)-1(re)]TJ 0 -13.5492 Td[(PS)1(BLAS)-333(and)-333(M)1(PI)-333(im)-1(p)1(lem)-1(en)28(tati)1(ons)-334(ar)1(e)-334(a)28(v)55(ai)1(lable.)]TJ 16.9365 -13.5492 Td[(MLD2P)1(4)-342(h)1(as)-342(a)-342(la)28(y)28(e)-1(r)1(e)-1(d)-341(an)1(d)-342(mo)-28(d)1(ular)-341(soft)28(w)27(ar)1(e)-342(arc)27(h)1(itec)-1(tu)1(re)-342(where)-342(th)1(re)-1(e)-342(main)-341(la)28(y)28(ers)]TJ -16.9365 -13.5492 Td[(can)-458(b)-27(e)-459(id)1(e)-1(n)28(t)1(i\014ed.)-818(The)-459(l)1(o)27(w)28(er)-458(la)28(y)28(e)-1(r)-457(c)-1(on)1(s)-1(ists)-459(of)-457(the)-458(PS)1(B)-1(LAS)-457(k)28(e)-1(r)1(nels,)-490(t)1(he)-458(m)-1(id)1(dl)1(e)-459(one)]TJ 0 -13.5492 Td[(impl)1(e)-1(me)-1(n)29(ts)-458(the)-458(constru)1(c)-1(t)1(ion)-457(and)-457(ap)1(pli)1(c)-1(ati)1(on)-457(phases)-458(of)-457(the)-458(p)1(rec)-1(on)1(dit)1(ioners,)-489(an)1(d)-457(the)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -171 0 obj << +176 0 obj << /Type /Page -/Contents 172 0 R -/Resources 170 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 177 0 R -/Annots [ 169 0 R 163 0 R 164 0 R 165 0 R 166 0 R 167 0 R 168 0 R ] +/Contents 177 0 R +/Resources 175 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 195 0 R +/Annots [ 178 0 R 182 0 R 190 0 R 191 0 R 192 0 R 193 0 R 194 0 R ] >> endobj -169 0 obj << +178 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.1) >> >> endobj -163 0 obj << +182 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [488.085 665.239 500.987 674.261] +/Rect [488.0853 665.2387 500.987 674.2615] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -164 0 obj << +190 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [476.497 467.091 483.944 476.114] +/Rect [476.4966 467.0911 483.9437 476.1139] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -165 0 obj << +191 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [488.085 467.091 500.987 476.114] +/Rect [488.0853 467.0911 500.987 476.1139] /Subtype /Link /A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> >> endobj -166 0 obj << +192 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [122.921 337.312 135.822 346.335] +/Rect [122.9207 337.3118 135.8224 346.3346] /Subtype /Link /A << /S /GoTo /D (cite.psblas_00) >> >> endobj -167 0 obj << +193 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [267.662 201.82 280.564 210.843] +/Rect [267.6624 201.8198 280.564 210.8426] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -168 0 obj << +194 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [491.116 188.271 504.017 197.293] +/Rect [491.1157 188.2706 504.0173 197.2934] /Subtype /Link /A << /S /GoTo /D (cite.MPI1) >> >> endobj 14 0 obj << -/D [171 0 R /XYZ 93.6 715.095 null] +/D [176 0 R /XYZ 93.6002 715.0952 null] >> endobj -174 0 obj << -/D [171 0 R /XYZ 280.58 643.083 null] +183 0 obj << +/D [176 0 R /XYZ 280.5796 643.0826 null] >> endobj -170 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F18 173 0 R /F22 175 0 R /F25 176 0 R >> +175 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F20 181 0 R /F24 186 0 R /F27 189 0 R >> /ProcSet [ /PDF /Text ] >> endobj -193 0 obj << -/Length 3833 +204 0 obj << +/Length 6211 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(2)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(2)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(upp)-28(er)-310(one)-310(pro)28(vides)-310(a)-310(uniform)-310(and)-310(easy-to-use)-310(in)28(terface)-310(to)-310(all)-310(the)-310(preconditioners.)-437(This)]TJ 0 -13.549 Td [(arc)28(hitecture)-446(allo)28(w)-1(s)-446(for)-446(di\013eren)28(t)-446(lev)28(els)-446(of)-447(use)-446(of)-446(the)-446(pac)28(k)55(age:)-670(few)-446(blac)28(k-b)-28(o)28(x)-446(routines)]TJ 0 -13.549 Td [(at)-384(the)-384(upp)-28(er)-384(la)28(y)28(er)-384(allo)28(w)-384(non-exp)-28(ert)-384(users)-384(to)-384(easily)-384(build)-384(an)28(y)-384(preconditioner)-384(a)28(v)56(ailable)]TJ 0 -13.549 Td [(in)-365(MLD2P4)-365(and)-364(to)-365(apply)-365(it)-365(within)-365(a)-364(PSBLAS)-365(Krylo)28(v)-365(solv)28(er.)-539(On)-365(the)-365(other)-365(hand,)-373(the)]TJ 0 -13.549 Td [(routines)-253(of)-253(the)-253(middle)-253(and)-253(lo)28(w)27(er)-253(la)28(y)28(er)-253(can)-253(b)-28(e)-253(used)-253(and)-253(extended)-253(b)27(y)-253(exp)-28(ert)-253(users)-253(to)-253(build)]TJ 0 -13.55 Td [(new)-367(v)28(ersions)-367(of)-366(m)28(ulti-lev)27(el)-366(Sc)28(h)27(w)28(arz)-366(prec)-1(on)1(ditioners.)-545(W)84(e)-367(pro)28(vide)-367(here)-366(a)-367(description)-367(of)]TJ 0 -13.549 Td [(the)-333(upp)-28(er-la)28(y)28(er)-334(routines,)-333(but)-333(not)-334(of)-333(the)-333(medium-la)28(y)27(er)-333(ones.)]TJ 16.936 -13.549 Td [(This)-380(guide)-380(is)-380(organized)-380(as)-380(follo)28(ws.)-585(General)-380(information)-380(on)-380(the)-380(distribution)-380(of)-380(the)]TJ -16.936 -13.549 Td [(source)-239(co)-27(de)-239(is)-238(rep)-28(orted)-239(in)-238(Section)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F15 10.9091 Tf 86.3998 704.1363 Td[(up)1(p)-27(e)-1(r)-310(on)1(e)-311(p)1(ro)28(vid)1(e)-1(s)-310(a)-310(un)1(ifor)1(m)-311(an)1(d)-310(eas)-1(y)1(-)-1(to-u)1(s)-1(e)-310(in)28(terf)1(ac)-1(e)-310(to)-310(all)-310(th)1(e)-311(p)1(rec)-1(on)1(diti)1(oners)-1(.)-436(This)]TJ 0 -13.5492 Td[(arc)28(hitecture)-446(allo)28(ws)-447(f)1(or)-446(di)1(\013)-1(eren)28(t)-446(lev)28(e)-1(ls)-446(of)-446(u)1(s)-1(e)-446(of)-446(th)1(e)-447(pac)28(k)55(age:)-670(f)1(e)-1(w)-446(bl)1(ac)27(k-b)-28(o)28(x)-446(r)1(outin)1(e)-1(s)]TJ 0 -13.5492 Td[(at)-384(th)1(e)-385(u)1(pp)-27(e)-1(r)-383(la)28(y)28(e)-1(r)-383(allo)28(w)-384(non-exp)-27(e)-1(rt)-383(use)-1(rs)-384(to)-384(eas)-1(il)1(y)-384(bu)1(ild)-383(an)28(y)-384(p)1(re)-1(cond)1(ition)1(e)-1(r)-383(a)28(v)55(ai)1(lable)]TJ 0 -13.5492 Td[(in)-364(MLD2P)1(4)-365(and)-364(to)-365(app)1(ly)-365(i)1(t)-365(withi)1(n)-365(a)-365(P)1(SBLAS)-364(Kryl)1(o)27(v)-364(s)-1(olv)28(er.)-539(O)1(n)-365(th)1(e)-366(ot)1(her)-365(h)1(and,)-372(the)]TJ 0 -13.5492 Td[(rou)1(tin)1(e)-1(s)-253(of)-253(the)-253(midd)1(le)-254(an)1(d)-253(lo)28(w)28(e)-1(r)-253(l)1(a)27(y)28(er)-253(can)-253(b)-27(e)-254(u)1(s)-1(ed)-253(an)1(d)-253(exte)-1(n)1(ded)-253(b)28(y)-252(e)-1(xp)-27(ert)-253(use)-1(r)1(s)-254(to)-253(b)1(uil)1(d)]TJ 0 -13.5492 Td[(new)-367(v)28(ersions)-367(of)-366(m)27(u)1(lti-lev)28(e)-1(l)-366(Sc)28(h)28(w)28(arz)-367(pr)1(e)-1(cond)1(ition)1(e)-1(rs.)-544(W)83(e)-367(p)1(ro)28(vid)1(e)-367(here)-367(a)-367(d)1(e)-1(sc)-1(r)1(ipt)1(ion)-366(of)]TJ 0 -13.5492 Td[(th)1(e)-334(up)1(p)-28(er-la)28(y)28(e)-1(r)-333(r)1(outi)1(nes)-1(,)-333(bu)1(t)-333(not)-333(of)-333(th)1(e)-334(m)-1(edi)1(um-)-1(l)1(a)27(y)28(er)-333(ones.)]TJ 16.9365 -13.5492 Td[(This)-380(gui)1(de)-380(is)-381(or)1(ganize)-1(d)-379(as)-381(f)1(ollo)28(ws)-1(.)-584(General)-380(in)1(for)1(m)-1(ati)1(on)-380(on)-380(t)1(he)-381(d)1(istrib)1(uti)1(on)-380(of)-380(th)1(e)]TJ -16.9365 -13.5492 Td[(source)-239(c)-1(o)-27(de)-239(is)-239(r)1(e)-1(p)-27(orted)-238(in)-238(S)1(e)-1(ction)]TJ +ET +1 0 0 1 244.6472 595.7428 cm 0 0 1 rg 0 0 1 RG - [-239(2)]TJ +1 0 0 1 -244.6472 -595.7428 cm +BT +/F15 10.9091 Tf 244.6472 595.7428 Td[(2)]TJ +ET +1 0 0 1 250.1018 595.7428 cm 0 g 0 G - [(,)-257(while)-238(details)-239(on)-238(the)-239(con\014guration)-238(and)-239(installati)1(on)-239(of)]TJ 0 -13.549 Td [(the)-280(pac)28(k)56(age)-280(are)-280(giv)28(e)-1(n)-279(in)-280(Section)]TJ +1 0 0 1 -250.1018 -595.7428 cm +BT +/F15 10.9091 Tf 250.1018 595.7428 Td[(,)-257(while)-239(d)1(e)-1(t)1(ails)-239(on)-238(th)1(e)-239(c)-1(on)1(\014gu)1(ration)-238(an)1(d)-238(installati)1(on)-238(of)]TJ -163.702 -13.5492 Td[(th)1(e)-281(p)1(ac)27(k)56(age)-281(ar)1(e)-281(gi)1(v)28(e)-1(n)-279(in)-279(Sec)-1(tion)]TJ +ET +1 0 0 1 239.9009 582.1936 cm 0 0 1 rg 0 0 1 RG - [-280(3)]TJ +1 0 0 1 -239.9009 -582.1936 cm +BT +/F15 10.9091 Tf 239.9009 582.1936 Td[(3)]TJ +ET +1 0 0 1 245.3554 582.1936 cm 0 g 0 G - [(.)-427(A)-279(desc)-1(r)1(iption)-280(of)-280(m)28(ulti-lev)28(e)-1(l)-279(Sc)27(h)28(w)28(arz)-280(preconditioners)]TJ 0 -13.55 Td [(based)-354(on)-354(smo)-28(othed)-354(aggregation)-354(is)-354(pr)1(o)27(vided)-354(in)-354(S)1(e)-1(ction)]TJ +1 0 0 1 -245.3554 -582.1936 cm +BT +/F15 10.9091 Tf 245.3554 582.1936 Td[(.)-426(A)-280(des)-1(crip)1(tion)-279(of)-280(m)28(ult)1(i-)-1(l)1(e)-1(v)28(el)-280(S)1(c)27(h)28(w)28(arz)-280(precondi)1(tioners)]TJ -158.9556 -13.5492 Td[(based)-354(on)-353(s)-1(mo)-28(othed)-353(aggre)-1(gat)1(ion)-354(is)-354(pr)1(o)28(vided)-354(i)1(n)-354(S)1(e)-1(ction)]TJ +ET +1 0 0 1 348.7466 568.6444 cm 0 0 1 rg 0 0 1 RG - [-353(4)]TJ +1 0 0 1 -348.7466 -568.6444 cm +BT +/F15 10.9091 Tf 348.7466 568.6444 Td[(4)]TJ +ET +1 0 0 1 354.2012 568.6444 cm 0 g 0 G - [(,)-360(to)-354(h)1(e)-1(l)1(p)-354(the)-354(users)-354(in)-354(c)27(ho)-27(osing)]TJ 0 -13.549 Td [(among)-339(the)-340(di\013eren)28(t)-339(preconditioners)-339(implemen)27(ted)-339(in)-339(MLD2P4.)-462(The)-340(basics)-339(for)-339(building)]TJ 0 -13.549 Td [(and)-322(applying)-322(the)-322(p)1(rec)-1(on)1(ditioners)-322(with)-322(the)-322(Krylo)28(v)-322(solv)28(ers)-322(implemen)27(ted)-322(in)-321(PSBLAS)-322(are)]TJ 0 -13.549 Td [(rep)-28(orted)-389(in)-390(Section)]TJ +1 0 0 1 -354.2012 -568.6444 cm +BT +/F15 10.9091 Tf 354.2012 568.6444 Td[(,)-359(to)-354(h)1(e)-1(lp)-353(the)-354(u)1(s)-1(ers)-354(in)-354(c)28(ho)-28(osing)]TJ -267.8014 -13.5492 Td[(among)-339(the)-339(di\013e)-1(r)1(e)-1(n)29(t)-340(p)1(rec)-1(on)1(diti)1(oners)-340(imp)1(le)-1(men)28(te)-1(d)-338(in)-339(MLD2P)1(4.)-462(T)-1(h)1(e)-340(b)1(as)-1(ics)-340(f)1(or)-339(bui)1(ldi)1(ng)]TJ 0 -13.5492 Td[(and)-321(app)1(lyi)1(ng)-322(th)1(e)-323(p)1(rec)-1(on)1(diti)1(one)-1(r)1(s)-323(wit)1(h)-322(th)1(e)-323(Kr)1(ylo)28(v)-322(solv)28(ers)-322(im)-1(p)1(lem)-1(en)28(ted)-322(i)1(n)-322(PS)1(BLAS)-322(are)]TJ 0 -13.5492 Td[(rep)-27(orted)-390(in)-389(S)1(e)-1(ction)]TJ +ET +1 0 0 1 183.1562 527.9968 cm 0 0 1 rg 0 0 1 RG - [-390(5)]TJ +1 0 0 1 -183.1562 -527.9968 cm +BT +/F15 10.9091 Tf 183.1562 527.9968 Td[(5)]TJ +ET +1 0 0 1 188.6108 527.9968 cm 0 g 0 G - [(,)-404(where)-390(the)-389(F)83(ortran)-390(95)-389(co)-28(des)-390(of)-390(a)-390(few)-389(sample)-390(programs)-390(are)-390(also)]TJ 0 -13.549 Td [(sho)28(wn.)-637(A)-397(reference)-398(guide)-397(for)-397(the)-398(upp)-28(er-la)28(y)28(er)-397(routines)-398(of)-397(MLD2P4,)-414(that)-397(are)-397(the)-398(user)]TJ 0 -13.55 Td [(in)28(terface,)-328(is)-326(pro)27(vid)1(e)-1(d)-326(in)-326(Section)]TJ +1 0 0 1 -188.6108 -527.9968 cm +BT +/F15 10.9091 Tf 188.6108 527.9968 Td[(,)-404(wh)1(e)-1(re)-390(th)1(e)-390(F)83(ort)1(ran)-389(95)-390(c)-1(o)-27(des)-391(of)-389(a)-390(f)1(e)-1(w)-390(sam)-1(p)1(le)-390(pr)1(ograms)-391(ar)1(e)-390(als)-1(o)]TJ -102.211 -13.5492 Td[(sho)28(wn.)-637(A)-397(reference)-398(gui)1(de)-398(f)1(or)-397(the)-398(u)1(pp)-27(e)-1(r)1(-)-1(l)1(a)27(y)28(er)-397(rou)1(tines)-398(of)-397(MLD)1(2P4,)-413(that)-397(are)-398(t)1(he)-398(u)1(s)-1(er)]TJ 0 -13.5492 Td[(in)28(t)1(e)-1(rf)1(ac)-1(e,)-328(i)1(s)-327(pr)1(o)27(v)1(ided)-326(in)-326(Section)]TJ +ET +1 0 0 1 240.0994 500.8984 cm 0 0 1 rg 0 0 1 RG - [-327(6)]TJ +1 0 0 1 -240.0994 -500.8984 cm +BT +/F15 10.9091 Tf 240.0994 500.8984 Td[(6)]TJ +ET +1 0 0 1 245.5539 500.8984 cm 0 g 0 G - [(.)-442(The)-326(error)-327(handlin)1(g)-327(mec)28(hanism)-327(used)-326(b)28(y)-327(the)-326(pac)28(k)55(age)]TJ 0 -13.549 Td [(is)-359(b)1(rie\015y)-359(describ)-28(ed)-358(in)-359(Section)]TJ +1 0 0 1 -245.5539 -500.8984 cm +BT +/F15 10.9091 Tf 245.5539 500.8984 Td[(.)-442(The)-327(err)1(or)-326(hand)1(lin)1(g)-327(mec)27(han)1(ism)-327(use)-1(d)-326(b)29(y)-327(th)1(e)-327(pac)28(k)56(age)]TJ -159.1541 -13.5492 Td[(is)-359(b)1(rie\015y)-358(desc)-1(ri)1(b)-28(ed)-358(in)-358(Section)]TJ +ET +1 0 0 1 231.5912 487.3492 cm 0 0 1 rg 0 0 1 RG - [-358(7)]TJ +1 0 0 1 -231.5912 -487.3492 cm +BT +/F15 10.9091 Tf 231.5912 487.3492 Td[(7)]TJ +ET +1 0 0 1 237.0457 487.3492 cm 0 g 0 G - [(.)-520(The)-359(cop)28(yrigh)28(t)-358(terms)-359(concerning)-358(the)-359(distribution)-358(and)]TJ 0 -13.549 Td [(mo)-28(di\014cation)-333(of)-333(MLD2P4)-334(ar)1(e)-334(rep)-28(orted)-333(in)-333(App)-28(endix)]TJ +1 0 0 1 -237.0457 -487.3492 cm +BT +/F15 10.9091 Tf 237.0457 487.3492 Td[(.)-520(The)-358(c)-1(op)28(y)1(righ)28(t)-358(terms)-359(c)-1(on)1(c)-1(erni)1(ng)-358(the)-359(d)1(is)-1(t)1(rib)1(ution)-358(an)1(d)]TJ -150.6459 -13.5492 Td[(mo)-28(di)1(\014cation)-333(of)-333(MLD)1(2P4)-333(are)-334(r)1(e)-1(p)-27(orted)-333(in)-333(Ap)1(p)-28(end)1(ix)]TJ +ET +1 0 0 1 333.6122 473.8 cm 0 0 1 rg 0 0 1 RG - [-333(A)]TJ +1 0 0 1 -333.6122 -473.8 cm +BT +/F15 10.9091 Tf 333.6122 473.8 Td[(A)]TJ +ET +1 0 0 1 341.794 473.8 cm 0 g 0 G - [(.)]TJ +1 0 0 1 -341.794 -473.8 cm +BT +/F15 10.9091 Tf 341.794 473.8 Td[(.)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -192 0 obj << +203 0 obj << /Type /Page -/Contents 193 0 R -/Resources 191 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 177 0 R -/Annots [ 184 0 R 185 0 R 186 0 R 187 0 R 188 0 R 189 0 R 190 0 R ] +/Contents 204 0 R +/Resources 202 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 195 0 R +/Annots [ 205 0 R 206 0 R 207 0 R 208 0 R 209 0 R 210 0 R 211 0 R ] >> endobj -184 0 obj << +205 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [243.651 592.625 251.098 604.315] +/Rect [243.651 592.6253 251.0981 604.3148] /Subtype /Link /A << /S /GoTo /D (section.2) >> >> endobj -185 0 obj << +206 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [238.905 579.076 246.352 590.766] +/Rect [238.9046 579.0761 246.3517 590.7656] /Subtype /Link /A << /S /GoTo /D (section.3) >> >> endobj -186 0 obj << +207 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [347.75 565.527 355.197 577.216] +/Rect [347.7504 565.5269 355.1975 577.2164] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -187 0 obj << +208 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [182.16 524.879 189.607 536.569] +/Rect [182.1599 524.8793 189.607 536.5688] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -188 0 obj << +209 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [239.103 497.781 246.55 509.47] +/Rect [239.1031 497.7809 246.5502 509.4704] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -189 0 obj << +210 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [230.595 484.232 238.042 495.921] +/Rect [230.5949 484.2317 238.042 495.9212] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -190 0 obj << +211 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [332.616 470.683 342.79 482.372] +/Rect [332.6159 470.6825 342.7903 482.372] /Subtype /Link -/A << /S /GoTo /D (appendix.A) >> +/A << /S /GoTo /D (section.A) >> >> endobj -191 0 obj << -/Font << /F15 123 0 R /F41 124 0 R >> +202 0 obj << +/Font << /F15 131 0 R /F43 134 0 R >> /ProcSet [ /PDF /Text ] >> endobj -198 0 obj << -/Length 1367 +214 0 obj << +/Length 2099 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(2)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(2)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(Code)-378(D)1(istri)-1(bution)]TJ/F15 10.9091 Tf 406.997 0 Td [(3)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Code)-378(Distribu)-1(tion)]TJ/F15 10.9091 Tf 396.8452 0 Td[(3)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -406.997 -35.866 Td [(2)-1125(Co)-31(de)-375(Distribution)]TJ/F15 10.9091 Tf 0 -24.352 Td [(MLD2P4)-333(is)-334(a)28(v)56(ailable)-334(f)1(rom)-334(the)-333(w)28(eb)-334(site)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 14.3462 Tf 93.6002 704.1363 Td[(2)-1125(C)-1(o)-32(de)-375(Di)-1(str)-1(ibut)-1(io)-1(n)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(MLD2P)1(4)-333(is)-334(a)28(v)56(ailabl)1(e)-334(fr)1(om)-334(th)1(e)-334(w)27(eb)-333(site)]TJ +ET +1 0 0 1 109.9639 657.2685 cm 0 g 0 G +1 0 0 1 21.8182 0 cm 0 g 0 G -/F44 10.9091 Tf 43.637 -22.515 Td [(http://www.mld2p4.it)]TJ/F15 10.9091 Tf -43.637 -22.516 Td [(where)-333(con)27(tact)-333(p)-28(oin)28(ts)-333(for)-333(further)-334(information)-333(can)-333(b)-28(e)-333(also)-334(foun)1(d.)]TJ 16.937 -13.549 Td [(The)-299(soft)28(w)28(are)-299(is)-298(a)27(v)56(ailable)-298(under)-299(a)-299(mo)-27(di\014ed)-299(BSD)-298(lice)-1(n)1(s)-1(e,)-305(as)-299(sp)-28(eci\014ed)-298(in)-299(App)-27(endix)]TJ +1 0 0 1 -131.7821 -657.2685 cm +BT +/F46 10.9091 Tf 137.2367 657.2685 Td[(http://www.mld2p4.it)]TJ/F15 10.9091 Tf -43.6365 -22.5155 Td[(where)-334(con)28(tact)-333(p)-28(oin)29(ts)-334(for)-333(f)1(ur)1(ther)-333(inf)1(ormation)-333(can)-333(b)-27(e)-334(also)-334(f)1(oun)1(d.)]TJ 16.9365 -13.5492 Td[(The)-299(soft)28(w)28(are)-299(is)-299(a)28(v)56(ailab)1(le)-299(un)1(der)-299(a)-298(m)-1(o)-27(di\014)1(e)-1(d)-298(BSD)-298(lice)-1(n)1(s)-1(e,)-306(as)-299(sp)-27(e)-1(ci\014ed)-298(in)-298(App)-27(endi)1(x)]TJ +ET +1 0 0 1 494.8392 621.2038 cm 0 0 1 rg 0 0 1 RG - [-299(A)]TJ +1 0 0 1 -494.8392 -621.2038 cm +BT +/F15 10.9091 Tf 494.8392 621.2038 Td[(A)]TJ +ET +1 0 0 1 503.021 621.2038 cm 0 g 0 G - [(;)]TJ -16.937 -13.549 Td [(please)-448(note)-448(that)-448(some)-448(of)-448(the)-448(optional)-448(third)-448(part)28(y)-448(libraries)-448(ma)28(y)-448(b)-28(e)-448(licensed)-448(under)-448(a)]TJ 0 -13.55 Td [(di\013eren)28(t)-366(and)-366(more)-366(stringen)28(t)-366(license,)-374(most)-366(notably)-366(the)-366(GPL,)-366(and)-365(this)-366(should)-366(b)-28(e)-366(tak)28(en)]TJ 0 -13.549 Td [(in)28(to)-333(ac)-1(coun)28(t)-333(when)-333(treating)-334(deriv)28(ed)-333(w)28(orks.)]TJ +1 0 0 1 -503.021 -621.2038 cm +BT +/F15 10.9091 Tf 503.021 621.2038 Td[(;)]TJ -409.4208 -13.5492 Td[(pl)1(e)-1(ase)-449(n)1(ote)-449(t)1(hat)-448(som)-1(e)-448(of)-448(th)1(e)-449(op)1(tion)1(al)-448(thi)1(rd)-448(p)1(art)28(y)-448(l)1(ibr)1(aries)-449(ma)28(y)-448(b)-27(e)-449(li)1(c)-1(ense)-1(d)-447(un)1(der)-448(a)]TJ 0 -13.5492 Td[(di)1(\013)-1(eren)28(t)-366(an)1(d)-366(more)-366(s)-1(tr)1(ingen)28(t)-366(l)1(ic)-1(ense,)-374(m)-1(ost)-366(n)1(otably)-365(the)-366(GP)1(L,)-366(and)-365(thi)1(s)-367(shou)1(ld)-365(b)-28(e)-366(tak)28(en)]TJ 0 -13.5492 Td[(in)28(t)1(o)-334(acc)-1(ou)1(n)28(t)-333(when)-333(treating)-333(d)1(e)-1(ri)1(v)28(e)-1(d)-333(w)28(orks.)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -197 0 obj << +213 0 obj << /Type /Page -/Contents 198 0 R -/Resources 196 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 177 0 R -/Annots [ 195 0 R 194 0 R ] +/Contents 214 0 R +/Resources 212 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 195 0 R +/Annots [ 216 0 R 220 0 R ] >> endobj -195 0 obj << +216 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.2) >> >> endobj -194 0 obj << +220 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [493.843 618.086 504.017 629.776] +/Rect [493.8429 618.0863 504.0173 629.7758] /Subtype /Link -/A << /S /GoTo /D (appendix.A) >> +/A << /S /GoTo /D (section.A) >> >> endobj -199 0 obj << -/D [197 0 R /XYZ 93.6 740.002 null] +215 0 obj << +/D [213 0 R /XYZ 93.6002 740.0018 null] >> endobj 18 0 obj << -/D [197 0 R /XYZ 93.6 715.095 null] +/D [213 0 R /XYZ 93.6002 715.0952 null] >> endobj -196 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F44 200 0 R >> +212 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -211 0 obj << -/Length 6973 +223 0 obj << +/Length 10655 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(4)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(4)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -203.265 -35.866 Td [(3)-1125(Con\014guring)-375(and)-375(Building)-375(MLD2P4)]TJ/F15 10.9091 Tf 0 -24.539 Td [(T)83(o)-324(build)-324(MLD2P4)-324(it)-324(is)-325(necessary)-324(to)-324(set)-324(up)-325(a)-324(Mak)28(e\014le)-324(with)-324(appropriate)-325(v)56(alues)-324(for)-324(y)27(our)]TJ 0 -13.549 Td [(system;)-363(this)-353(is)-353(done)-353(b)28(y)-353(means)-353(of)-353(the)]TJ/F44 10.9091 Tf 179.099 0 Td [(configure)]TJ/F15 10.9091 Tf 55.396 0 Td [(script.)-503(T)-1(h)1(e)-354(d)1(is)-1(tr)1(ibution)-353(also)-353(includes)]TJ -234.495 -13.55 Td [(the)-311(auto)-27(conf)-311(and)-311(automak)28(e)-311(sources)-311(emplo)28(y)28(ed)-311(to)-310(ge)-1(n)1(e)-1(r)1(ate)-311(the)-311(script,)-315(but)-311(usually)-310(this)-311(is)]TJ 0 -13.549 Td [(not)-333(needed)-334(to)-333(build)-333(the)-333(soft)27(w)28(are.)]TJ 16.936 -13.645 Td [(MLD2P4)-479(is)-479(implemen)28(ted)-479(almost)-479(en)28(tirely)-479(in)-479(F)83(ortran)-479(95,)-515(with)-479(some)-479(in)27(terfaces)-479(to)]TJ -16.936 -13.55 Td [(external)-284(libraries)-285(in)-284(C;)-284(the)-285(F)84(ortran)-285(compiler)-284(m)28(ust)-285(supp)-27(ort)-285(the)-284(F)83(ortran)-284(95)-284(standard)-284(plus)]TJ 0 -13.549 Td [(the)-353(extension)-353(TR15581,)-357(whic)27(h)-352(enhances)-353(the)-353(usabilit)28(y)-353(of)]TJ/F44 10.9091 Tf 271.48 0 Td [(ALLOCATABLE)]TJ/F15 10.9091 Tf 66.848 0 Td [(v)56(ariables.)-503(Most)]TJ -338.328 -13.549 Td [(mo)-28(dern)-343(F)84(ortran)-343(compilers)-343(supp)-28(ort)-343(this)-343(language)-343(lev)28(el.)-473(In)-343(particular,)-345(this)-343(is)-343(supp)-28(orted)]TJ 0 -13.549 Td [(b)28(y)-401(the)-400(GNU)-401(F)83(ortran)-400(compiler)-401(as)-401(of)-400(v)28(ersion)-401(4.2.0;)-434(ho)28(w)27(ev)28(er)-401(w)28(e)-401(recommend)-400(to)-401(use)-401(the)]TJ 0 -13.549 Td [(latest)-414(a)27(v)56(ailable)-414(releas)-1(e)-414(\0504.3.1)-414(at)-415(the)-414(time)-415(of)-414(this)-414(writing\051.)-688(The)-414(soft)27(w)28(are)-414(de\014nes)-415(data)]TJ 0 -13.55 Td [(t)28(yp)-28(es)-333(and)-334(in)28(terfaces)-333(for)-333(real)-334(and)-333(complex)-333(data,)-334(in)-333(b)-28(oth)-333(single)-333(and)-333(double)-334(precision.)]TJ/F17 11.9552 Tf 0 -29.764 Td [(3.1)-1125(Prerequisites)]TJ/F15 10.9091 Tf 0 -20.782 Td [(The)-333(follo)28(wing)-334(base)-333(libraries)-333(are)-334(needed:)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F19 14.3462 Tf 86.3998 704.1363 Td[(3)-1125(C)-1(on\014g)-1(uri)-1(ng)-375(and)-375(Bui)-1(ldi)-1(ng)-375(MLD2)-1(P)1(4)]TJ/F15 10.9091 Tf 0 -24.5396 Td[(T)83(o)-324(bu)1(ild)-324(M)1(LD2P4)-324(it)-324(is)-324(nec)-1(es)-1(sary)-324(to)-324(se)-1(t)-324(u)1(p)-324(a)-324(Mak)28(e)-1(\014)1(le)-325(with)-323(app)1(ropr)1(iate)-325(v)56(alu)1(e)-1(s)-324(for)-324(y)28(ou)1(r)]TJ 0 -13.5492 Td[(sys)-1(tem;)-363(th)1(is)-354(i)1(s)-354(d)1(one)-354(b)29(y)-353(me)-1(an)1(s)-354(of)-353(t)1(he)]TJ/F46 10.9091 Tf 179.0991 0 Td[(configure)]TJ/F15 10.9091 Tf 55.3961 0 Td[(sc)-1(ri)1(pt.)-503(The)-353(distri)1(but)1(ion)-353(also)-353(in)1(c)-1(lu)1(des)]TJ -234.4952 -13.5492 Td[(th)1(e)-312(au)1(to)-28(conf)-310(and)-310(aut)1(om)-1(ak)28(e)-311(source)-1(s)-311(emplo)28(y)28(ed)-311(to)-310(ge)-1(n)1(e)-1(rat)1(e)-312(t)1(he)-311(s)-1(crip)1(t,)-315(bu)1(t)-311(u)1(s)-1(u)1(ally)-310(this)-311(is)]TJ 0 -13.5492 Td[(not)-333(n)1(e)-1(eded)-333(to)-333(bu)1(ild)-333(th)1(e)-334(s)-1(of)1(t)28(w)27(ar)1(e)-1(.)]TJ 16.9365 -13.6456 Td[(MLD2P)1(4)-479(is)-479(implem)-1(en)28(ted)-479(al)1(m)-1(ost)-479(e)-1(n)29(tirely)-479(i)1(n)-479(F)83(or)1(tran)-478(95,)-515(w)-1(i)1(th)-479(som)-1(e)-479(in)28(terf)1(ac)-1(es)-480(to)]TJ -16.9365 -13.5492 Td[(exte)-1(r)1(nal)-284(li)1(brar)1(ie)-1(s)-284(in)-284(C;)-285(t)1(he)-285(F)84(ortr)1(an)-284(c)-1(ompi)1(le)-1(r)-284(m)28(ust)-285(sup)1(p)-27(ort)-284(the)-285(F)84(ortr)1(an)-284(95)-285(stand)1(ard)-284(p)1(lus)]TJ 0 -13.5492 Td[(th)1(e)-354(extension)-352(T)-1(R15581,)-357(whic)28(h)-353(enh)1(ance)-1(s)-353(the)-353(u)1(s)-1(ab)1(ilit)28(y)-352(of)]TJ/F46 10.9091 Tf 271.4807 0 Td[(ALLOCATABLE)]TJ/F15 10.9091 Tf 66.848 0 Td[(v)56(ariab)1(les)-1(.)-503(M)1(os)-1(t)]TJ -338.3287 -13.5492 Td[(mo)-28(dern)-342(F)83(or)1(tran)-342(c)-1(ompil)1(e)-1(r)1(s)-344(sup)1(p)-28(or)1(t)-343(thi)1(s)-344(lan)1(guage)-343(lev)28(e)-1(l.)-473(In)-342(part)1(ic)-1(u)1(lar,)-345(th)1(is)-343(is)-344(sup)1(p)-27(orted)]TJ 0 -13.5492 Td[(b)28(y)-400(the)-401(G)1(NU)-401(F)83(or)1(tran)-400(com)-1(p)1(iler)-401(as)-401(of)-400(v)28(ersion)-400(4.2.0;)-434(ho)28(w)28(e)-1(v)28(er)-401(w)28(e)-401(rec)-1(omme)-1(n)1(d)-401(t)1(o)-401(use)-401(the)]TJ 0 -13.5492 Td[(lates)-1(t)-414(a)28(v)56(ailab)1(le)-415(releas)-1(e)-415(\0504.)1(3.1)-415(at)-414(th)1(e)-415(time)-415(of)-414(thi)1(s)-415(writi)1(ng\051.)-687(T)-1(h)1(e)-415(s)-1(of)1(t)28(w)27(ar)1(e)-415(de\014n)1(e)-1(s)-415(d)1(ata)]TJ 0 -13.5492 Td[(t)28(yp)-27(e)-1(s)-333(and)-333(in)29(te)-1(r)1(face)-1(s)-334(f)1(or)-333(real)-333(and)-333(com)-1(p)1(lex)-334(d)1(ata,)-333(in)-333(b)-27(oth)-333(singl)1(e)-334(and)-333(d)1(oub)1(le)-334(p)1(re)-1(cision.)]TJ/F19 11.9552 Tf 0 -29.7639 Td[(3.)-1(1)-1125(Pre)-1(re)-1(q)1(ui)-1(sit)-1(es)]TJ/F15 10.9091 Tf 0 -20.782 Td[(The)-334(f)1(ollo)28(win)1(g)-334(b)1(as)-1(e)-334(l)1(ibr)1(aries)-334(are)-333(nee)-1(d)1(e)-1(d)1(:)]TJ +ET +1 0 0 1 80.9452 470.561 cm 0 g 0 G -/F43 10.9091 Tf 0 -22.901 Td [(BLAS)]TJ +1 0 0 1 -80.9452 -470.561 cm +BT +/F45 10.9091 Tf 86.3998 470.561 Td[(BLAS)]TJ +ET +1 0 0 1 119.3238 470.561 cm 0 g 0 G -/F15 10.9091 Tf 38.378 0 Td [([)]TJ +1 0 0 1 -119.3238 -470.561 cm +BT +/F15 10.9091 Tf 124.7784 470.561 Td[([)]TJ +ET +1 0 0 1 127.8087 470.561 cm 1 0 0 rg 1 0 0 RG - [(10)]TJ +1 0 0 1 -127.8087 -470.561 cm +BT +/F15 10.9091 Tf 127.8087 470.561 Td[(10)]TJ +ET +1 0 0 1 138.7178 470.561 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -138.7178 -470.561 cm +BT +/F15 10.9091 Tf 138.7178 470.561 Td[(,)]TJ +ET +1 0 0 1 145.1884 470.561 cm 1 0 0 rg 1 0 0 RG - [-315(11)]TJ +1 0 0 1 -145.1884 -470.561 cm +BT +/F15 10.9091 Tf 145.1884 470.561 Td[(11)]TJ +ET +1 0 0 1 156.0975 470.561 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -156.0975 -470.561 cm +BT +/F15 10.9091 Tf 156.0975 470.561 Td[(,)]TJ +ET +1 0 0 1 162.5682 470.561 cm 1 0 0 rg 1 0 0 RG - [-316(17)]TJ +1 0 0 1 -162.5682 -470.561 cm +BT +/F15 10.9091 Tf 162.5682 470.561 Td[(17)]TJ +ET +1 0 0 1 173.4773 470.561 cm 0 g 0 G - [(])-315(Man)28(y)-316(v)28(endors)-315(pro)28(vide)-316(opt)1(im)-1(i)1(z)-1(ed)-315(v)28(ersions)-316(of)-315(the)-315(Basic)-316(Linear)-315(Alge-)]TJ -11.105 -13.549 Td [(bra)-229(Subprograms;)-264(if)-229(no)-229(v)28(e)-1(n)1(dor)-230(v)28(ersion)-229(is)-229(a)27(v)56(ailable)-229(for)-229(a)-230(giv)28(en)-229(platform,)-250(the)-229(A)83(TLAS)]TJ 0 -13.549 Td [(soft)28(w)28(are)-404(\050)]TJ/F44 10.9091 Tf 47.821 0 Td [(http://math-atlas.sourceforge.net/)]TJ/F15 10.9091 Tf 194.726 0 Td [(\051)-403(ma)28(y)-403(b)-28(e)-403(emplo)27(y)28(ed.)-653(The)-404(ref-)]TJ -242.547 -13.55 Td [(erence)-415(BLAS)-414(from)-415(Netlib)-414(\050)]TJ/F44 10.9091 Tf 132.392 0 Td [(http://www.netlib.org/blas)]TJ/F15 10.9091 Tf 148.908 0 Td [(\051)-415(ar)1(e)-415(mean)28(t)-415(to)-414(de\014ne)]TJ -281.3 -13.549 Td [(the)-332(stand)1(ard)-332(b)-28(eha)28(viour)-331(of)-332(the)-331(BLAS)-332(in)28(terface,)-332(so)-332(they)-331(are)-332(not)-331(optimized)-332(for)-331(an)27(y)]TJ 0 -13.549 Td [(particular)-396(plaftorm,)-412(and)-396(should)-397(onl)1(y)-397(b)-28(e)-396(used)-396(as)-397(a)-396(last)-396(resort.)-634(Note)-396(that)-396(BLAS)]TJ 0 -13.549 Td [(computations)-223(form)-222(a)-223(relativ)28(e)-1(l)1(y)-223(small)-223(part)-223(of)-223(the)-222(MLD2P4/PSBLAS)-223(computations;)]TJ 0 -13.549 Td [(they)-308(are)-308(ho)28(w)28(ev)28(er)-308(critical)-308(when)-308(using)-307(preconditioners)-308(based)-308(on)-308(the)-307(UMFP)83(A)28(CK)-308(or)]TJ 0 -13.549 Td [(Sup)-28(erLU)-333(third)-333(part)28(y)-334(libr)1(aries)-1(.)]TJ +1 0 0 1 -173.4773 -470.561 cm +BT +/F15 10.9091 Tf 173.4773 470.561 Td[(])-315(Man)28(y)-315(v)28(end)1(ors)-316(p)1(ro)28(vid)1(e)-316(opti)1(m)-1(i)1(z)-1(ed)-315(v)28(e)-1(r)1(s)-1(ion)1(s)-316(of)-315(th)1(e)-316(B)-1(asic)-316(Li)1(near)-315(Alge)-1(-)]TJ -59.8047 -13.5492 Td[(br)1(a)-229(Sub)1(pr)1(ograms)-1(;)-264(i)1(f)-229(no)-229(v)28(end)1(or)-229(v)28(e)-1(rsion)-229(i)1(s)-230(a)28(v)56(ailabl)1(e)-230(for)-229(a)-229(giv)28(en)-229(p)1(latfor)1(m)-1(,)-249(the)-230(A)84(TLAS)]TJ 0 -13.5492 Td[(soft)28(w)27(ar)1(e)-404(\050)]TJ/F46 10.9091 Tf 47.8218 0 Td[(http://math-atlas.sourceforge.net/)]TJ/F15 10.9091 Tf 194.7251 0 Td[(\051)-403(ma)27(y)-402(b)-28(e)-403(e)-1(mpl)1(o)27(y)28(ed.)-653(The)-404(r)1(e)-1(f)1(-)]TJ -242.5469 -13.5492 Td[(ere)-1(n)1(c)-1(e)-415(BLAS)-414(fr)1(om)-415(Ne)-1(t)1(lib)-414(\050)]TJ/F46 10.9091 Tf 132.3926 0 Td[(http://www.netlib.org/blas)]TJ/F15 10.9091 Tf 148.9074 0 Td[(\051)-414(are)-415(me)-1(an)28(t)-414(to)-415(d)1(e)-1(\014)1(ne)]TJ -281.3 -13.5492 Td[(th)1(e)-332(s)-1(tan)1(dard)-331(b)-27(eha)28(viou)1(r)-332(of)-331(th)1(e)-332(B)-1(LAS)-331(i)1(n)28(te)-1(r)1(face)-1(,)-331(s)-1(o)-331(they)-332(ar)1(e)-332(not)-331(optimize)-1(d)-331(f)1(or)-331(an)28(y)]TJ 0 -13.5492 Td[(par)1(ticular)-396(p)1(laft)1(orm,)-412(and)-396(shou)1(ld)-396(onl)1(y)-396(b)-28(e)-397(u)1(s)-1(ed)-396(as)-397(a)-396(last)-396(re)-1(sort.)-633(Note)-396(that)-396(BLAS)]TJ 0 -13.5492 Td[(com)-1(p)1(utati)1(ons)-223(for)1(m)-224(a)-222(re)-1(l)1(ativ)28(ely)-223(sm)-1(al)1(l)-223(par)1(t)-223(of)-222(the)-223(MLD2P)1(4/PS)1(B)-1(LAS)-222(com)-1(p)1(utat)1(ions;)]TJ 0 -13.5492 Td[(th)1(e)-1(y)-307(are)-308(ho)28(w)27(ev)28(er)-308(critical)-308(wh)1(e)-1(n)-307(usin)1(g)-308(pr)1(e)-1(cond)1(ition)1(e)-1(rs)-308(b)1(as)-1(ed)-308(on)-307(th)1(e)-309(UM)1(FP)84(A)27(CK)-307(or)]TJ 0 -13.5492 Td[(Su)1(p)-27(e)-1(rLU)-333(th)1(ird)-333(p)1(art)28(y)-333(lib)1(rari)1(e)-1(s.)]TJ +ET +1 0 0 1 80.9452 339.2661 cm 0 g 0 G -/F43 10.9091 Tf -27.273 -22.902 Td [(MPI)]TJ +1 0 0 1 -80.9452 -339.2661 cm +BT +/F45 10.9091 Tf 86.3998 339.2661 Td[(MPI)]TJ +ET +1 0 0 1 111.6421 339.2661 cm 0 g 0 G -/F15 10.9091 Tf 30.697 0 Td [([)]TJ +1 0 0 1 -111.6421 -339.2661 cm +BT +/F15 10.9091 Tf 117.0966 339.2661 Td[([)]TJ +ET +1 0 0 1 120.1269 339.2661 cm 1 0 0 rg 1 0 0 RG - [(16)]TJ +1 0 0 1 -120.1269 -339.2661 cm +BT +/F15 10.9091 Tf 120.1269 339.2661 Td[(16)]TJ +ET +1 0 0 1 131.036 339.2661 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -131.036 -339.2661 cm +BT +/F15 10.9091 Tf 131.036 339.2661 Td[(,)]TJ +ET +1 0 0 1 137.7781 339.2661 cm 1 0 0 rg 1 0 0 RG - [-340(21)]TJ +1 0 0 1 -137.7781 -339.2661 cm +BT +/F15 10.9091 Tf 137.7781 339.2661 Td[(21)]TJ +ET +1 0 0 1 148.6873 339.2661 cm 0 g 0 G - [(])-340(A)-341(v)28(ersion)-340(of)-340(MPI)-340(is)-341(a)28(v)56(ailable)-341(on)-340(most)-340(high-p)-28(erformance)-340(computing)-340(sys-)]TJ -3.424 -13.549 Td [(tems;)-333(only)-334(v)28(ersion)-333(1.1)-333(is)-334(required.)]TJ +1 0 0 1 -148.6873 -339.2661 cm +BT +/F15 10.9091 Tf 148.6873 339.2661 Td[(])-340(A)-340(v)28(e)-1(r)1(s)-1(ion)-339(of)-340(MP)1(I)-341(is)-340(a)28(v)55(ai)1(lable)-340(on)-340(mos)-1(t)-340(hi)1(gh-p)-28(erf)1(ormance)-341(com)-1(p)1(utin)1(g)-340(s)-1(ys-)]TJ -35.0147 -13.5492 Td[(tem)-1(s;)-333(only)-333(v)28(ersion)-333(1.1)-333(is)-334(r)1(e)-1(q)1(uir)1(e)-1(d)1(.)]TJ +ET +1 0 0 1 80.9452 302.8156 cm 0 g 0 G -/F43 10.9091 Tf -27.273 -22.901 Td [(BLA)32(CS)]TJ +1 0 0 1 -80.9452 -302.8156 cm +BT +/F45 10.9091 Tf 86.3998 302.8156 Td[(BLA)32(CS)]TJ +ET +1 0 0 1 128.0359 302.8156 cm 0 g 0 G -/F15 10.9091 Tf 47.09 0 Td [([)]TJ +1 0 0 1 -128.0359 -302.8156 cm +BT +/F15 10.9091 Tf 133.4904 302.8156 Td[([)]TJ +ET +1 0 0 1 136.5207 302.8156 cm 1 0 0 rg 1 0 0 RG - [(12)]TJ +1 0 0 1 -136.5207 -302.8156 cm +BT +/F15 10.9091 Tf 136.5207 302.8156 Td[(12)]TJ +ET +1 0 0 1 147.4298 302.8156 cm 0 g 0 G - [(])-342(The)-342(Basic)-342(Linear)-342(Algebra)-342(Comm)28(unication)-342(Subprograms)-342(are)-342(a)28(v)56(ailable)-342(in)]TJ -19.817 -13.55 Td [(source)-296(form)-297(from)]TJ/F44 10.9091 Tf 83.789 0 Td [(http://www.netlib.org/blacs)]TJ/F15 10.9091 Tf 154.635 0 Td [(;)-309(some)-296(v)28(endors)-297(include)-296(them)-296(in)]TJ -238.424 -13.549 Td [(their)-333(parallel)-333(c)-1(ompu)1(ting)-334(supp)-27(ort)-334(libraries.)]TJ +1 0 0 1 -147.4298 -302.8156 cm +BT +/F15 10.9091 Tf 147.4298 302.8156 Td[(])-342(The)-342(Bas)-1(i)1(c)-343(Lin)1(e)-1(ar)-341(Algebra)-342(Comm)27(u)1(nication)-341(Su)1(bp)1(rograms)-342(are)-343(a)28(v)56(ailab)1(le)-342(in)]TJ -33.7572 -13.5492 Td[(source)-297(f)1(orm)-297(f)1(rom)]TJ/F46 10.9091 Tf 83.7898 0 Td[(http://www.netlib.org/blacs)]TJ/F15 10.9091 Tf 154.6347 0 Td[(;)-308(s)-1(ome)-297(v)28(endor)1(s)-297(in)1(c)-1(lu)1(de)-297(t)1(hem)-297(in)]TJ -238.4245 -13.5492 Td[(th)1(e)-1(ir)-333(p)1(arall)1(e)-1(l)-333(com)-1(p)1(utin)1(g)-333(s)-1(u)1(pp)-27(ort)-333(lib)1(rari)1(e)-1(s.)]TJ +ET +1 0 0 1 80.9452 252.8158 cm 0 g 0 G -/F43 10.9091 Tf -27.273 -22.901 Td [(PSBLAS)]TJ +1 0 0 1 -80.9452 -252.8158 cm +BT +/F45 10.9091 Tf 86.3998 252.8158 Td[(PSBLAS)]TJ +ET +1 0 0 1 134.8692 252.8158 cm 0 g 0 G -/F15 10.9091 Tf 53.924 0 Td [([)]TJ +1 0 0 1 -134.8692 -252.8158 cm +BT +/F15 10.9091 Tf 140.3237 252.8158 Td[([)]TJ +ET +1 0 0 1 143.354 252.8158 cm 1 0 0 rg 1 0 0 RG - [(14)]TJ +1 0 0 1 -143.354 -252.8158 cm +BT +/F15 10.9091 Tf 143.354 252.8158 Td[(14)]TJ +ET +1 0 0 1 154.2631 252.8158 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -154.2631 -252.8158 cm +BT +/F15 10.9091 Tf 154.2631 252.8158 Td[(,)]TJ +ET +1 0 0 1 160.9298 252.8158 cm 1 0 0 rg 1 0 0 RG - [-333(15)]TJ +1 0 0 1 -160.9298 -252.8158 cm +BT +/F15 10.9091 Tf 160.9298 252.8158 Td[(15)]TJ +ET +1 0 0 1 171.8389 252.8158 cm 0 g 0 G - [(])-334(P)28(arallel)-333(Sparse)-333(BLAS)-334(is)-333(a)28(v)55(ailable)-333(from)]TJ/F44 10.9091 Tf -26.651 -13.549 Td [(http://www.ce.uniroma2.it/psblas)]TJ/F15 10.9091 Tf 183.27 0 Td [(;)-339(v)27(ersion)-337(2.3)-337(\050or)-338(later\051)-337(is)-338(required.)-456(Indeed,)]TJ -183.27 -13.549 Td [(all)-364(the)-365(prerequisites)-364(listed)-365(so)-364(far)-365(are)-364(also)-365(prerequisites)-364(of)-365(PSBLAS.)-364(T)83(o)-364(build)-365(the)]TJ 0 -13.55 Td [(MLD2P4)-443(library)-442(it)-443(is)-443(necessary)-443(to)-443(get)-442(ac)-1(cess)-443(t)1(o)-443(the)-443(source)-443(PSBLAS)-443(di)1(re)-1(ctory)]TJ 0 -13.549 Td [(emplo)28(y)28(ed)-381(to)-381(build)-381(the)-381(v)28(ersion)-381(under)-380(use)-1(;)-404(after)-381(the)-381(MLD2P4)-381(bu)1(ild)-381(pro)-28(cess)-381(com-)]TJ 0 -13.549 Td [(pletes,)-368(only)-360(the)-361(compiled)-361(form)-361(of)-360(the)-361(PSBLAS)-361(library)-360(is)-361(necessary)-361(to)-361(build)-360(user)]TJ 0 -13.549 Td [(applications.)]TJ -10.337 -22.902 Td [(Please)-289(note)-289(that)-289(the)-290(fou)1(r)-290(pr)1(e)-1(vi)1(ous)-290(librar)1(ie)-1(s)-289(m)28(ust)-289(ha)28(v)28(e)-290(F)84(ortran)-289(in)28(terfaces)-290(compatible)]TJ -16.936 -13.549 Td [(with)-300(MLD2P4;)-311(usual)1(ly)-300(this)-300(means)-300(that)-300(th)1(e)-1(y)-299(should)-300(all)-300(b)-27(e)-300(built)-300(with)-300(the)-299(same)-300(compiler)]TJ 0 -13.549 Td [(as)-333(MLD2P4.)]TJ +1 0 0 1 -171.8389 -252.8158 cm +BT +/F15 10.9091 Tf 171.8389 252.8158 Td[(])-333(P)28(aral)1(le)-1(l)-333(S)1(par)1(s)-1(e)-334(BLAS)-333(is)-333(a)27(v)56(ail)1(able)-334(f)1(rom)]TJ/F46 10.9091 Tf -58.1663 -13.5492 Td[(http://www.ce.uniroma2.it/psblas)]TJ/F15 10.9091 Tf 183.2707 0 Td[(;)-339(v)28(e)-1(r)1(s)-1(ion)-337(2.)1(3)-338(\050or)-337(l)1(ate)-1(r)1(\051)-338(is)-337(re)-1(q)1(uir)1(e)-1(d)1(.)-457(In)1(dee)-1(d)1(,)]TJ -183.2707 -13.5492 Td[(all)-364(the)-364(prerequi)1(s)-1(it)1(e)-1(s)-365(li)1(s)-1(ted)-364(s)-1(o)-364(far)-364(are)-365(al)1(s)-1(o)-364(pr)1(e)-1(requ)1(is)-1(i)1(te)-1(s)-365(of)-364(P)1(SBLAS.)-364(T)83(o)-364(bui)1(ld)-364(the)]TJ 0 -13.5492 Td[(MLD2P)1(4)-443(li)1(brar)1(y)-443(it)-442(is)-443(nec)-1(es)-1(sary)-442(to)-443(ge)-1(t)-442(ac)-1(ce)-1(ss)-443(to)-443(th)1(e)-444(sour)1(c)-1(e)-443(PS)1(B)-1(LAS)-442(d)1(irec)-1(tor)1(y)]TJ 0 -13.5492 Td[(em)-1(p)1(lo)28(y)28(e)-1(d)-380(to)-381(bu)1(ild)-380(th)1(e)-382(v)28(ersion)-381(u)1(nd)1(e)-1(r)-380(use)-1(;)-404(aft)1(e)-1(r)-380(the)-381(MLD2P)1(4)-381(bu)1(ild)-380(pr)1(o)-28(c)-1(es)-1(s)-381(com)-1(-)]TJ 0 -13.5492 Td[(pl)1(e)-1(tes)-1(,)-367(onl)1(y)-361(th)1(e)-362(compil)1(e)-1(d)-360(for)1(m)-362(of)-360(th)1(e)-362(P)1(SBLAS)-360(lib)1(rary)-360(is)-361(nec)-1(es)-1(sary)-360(to)-361(b)1(uild)-360(u)1(s)-1(er)]TJ 0 -13.5492 Td[(app)1(lication)1(s)-1(.)]TJ -10.3363 -22.9013 Td[(Pl)1(e)-1(ase)-290(n)1(ote)-290(th)1(at)-289(the)-289(fou)1(r)-289(pr)1(e)-1(vi)1(ous)-290(l)1(ibr)1(aries)-290(m)28(ust)-289(ha)28(v)28(e)-290(F)84(ortr)1(an)-289(in)28(terf)1(ac)-1(es)-290(com)-1(p)1(atib)1(le)]TJ -16.9365 -13.5492 Td[(with)-299(MLD2P)1(4;)-311(usual)1(ly)-300(th)1(is)-300(m)-1(eans)-300(th)1(at)-300(th)1(e)-1(y)-299(s)-1(h)1(ould)-299(all)-299(b)-28(e)-300(b)1(uil)1(t)-300(with)-299(the)-300(sam)-1(e)-300(com)-1(p)1(iler)]TJ 0 -13.5492 Td[(as)-334(M)1(LD2P4.)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -210 0 obj << +222 0 obj << /Type /Page -/Contents 211 0 R -/Resources 209 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 177 0 R -/Annots [ 201 0 R 202 0 R 203 0 R 204 0 R 205 0 R 206 0 R 207 0 R 208 0 R ] +/Contents 223 0 R +/Resources 221 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 195 0 R +/Annots [ 225 0 R 226 0 R 227 0 R 228 0 R 229 0 R 230 0 R 231 0 R 232 0 R ] >> endobj -201 0 obj << +225 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [126.812 469.565 139.714 478.588] +/Rect [126.8124 469.5648 139.714 478.5876] /Subtype /Link /A << /S /GoTo /D (cite.blas3) >> >> endobj -202 0 obj << +226 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [144.192 469.565 157.094 478.588] +/Rect [144.1922 469.5648 157.0938 478.5876] /Subtype /Link /A << /S /GoTo /D (cite.blas2) >> >> endobj -203 0 obj << +227 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [161.572 469.565 174.474 478.588] +/Rect [161.5719 469.5648 174.4736 478.5876] /Subtype /Link /A << /S /GoTo /D (cite.blas1) >> >> endobj -204 0 obj << +228 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [119.131 338.27 132.032 347.293] +/Rect [119.1307 338.2698 132.0323 347.2927] /Subtype /Link /A << /S /GoTo /D (cite.MPI2) >> >> endobj -205 0 obj << +229 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [136.782 338.27 149.683 347.293] +/Rect [136.7819 338.2698 149.6835 347.2927] /Subtype /Link /A << /S /GoTo /D (cite.MPI1) >> >> endobj -206 0 obj << +230 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [135.524 301.819 148.426 310.842] +/Rect [135.5245 301.8193 148.4261 310.8421] /Subtype /Link /A << /S /GoTo /D (cite.BLACS) >> >> endobj -207 0 obj << +231 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [142.358 251.82 155.259 260.842] +/Rect [142.3578 251.8195 155.2594 260.8424] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -208 0 obj << +232 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [159.934 251.82 172.835 260.842] +/Rect [159.9335 251.8195 172.8352 260.8424] /Subtype /Link /A << /S /GoTo /D (cite.psblas_00) >> >> endobj -212 0 obj << -/D [210 0 R /XYZ 86.4 740.002 null] +224 0 obj << +/D [222 0 R /XYZ 86.3998 740.0018 null] >> endobj 22 0 obj << -/D [210 0 R /XYZ 86.4 715.095 null] +/D [222 0 R /XYZ 86.3998 715.0952 null] >> endobj 26 0 obj << -/D [210 0 R /XYZ 86.4 526.167 null] +/D [222 0 R /XYZ 86.3998 526.1673 null] >> endobj -209 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F17 111 0 R /F44 200 0 R /F43 158 0 R >> +221 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F19 113 0 R /F46 219 0 R /F45 147 0 R >> /ProcSet [ /PDF /Text ] >> endobj -224 0 obj << -/Length 5602 +240 0 obj << +/Length 7822 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(3)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(3)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(Configuring)-378(and)-377(B)-1(uilding)-377(MLD2P4)]TJ/F15 10.9091 Tf 406.997 0 Td [(5)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Configuri)-1(ng)-378(an)-1(d)-378(Build)-1(ing)-378(ML)-1(D2)1(P4)]TJ/F15 10.9091 Tf 396.8452 0 Td[(5)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 11.9552 Tf -406.997 -35.866 Td [(3.2)-1125(Optional)-375(third)-375(part)31(y)-375(libraries)]TJ/F15 10.9091 Tf 0 -20.594 Td [(W)83(e)-426(pro)28(vide)-427(in)28(terfaces)-427(to)-426(the)-427(follo)28(wing)-426(third-part)28(y)-427(soft)28(w)28(are)-427(libraries;)-473(note)-426(that)-427(these)]TJ 0 -13.549 Td [(are)-370(optional,)-379(but)-369(if)-370(y)28(ou)-370(enable)-370(them)-370(some)-370(default)1(s)-370(for)-370(m)28(ultilev)28(e)-1(l)-369(preconditioners)-370(ma)28(y)]TJ 0 -13.55 Td [(c)28(hange)-334(to)-333(re\015ect)-333(their)-334(pr)1(e)-1(sence.)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 11.9552 Tf 93.6002 704.1363 Td[(3.)-1(2)-1125(Opt)-1(io)-1(nal)-375(t)-1(hir)-1(d)-375(part)31(y)-375(l)-1(ibr)-1(a)1(r)-1(ie)-1(s)]TJ/F15 10.9091 Tf 0 -20.5946 Td[(W)84(e)-427(pro)28(vi)1(de)-427(in)28(t)1(e)-1(rf)1(ac)-1(es)-427(to)-426(the)-427(f)1(ollo)28(wing)-426(thi)1(rd-par)1(t)28(y)-427(soft)28(w)28(are)-427(li)1(brar)1(ie)-1(s;)-473(not)1(e)-427(that)-426(thes)-1(e)]TJ 0 -13.5492 Td[(are)-370(op)1(tional)1(,)-379(bu)1(t)-370(if)-369(y)28(ou)-370(enab)1(le)-370(them)-370(s)-1(ome)-370(defau)1(lts)-370(for)-369(m)27(u)1(ltilev)28(el)-370(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-371(ma)28(y)]TJ 0 -13.5492 Td[(c)27(h)1(ange)-334(t)1(o)-334(r)1(e)-1(\015)1(e)-1(ct)-334(t)1(heir)-333(pr)1(e)-1(se)-1(n)1(c)-1(e.)]TJ +ET +1 0 0 1 88.1457 632.1523 cm 0 g 0 G -/F43 10.9091 Tf 0 -24.291 Td [(UMFP)96(A)32(CK)]TJ +1 0 0 1 -88.1457 -632.1523 cm +BT +/F45 10.9091 Tf 93.6002 632.1523 Td[(UM)1(FP)96(A)31(C)1(K)]TJ +ET +1 0 0 1 158.615 632.1523 cm 0 g 0 G -/F15 10.9091 Tf 70.47 0 Td [([)]TJ +1 0 0 1 -158.615 -632.1523 cm +BT +/F15 10.9091 Tf 164.0695 632.1523 Td[([)]TJ +ET +1 0 0 1 167.0998 632.1523 cm 1 0 0 rg 1 0 0 RG - [(8)]TJ +1 0 0 1 -167.0998 -632.1523 cm +BT +/F15 10.9091 Tf 167.0998 632.1523 Td[(8)]TJ +ET +1 0 0 1 172.5544 632.1523 cm 0 g 0 G - [(])-333(A)-334(sparse)-333(direct)-333(factorization)-334(p)1(ac)27(k)56(age)-334(a)28(v)56(ailable)-333(from)]TJ/F44 10.9091 Tf -43.197 -13.549 Td [(http://www.cise.ufl.edu/research/sparse/umfpack/)]TJ/F15 10.9091 Tf 274.906 0 Td [(;)-359(pro)27(vides)-350(se)-1(r)1(ial)-351(factor-)]TJ -274.906 -13.549 Td [(ization)-275(and)-274(triangular)-275(system)-275(solution)-274(for)-275(double)-275(p)1(rec)-1(ision)-274(real)-275(and)-275(complex)-274(data.)]TJ 0 -13.549 Td [(W)83(e)-333(ha)28(v)28(e)-334(tested)-333(v)28(ersions)-334(4.4)-333(and)-333(5.1.)]TJ +1 0 0 1 -172.5544 -632.1523 cm +BT +/F15 10.9091 Tf 172.5544 632.1523 Td[(])-333(A)-333(s)-1(p)1(ars)-1(e)-333(dir)1(e)-1(ct)-333(factorization)-333(p)1(ac)27(k)56(age)-334(a)28(v)56(ailabl)1(e)-334(fr)1(om)]TJ/F46 10.9091 Tf -51.6814 -13.5492 Td[(http://www.cise.ufl.edu/research/sparse/umfpack/)]TJ/F15 10.9091 Tf 274.9061 0 Td[(;)-359(pro)28(vi)1(des)-352(serial)-350(factor-)]TJ -274.9061 -13.5492 Td[(ization)-274(and)-274(tri)1(angu)1(lar)-275(syste)-1(m)-275(solu)1(tion)-274(for)-274(dou)1(ble)-275(p)1(re)-1(cision)-274(real)-275(an)1(d)-275(com)-1(p)1(lex)-275(d)1(ata.)]TJ 0 -13.5492 Td[(W)84(e)-334(ha)28(v)28(e)-334(tes)-1(t)1(e)-1(d)-333(v)28(ersions)-333(4.4)-334(an)1(d)-333(5.1.)]TJ +ET +1 0 0 1 88.1457 569.3936 cm 0 g 0 G -/F43 10.9091 Tf -27.273 -22.111 Td [(Sup)-32(erLU)]TJ +1 0 0 1 -88.1457 -569.3936 cm +BT +/F45 10.9091 Tf 93.6002 569.3936 Td[(Sup)-32(er)1(LU)]TJ +ET +1 0 0 1 142.9711 569.3936 cm 0 g 0 G -/F15 10.9091 Tf 54.826 0 Td [([)]TJ +1 0 0 1 -142.9711 -569.3936 cm +BT +/F15 10.9091 Tf 148.4257 569.3936 Td[([)]TJ +ET +1 0 0 1 151.456 569.3936 cm 1 0 0 rg 1 0 0 RG - [(9)]TJ +1 0 0 1 -151.456 -569.3936 cm +BT +/F15 10.9091 Tf 151.456 569.3936 Td[(9)]TJ +ET +1 0 0 1 156.9105 569.3936 cm 0 g 0 G - [(])-333(A)-334(sparse)-333(direct)-333(factorization)-334(p)1(ac)27(k)56(age)-334(a)28(v)56(ailable)-333(from)]TJ/F44 10.9091 Tf -27.553 -13.55 Td [(http://crd.lbl.gov/~xiaoye/SuperLU/)]TJ/F15 10.9091 Tf 200.452 0 Td [(;)-498(pro)27(vides)-443(serial)-443(factorization)-444(and)-443(tri-)]TJ -200.452 -13.549 Td [(angular)-389(system)-390(solution)-389(for)-389(single)-390(and)-389(double)-389(precision,)-403(real)-390(and)-389(complex)-389(data.)]TJ 0 -13.549 Td [(W)83(e)-333(ha)28(v)28(e)-334(tested)-333(v)28(ersions)-334(3.0)-333(and)-333(3.1.)]TJ +1 0 0 1 -156.9105 -569.3936 cm +BT +/F15 10.9091 Tf 156.9105 569.3936 Td[(])-333(A)-333(s)-1(p)1(ars)-1(e)-333(dir)1(e)-1(ct)-333(factorization)-333(p)1(ac)27(k)56(age)-334(a)28(v)56(ailabl)1(e)-334(fr)1(om)]TJ/F46 10.9091 Tf -36.0375 -13.5492 Td[(http://crd.lbl.gov/~xiaoye/SuperLU/)]TJ/F15 10.9091 Tf 200.4524 0 Td[(;)-498(pr)1(o)27(v)1(ides)-444(s)-1(eri)1(al)-444(f)1(ac)-1(t)1(orization)-443(and)-443(t)1(ri-)]TJ -200.4524 -13.5492 Td[(angu)1(lar)-389(sys)-1(t)1(e)-1(m)-390(solu)1(tion)-389(for)-389(sin)1(gle)-390(an)1(d)-389(dou)1(ble)-390(p)1(rec)-1(i)1(s)-1(ion)1(,)-403(re)-1(al)-389(an)1(d)-389(c)-1(omp)1(le)-1(x)-389(d)1(ata.)]TJ 0 -13.5492 Td[(W)84(e)-334(ha)28(v)28(e)-334(tes)-1(t)1(e)-1(d)-333(v)28(ersions)-333(3.0)-334(an)1(d)-333(3.1.)]TJ +ET +1 0 0 1 88.1457 506.6349 cm 0 g 0 G -/F43 10.9091 Tf -27.273 -22.111 Td [(Sup)-32(erLU)]TJ +1 0 0 1 -88.1457 -506.6349 cm +BT +/F45 10.9091 Tf 93.6002 506.6349 Td[(Sup)-32(er)1(LU)]TJ ET +1 0 0 1 143.7238 506.6349 cm q -1 0 0 1 143.724 506.834 cm -[]0 d 0 J 0.398 w 0 0 m 3.764 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.7636 0.1992 l +S Q +1 0 0 1 -143.7238 -506.6349 cm BT -/F43 10.9091 Tf 147.487 506.635 Td [(Dist)]TJ +/F45 10.9091 Tf 147.4874 506.6349 Td[(Dist)]TJ +ET +1 0 0 1 170.4206 506.6349 cm 0 g 0 G -/F15 10.9091 Tf 28.388 0 Td [([)]TJ +1 0 0 1 -170.4206 -506.6349 cm +BT +/F15 10.9091 Tf 175.8752 506.6349 Td[([)]TJ +ET +1 0 0 1 178.9055 506.6349 cm 1 0 0 rg 1 0 0 RG - [(18)]TJ +1 0 0 1 -178.9055 -506.6349 cm +BT +/F15 10.9091 Tf 178.9055 506.6349 Td[(18)]TJ +ET +1 0 0 1 189.8146 506.6349 cm 0 g 0 G - [(])-304(A)-304(sparse)-304(d)1(irec)-1(t)-303(factorization)-304(pac)28(k)55(age)-304(a)28(v)56(ailable)-304(from)-304(the)-304(same)-304(site)]TJ -55.002 -13.549 Td [(as)-481(Sup)-28(erLU;)-481(pro)28(vides)-481(parallel)-481(factorization)-481(and)-481(triangular)-481(system)-482(solution)-481(for)]TJ 0 -13.549 Td [(double)-333(precision)-334(r)1(e)-1(al)-333(and)-333(complex)-333(data.)-445(W)84(e)-334(ha)28(v)28(e)-334(tested)-333(v)28(ersion)-334(2.1.)]TJ/F17 11.9552 Tf -27.273 -29.023 Td [(3.3)-1125(Con\014guration)-375(options)]TJ/F15 10.9091 Tf 0 -20.594 Td [(T)83(o)-302(build)-302(MLD2P4)-302(the)-302(\014rst)-303(step)-302(is)-302(to)-302(use)-303(the)]TJ/F44 10.9091 Tf 214.002 0 Td [(configure)]TJ/F15 10.9091 Tf 54.842 0 Td [(script)-302(in)-302(the)-303(main)-302(directory)-302(to)]TJ -268.844 -13.549 Td [(generate)-333(the)-334(necessary)-333(mak)28(e\014le\050s\051.)]TJ 16.937 -13.55 Td [(As)-333(a)-334(minimal)-333(example)-333(consider)-334(the)-333(follo)28(wing:)]TJ +1 0 0 1 -189.8146 -506.6349 cm +BT +/F15 10.9091 Tf 189.8146 506.6349 Td[(])-304(A)-303(s)-1(p)1(ars)-1(e)-304(d)1(irec)-1(t)-303(factorization)-303(pac)27(k)56(age)-304(a)28(v)56(ailabl)1(e)-305(f)1(rom)-304(th)1(e)-305(sam)-1(e)-304(site)]TJ -68.9416 -13.5492 Td[(as)-482(S)1(up)-27(erLU;)-481(pr)1(o)28(vides)-482(p)1(arall)1(e)-1(l)-481(f)1(ac)-1(tor)1(iz)-1(at)1(ion)-481(an)1(d)-481(tri)1(angul)1(ar)-481(s)-1(y)1(s)-1(tem)-482(solu)1(tion)-481(f)1(or)]TJ 0 -13.5492 Td[(dou)1(bl)1(e)-334(pr)1(e)-1(cis)-1(i)1(on)-333(real)-333(and)-333(com)-1(p)1(lex)-334(d)1(ata.)-444(W)83(e)-333(ha)28(v)28(e)-334(tes)-1(ted)-333(v)28(ers)-1(i)1(on)-333(2.1.)]TJ/F19 11.9552 Tf -27.2728 -29.0221 Td[(3.)-1(3)-1125(C)-1(on\014g)-1(urat)-1(io)-1(n)-375(opt)-1(io)-1(ns)]TJ/F15 10.9091 Tf 0 -20.5946 Td[(T)83(o)-302(bu)1(ild)-302(M)1(LD2P4)-302(th)1(e)-303(\014r)1(s)-1(t)-302(ste)-1(p)-301(is)-303(to)-302(use)-303(th)1(e)]TJ/F46 10.9091 Tf 214.002 0 Td[(configure)]TJ/F15 10.9091 Tf 54.842 0 Td[(sc)-1(ri)1(pt)-302(in)-302(t)1(he)-303(main)-302(d)1(irec)-1(t)1(ory)-302(to)]TJ -268.844 -13.5492 Td[(generate)-334(th)1(e)-334(nece)-1(ss)-1(ar)1(y)-334(mak)28(e\014le\050s\051.)]TJ 16.9365 -13.5492 Td[(As)-334(a)-333(minimal)-333(exam)-1(p)1(le)-334(consid)1(e)-1(r)-333(th)1(e)-334(fol)1(lo)28(w)-1(i)1(ng:)]TJ +ET +1 0 0 1 88.1457 381.3169 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf -16.937 -21.504 Td [(./configure)-525(--with-psblas=/home/user/PSBLAS/psblas-2.3)]TJ/F15 10.9091 Tf 0 -21.504 Td [(whic)28(h)-273(assumes)-273(that)-272(the)-273(v)56(arious)-273(MPI)-272(compilers)-273(and)-273(sup)1(p)-28(ort)-273(libraries)-272(are)-273(a)28(v)55(ailable)-272(in)-273(the)]TJ 0 -13.55 Td [(standard)-253(directories)-253(on)-253(the)-253(system,)-269(and)-253(sp)-28(eci\014es)-253(only)-253(the)-253(PSBLAS)-253(build)-253(directory)-253(\050note)]TJ 0 -13.549 Td [(that)-250(the)-249(latter)-250(directory)-250(m)28(ust)-250(b)-28(e)-249(sp)-28(eci\014ed)-250(with)-250(an)]TJ/F18 10.9091 Tf 236.248 0 Td [(absolute)]TJ/F15 10.9091 Tf 40.639 0 Td [(path\051.)-416(T)-1(h)1(e)-250(full)-250(set)-250(of)-249(options)]TJ -276.887 -13.549 Td [(ma)28(y)-334(b)-27(e)-334(lo)-27(ok)27(ed)-333(at)-333(b)28(y)-334(issuing)-333(the)-333(comm)-1(an)1(d)]TJ/F44 10.9091 Tf 205.576 0 Td [(./configure)-525(--help)]TJ/F15 10.9091 Tf 103.09 0 Td [(,)-333(whic)27(h)-333(pro)-28(d)1(uce)-1(s:)]TJ +1 0 0 1 -88.1457 -381.3169 cm +BT +/F46 10.9091 Tf 93.6002 381.3169 Td[(./configure)-525(--with-psblas=/home/user/PSBLAS/psblas-2.3)]TJ/F15 10.9091 Tf 0 -21.5044 Td[(whic)28(h)-272(as)-1(sume)-1(s)-273(th)1(at)-273(th)1(e)-273(v)56(ariou)1(s)-273(MPI)-272(c)-1(ompil)1(e)-1(r)1(s)-273(and)-272(s)-1(u)1(pp)-27(ort)-272(lib)1(raries)-273(are)-273(a)28(v)56(ailab)1(le)-273(in)-272(the)]TJ 0 -13.5492 Td[(stand)1(ard)-253(d)1(irec)-1(t)1(ories)-254(on)-252(the)-253(s)-1(ystem)-1(,)-269(an)1(d)-253(sp)-28(eci\014es)-254(on)1(ly)-253(th)1(e)-254(P)1(SBLAS)-253(b)1(uil)1(d)-253(di)1(rec)-1(tor)1(y)-253(\050note)]TJ 0 -13.5492 Td[(th)1(at)-250(the)-250(l)1(atte)-1(r)-249(di)1(re)-1(ctory)-249(m)27(u)1(s)-1(t)-249(b)-28(e)-250(sp)-28(eci\014ed)-250(wit)1(h)-250(an)]TJ/F20 10.9091 Tf 236.2479 0 Td[(absolu)1(t)-1(e)]TJ/F15 10.9091 Tf 40.6394 0 Td[(pat)1(h\051.)-416(The)-250(fu)1(ll)-250(se)-1(t)-249(of)-249(option)1(s)]TJ -276.8873 -13.5492 Td[(ma)27(y)-333(b)-27(e)-334(lo)-27(ok)28(e)-1(d)-333(at)-333(b)28(y)-333(issuin)1(g)-334(th)1(e)-334(com)-1(mand)]TJ/F46 10.9091 Tf 205.576 0 Td[(./configure)-525(--help)]TJ/F15 10.9091 Tf 103.0897 0 Td[(,)-333(whic)28(h)-333(pr)1(o)-28(du)1(c)-1(es)-1(:)]TJ +ET +1 0 0 1 88.1457 297.6604 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf -308.666 -21.505 Td [(`configure')-525(configures)-525(MLD2P4)-525(1.0)-525(to)-525(adapt)-525(to)-525(many)-525(kinds)-525(of)-525(systems.)]TJ 0 -27.098 Td [(Usage:)-525(./configure)-525([OPTION]...)-525([VAR=VALUE]...)]TJ 0 -27.098 Td [(To)-525(assign)-525(environment)-525(variables)-525(\050e.g.,)-525(CC,)-525(CFLAGS...\051,)-525(specify)-525(them)-525(as)]TJ 0 -13.549 Td [(VAR=VALUE.)-1050(See)-525(below)-525(for)-525(descriptions)-525(of)-525(some)-525(of)-525(the)-525(useful)-525(variables.)]TJ 0 -27.099 Td [(Defaults)-525(for)-525(the)-525(options)-525(are)-525(specified)-525(in)-525(brackets.)]TJ 0 -27.098 Td [(Configuration:)]TJ 11.455 -13.549 Td [(-h,)-525(--help)-7350(display)-525(this)-525(help)-525(and)-525(exit)]TJ 22.908 -13.55 Td [(--help=short)-4200(display)-525(options)-525(specific)-525(to)-525(this)-525(package)]TJ 0 -13.549 Td [(--help=recursive)-2100(display)-525(the)-525(short)-525(help)-525(of)-525(all)-525(the)-525(included)-525(packages)]TJ -22.908 -13.549 Td [(-V,)-525(--version)-5775(display)-525(version)-525(information)-525(and)-525(exit)]TJ +1 0 0 1 -88.1457 -297.6604 cm +BT +/F46 10.9091 Tf 93.6002 297.6604 Td[(`configure')-525(configures)-525(MLD2P4)-525(1.0)-525(to)-525(adapt)-525(to)-525(many)-525(kinds)-525(of)-525(systems.)]TJ 0 -27.0984 Td[(Usage:)-525(./configure)-525([OPTION]...)-525([VAR=VALUE]...)]TJ 0 -27.0984 Td[(To)-525(assign)-525(environment)-525(variables)-525(\050e.g.,)-525(CC,)-525(CFLAGS...\051,)-525(specify)-525(them)-525(as)]TJ 0 -13.5492 Td[(VAR=VALUE.)-1050(See)-525(below)-525(for)-525(descriptions)-525(of)-525(some)-525(of)-525(the)-525(useful)-525(variables.)]TJ 0 -27.0984 Td[(Defaults)-525(for)-525(the)-525(options)-525(are)-525(specified)-525(in)-525(brackets.)]TJ 0 -27.0984 Td[(Configuration:)]TJ 11.4544 -13.5492 Td[(-h,)-525(--help)-7350(display)-525(this)-525(help)-525(and)-525(exit)]TJ 22.9089 -13.5492 Td[(--help=short)-4200(display)-525(options)-525(specific)-525(to)-525(this)-525(package)]TJ 0 -13.5492 Td[(--help=recursive)-2100(display)-525(the)-525(short)-525(help)-525(of)-525(all)-525(the)-525(included)-525(packages)]TJ -22.9089 -13.5492 Td[(-V,)-525(--version)-5775(display)-525(version)-525(information)-525(and)-525(exit)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -223 0 obj << +239 0 obj << /Type /Page -/Contents 224 0 R -/Resources 222 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 177 0 R -/Annots [ 221 0 R 218 0 R 219 0 R 220 0 R ] +/Contents 240 0 R +/Resources 238 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 195 0 R +/Annots [ 242 0 R 243 0 R 244 0 R 245 0 R ] >> endobj -221 0 obj << +242 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.3) >> >> endobj -218 0 obj << +243 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [166.104 631.156 173.551 640.179] +/Rect [166.1036 631.156 173.5506 640.1789] /Subtype /Link /A << /S /GoTo /D (cite.UMFPACK) >> >> endobj -219 0 obj << +244 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [150.46 568.397 157.907 577.42] +/Rect [150.4597 568.3973 157.9068 577.4201] /Subtype /Link /A << /S /GoTo /D (cite.SUPERLU) >> >> endobj -220 0 obj << +245 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [177.909 505.639 190.811 514.661] +/Rect [177.9092 505.6386 190.8109 514.6614] /Subtype /Link /A << /S /GoTo /D (cite.SUPERLUDIST) >> >> endobj -225 0 obj << -/D [223 0 R /XYZ 93.6 740.002 null] +241 0 obj << +/D [239 0 R /XYZ 93.6002 740.0018 null] >> endobj 30 0 obj << -/D [223 0 R /XYZ 93.6 715.095 null] +/D [239 0 R /XYZ 93.6002 715.0952 null] >> endobj 34 0 obj << -/D [223 0 R /XYZ 93.6 462.341 null] +/D [239 0 R /XYZ 93.6002 462.3409 null] >> endobj -222 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F43 158 0 R /F44 200 0 R /F18 173 0 R >> +238 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F45 147 0 R /F46 219 0 R /F20 181 0 R >> /ProcSet [ /PDF /Text ] >> endobj -231 0 obj << -/Length 3805 +251 0 obj << +/Length 4022 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(6)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(6)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F44 10.9091 Tf -191.811 -35.866 Td [(-q,)-525(--quiet,)-525(--silent)-1575(do)-525(not)-525(print)-525(`checking...')-525(messages)]TJ 22.909 -13.549 Td [(--cache-file=FILE)-1575(cache)-525(test)-525(results)-525(in)-525(FILE)-525([disabled])]TJ -22.909 -13.549 Td [(-C,)-525(--config-cache)-3150(alias)-525(for)-525(`--cache-file=config.cache')]TJ 0 -13.549 Td [(-n,)-525(--no-create)-4725(do)-525(not)-525(create)-525(output)-525(files)]TJ 22.909 -13.549 Td [(--srcdir=DIR)-4200(find)-525(the)-525(sources)-525(in)-525(DIR)-525([configure)-525(dir)-525(or)-525(`..'])]TJ -34.363 -27.099 Td [(Installation)-525(directories:)]TJ 11.454 -13.549 Td [(--prefix=PREFIX)-4725(install)-525(architecture-independent)-525(files)-525(in)-525(PREFIX)]TJ 0 -13.549 Td [([/usr/local])]TJ 0 -13.549 Td [(--exec-prefix=EPREFIX)-1575(install)-525(architecture-dependent)-525(files)-525(in)-525(EPREFIX)]TJ 0 -13.55 Td [([PREFIX])]TJ -11.454 -27.098 Td [(By)-525(default,)-525(`make)-525(install')-525(will)-525(install)-525(all)-525(the)-525(files)-525(in)]TJ 0 -13.549 Td [(`/usr/local/bin',)-525(`/usr/local/lib')-525(etc.)-1050(You)-525(can)-525(specify)]TJ 0 -13.549 Td [(an)-525(installation)-525(prefix)-525(other)-525(than)-525(`/usr/local')-525(using)-525(`--prefix',)]TJ 0 -13.55 Td [(for)-525(instance)-525(`--prefix=$HOME'.)]TJ 0 -27.098 Td [(For)-525(better)-525(control,)-525(use)-525(the)-525(options)-525(below.)]TJ 0 -27.098 Td [(Fine)-525(tuning)-525(of)-525(the)-525(installation)-525(directories:)]TJ 11.454 -13.55 Td [(--bindir=DIR)-5775(user)-525(executables)-525([EPREFIX/bin])]TJ 0 -13.549 Td [(--sbindir=DIR)-5250(system)-525(admin)-525(executables)-525([EPREFIX/sbin])]TJ 0 -13.549 Td [(--libexecdir=DIR)-3675(program)-525(executables)-525([EPREFIX/libexec])]TJ 0 -13.549 Td [(--sysconfdir=DIR)-3675(read-only)-525(single-machine)-525(data)-525([PREFIX/etc])]TJ 0 -13.549 Td [(--sharedstatedir=DIR)-1575(modifiable)-525(architecture-independent)-525(data)-525([PREFIX/com])]TJ 0 -13.549 Td [(--localstatedir=DIR)-2100(modifiable)-525(single-machine)-525(data)-525([PREFIX/var])]TJ 0 -13.55 Td [(--libdir=DIR)-5775(object)-525(code)-525(libraries)-525([EPREFIX/lib])]TJ 0 -13.549 Td [(--includedir=DIR)-3675(C)-525(header)-525(files)-525([PREFIX/include])]TJ 0 -13.549 Td [(--oldincludedir=DIR)-2100(C)-525(header)-525(files)-525(for)-525(non-gcc)-525([/usr/include])]TJ 0 -13.549 Td [(--datarootdir=DIR)-3150(read-only)-525(arch.-independent)-525(data)-525(root)-525([PREFIX/share])]TJ 0 -13.549 Td [(--datadir=DIR)-5250(read-only)-525(architecture-independent)-525(data)-525([DATAROOTDIR])]TJ 0 -13.55 Td [(--infodir=DIR)-5250(info)-525(documentation)-525([DATAROOTDIR/info])]TJ 0 -13.549 Td [(--localedir=DIR)-4200(locale-dependent)-525(data)-525([DATAROOTDIR/locale])]TJ 0 -13.549 Td [(--mandir=DIR)-5775(man)-525(documentation)-525([DATAROOTDIR/man])]TJ 0 -13.549 Td [(--docdir=DIR)-5775(documentation)-525(root)-525([DATAROOTDIR/doc/mld2p4])]TJ 0 -13.549 Td [(--htmldir=DIR)-5250(html)-525(documentation)-525([DOCDIR])]TJ 0 -13.55 Td [(--dvidir=DIR)-5775(dvi)-525(documentation)-525([DOCDIR])]TJ 0 -13.549 Td [(--pdfdir=DIR)-5775(pdf)-525(documentation)-525([DOCDIR])]TJ 0 -13.549 Td [(--psdir=DIR)-6300(ps)-525(documentation)-525([DOCDIR])]TJ -11.454 -27.098 Td [(Optional)-525(Packages:)]TJ 11.454 -13.55 Td [(--with-PACKAGE[=ARG])-2100(use)-525(PACKAGE)-525([ARG=yes])]TJ 0 -13.549 Td [(--without-PACKAGE)-3675(do)-525(not)-525(use)-525(PACKAGE)-525(\050same)-525(as)-525(--with-PACKAGE=no\051)]TJ 0 -13.549 Td [(--with-psblas)-5775(The)-525(source)-525(directory)-525(for)-525(PSBLAS,)-525(for)-525(example,)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F46 10.9091 Tf 97.8542 704.1363 Td[(-q,)-525(--quiet,)-525(--silent)-1575(do)-525(not)-525(print)-525(`checking...')-525(messages)]TJ 22.9088 -13.5492 Td[(--cache-file=FILE)-1575(cache)-525(test)-525(results)-525(in)-525(FILE)-525([disabled])]TJ -22.9088 -13.5492 Td[(-C,)-525(--config-cache)-3150(alias)-525(for)-525(`--cache-file=config.cache')]TJ 0 -13.5492 Td[(-n,)-525(--no-create)-4725(do)-525(not)-525(create)-525(output)-525(files)]TJ 22.9088 -13.5492 Td[(--srcdir=DIR)-4200(find)-525(the)-525(sources)-525(in)-525(DIR)-525([configure)-525(dir)-525(or)-525(`..'])]TJ -34.3632 -27.0984 Td[(Installation)-525(directories:)]TJ 11.4544 -13.5492 Td[(--prefix=PREFIX)-4725(install)-525(architecture-independent)-525(files)-525(in)-525(PREFIX)]TJ 0 -13.5492 Td[([/usr/local])]TJ 0 -13.5492 Td[(--exec-prefix=EPREFIX)-1575(install)-525(architecture-dependent)-525(files)-525(in)-525(EPREFIX)]TJ 0 -13.5492 Td[([PREFIX])]TJ -11.4544 -27.0984 Td[(By)-525(default,)-525(`make)-525(install')-525(will)-525(install)-525(all)-525(the)-525(files)-525(in)]TJ 0 -13.5492 Td[(`/usr/local/bin',)-525(`/usr/local/lib')-525(etc.)-1050(You)-525(can)-525(specify)]TJ 0 -13.5492 Td[(an)-525(installation)-525(prefix)-525(other)-525(than)-525(`/usr/local')-525(using)-525(`--prefix',)]TJ 0 -13.5492 Td[(for)-525(instance)-525(`--prefix=$HOME'.)]TJ 0 -27.0984 Td[(For)-525(better)-525(control,)-525(use)-525(the)-525(options)-525(below.)]TJ 0 -27.0984 Td[(Fine)-525(tuning)-525(of)-525(the)-525(installation)-525(directories:)]TJ 11.4544 -13.5492 Td[(--bindir=DIR)-5775(user)-525(executables)-525([EPREFIX/bin])]TJ 0 -13.5492 Td[(--sbindir=DIR)-5250(system)-525(admin)-525(executables)-525([EPREFIX/sbin])]TJ 0 -13.5492 Td[(--libexecdir=DIR)-3675(program)-525(executables)-525([EPREFIX/libexec])]TJ 0 -13.5492 Td[(--sysconfdir=DIR)-3675(read-only)-525(single-machine)-525(data)-525([PREFIX/etc])]TJ 0 -13.5492 Td[(--sharedstatedir=DIR)-1575(modifiable)-525(architecture-independent)-525(data)-525([PREFIX/com])]TJ 0 -13.5492 Td[(--localstatedir=DIR)-2100(modifiable)-525(single-machine)-525(data)-525([PREFIX/var])]TJ 0 -13.5492 Td[(--libdir=DIR)-5775(object)-525(code)-525(libraries)-525([EPREFIX/lib])]TJ 0 -13.5492 Td[(--includedir=DIR)-3675(C)-525(header)-525(files)-525([PREFIX/include])]TJ 0 -13.5492 Td[(--oldincludedir=DIR)-2100(C)-525(header)-525(files)-525(for)-525(non-gcc)-525([/usr/include])]TJ 0 -13.5492 Td[(--datarootdir=DIR)-3150(read-only)-525(arch.-independent)-525(data)-525(root)-525([PREFIX/share])]TJ 0 -13.5492 Td[(--datadir=DIR)-5250(read-only)-525(architecture-independent)-525(data)-525([DATAROOTDIR])]TJ 0 -13.5492 Td[(--infodir=DIR)-5250(info)-525(documentation)-525([DATAROOTDIR/info])]TJ 0 -13.5492 Td[(--localedir=DIR)-4200(locale-dependent)-525(data)-525([DATAROOTDIR/locale])]TJ 0 -13.5492 Td[(--mandir=DIR)-5775(man)-525(documentation)-525([DATAROOTDIR/man])]TJ 0 -13.5492 Td[(--docdir=DIR)-5775(documentation)-525(root)-525([DATAROOTDIR/doc/mld2p4])]TJ 0 -13.5492 Td[(--htmldir=DIR)-5250(html)-525(documentation)-525([DOCDIR])]TJ 0 -13.5492 Td[(--dvidir=DIR)-5775(dvi)-525(documentation)-525([DOCDIR])]TJ 0 -13.5492 Td[(--pdfdir=DIR)-5775(pdf)-525(documentation)-525([DOCDIR])]TJ 0 -13.5492 Td[(--psdir=DIR)-6300(ps)-525(documentation)-525([DOCDIR])]TJ -11.4544 -27.0984 Td[(Optional)-525(Packages:)]TJ 11.4544 -13.5492 Td[(--with-PACKAGE[=ARG])-2100(use)-525(PACKAGE)-525([ARG=yes])]TJ 0 -13.5492 Td[(--without-PACKAGE)-3675(do)-525(not)-525(use)-525(PACKAGE)-525(\050same)-525(as)-525(--with-PACKAGE=no\051)]TJ 0 -13.5492 Td[(--with-psblas)-5775(The)-525(source)-525(directory)-525(for)-525(PSBLAS,)-525(for)-525(example,)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -230 0 obj << +250 0 obj << /Type /Page -/Contents 231 0 R -/Resources 229 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 177 0 R +/Contents 251 0 R +/Resources 249 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 195 0 R >> endobj -232 0 obj << -/D [230 0 R /XYZ 86.4 740.002 null] +252 0 obj << +/D [250 0 R /XYZ 86.3998 740.0018 null] >> endobj -229 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F44 200 0 R >> +249 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -236 0 obj << -/Length 3870 +255 0 obj << +/Length 4193 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(3)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(3)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(Configuring)-378(and)-377(B)-1(uilding)-377(MLD2P4)]TJ/F15 10.9091 Tf 406.997 0 Td [(7)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Configuri)-1(ng)-378(an)-1(d)-378(Build)-1(ing)-378(ML)-1(D2)1(P4)]TJ/F15 10.9091 Tf 396.8452 0 Td[(7)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F44 10.9091 Tf -258.089 -35.866 Td [(--with-psblas=/opt/packages/psblas-2.3)]TJ -137.453 -13.549 Td [(--with-libs)-6825(List)-525(additional)-525(link)-525(flags)-525(here.)-525(For)-525(example,)]TJ 137.453 -13.549 Td [(--with-libs=-lspecial_system_lib)-525(or)]TJ 0 -13.549 Td [(--with-libs=-L/path/to/libs)]TJ -137.453 -13.549 Td [(--with-clibs)-6300(additional)-525(CLIBS)-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.453 -13.55 Td [(to)-525(CLIBS)]TJ -137.453 -13.549 Td [(--with-flibs)-6300(additional)-525(FLIBS)-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.453 -13.549 Td [(to)-525(FLIBS)]TJ -137.453 -13.549 Td [(--with-library-path)-2625(additional)-525(LIBRARYPATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.453 -13.549 Td [(prepend)-525(to)-525(LIBRARYPATH)]TJ -137.453 -13.55 Td [(--with-include-path)-2625(additional)-525(INCLUDEPATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.453 -13.549 Td [(prepend)-525(to)-525(INCLUDEPATH)]TJ -137.453 -13.549 Td [(--with-module-path)-3150(additional)-525(MODULE_PATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.453 -13.549 Td [(prepend)-525(to)-525(MODULE_PATH)]TJ -137.453 -13.549 Td [(--with-umfpack=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(UMFPACK)-525(library.)]TJ 137.453 -13.55 Td [(Default:)-525("-lumfpack)-525(-lamd")]TJ -137.453 -13.549 Td [(--with-umfpackdir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(UMFPACK)-525(library)-525(and)]TJ 137.453 -13.549 Td [(includes.)]TJ -137.453 -13.549 Td [(--with-superlu=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(SUPERLU)-525(library.)]TJ 137.453 -13.549 Td [(Default:)-525("-lslu")]TJ -137.453 -13.55 Td [(--with-superludir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(library)-525(and)]TJ 137.453 -13.549 Td [(includes.)]TJ -137.453 -13.549 Td [(--with-superludist=LIBNAME)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(libname)-525(for)-525(SUPERLUDIST)-525(library.)]TJ 0 -13.549 Td [(Requires)-525(you)-525(also)-525(specify)-525(SuperLU.)-525(Default:)-525("-lslud")]TJ -137.453 -13.549 Td [(--with-superludistdir=DIR)]TJ 137.453 -13.55 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(library)-525(and)]TJ 0 -13.549 Td [(includes.)]TJ -148.908 -27.098 Td [(Some)-525(influential)-525(environment)-525(variables:)]TJ 11.455 -13.549 Td [(FC)-5250(Fortran)-525(compiler)-525(command)]TJ 0 -13.55 Td [(FCFLAGS)-2625(Fortran)-525(compiler)-525(flags)]TJ 0 -13.549 Td [(LDFLAGS)-2625(linker)-525(flags,)-525(e.g.)-525(-L)-525(if)-525(you)-525(have)-525(libraries)-525(in)-525(a)]TJ 68.726 -13.549 Td [(nonstandard)-525(directory)-525()]TJ -68.726 -13.549 Td [(LIBS)-4200(libraries)-525(to)-525(pass)-525(to)-525(the)-525(linker,)-525(e.g.)-525(-l)]TJ 0 -13.549 Td [(CC)-5250(C)-525(compiler)-525(command)]TJ 0 -13.55 Td [(CFLAGS)-3150(C)-525(compiler)-525(flags)]TJ 0 -13.549 Td [(CPPFLAGS)-2100(C/C++/Objective)-525(C)-525(preprocessor)-525(flags,)-525(e.g.)-525(-I)-525(if)]TJ 68.726 -13.549 Td [(you)-525(have)-525(headers)-525(in)-525(a)-525(nonstandard)-525(directory)-525()]TJ -68.726 -13.549 Td [(CPP)-4725(C)-525(preprocessor)]TJ 0 -13.549 Td [(MPICC)-3675(MPI)-525(C)-525(compiler)-525(command)]TJ -11.455 -27.099 Td [(Use)-525(these)-525(variables)-525(to)-525(override)-525(the)-525(choices)-525(made)-525(by)-525(`configure')-525(or)-525(to)-525(help)]TJ 0 -13.549 Td [(it)-525(to)-525(find)-525(libraries)-525(and)-525(programs)-525(with)-525(nonstandard)-525(names/locations.)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F46 10.9091 Tf 242.5077 704.1363 Td[(--with-psblas=/opt/packages/psblas-2.3)]TJ -137.4531 -13.5492 Td[(--with-libs)-6825(List)-525(additional)-525(link)-525(flags)-525(here.)-525(For)-525(example,)]TJ 137.4531 -13.5492 Td[(--with-libs=-lspecial_system_lib)-525(or)]TJ 0 -13.5492 Td[(--with-libs=-L/path/to/libs)]TJ -137.4531 -13.5492 Td[(--with-clibs)-6300(additional)-525(CLIBS)-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.4531 -13.5492 Td[(to)-525(CLIBS)]TJ -137.4531 -13.5492 Td[(--with-flibs)-6300(additional)-525(FLIBS)-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.4531 -13.5492 Td[(to)-525(FLIBS)]TJ -137.4531 -13.5492 Td[(--with-library-path)-2625(additional)-525(LIBRARYPATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.4531 -13.5492 Td[(prepend)-525(to)-525(LIBRARYPATH)]TJ -137.4531 -13.5492 Td[(--with-include-path)-2625(additional)-525(INCLUDEPATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.4531 -13.5492 Td[(prepend)-525(to)-525(INCLUDEPATH)]TJ -137.4531 -13.5492 Td[(--with-module-path)-3150(additional)-525(MODULE_PATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.4531 -13.5492 Td[(prepend)-525(to)-525(MODULE_PATH)]TJ -137.4531 -13.5492 Td[(--with-umfpack=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(UMFPACK)-525(library.)]TJ 137.4531 -13.5492 Td[(Default:)-525("-lumfpack)-525(-lamd")]TJ -137.4531 -13.5492 Td[(--with-umfpackdir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(UMFPACK)-525(library)-525(and)]TJ 137.4531 -13.5492 Td[(includes.)]TJ -137.4531 -13.5492 Td[(--with-superlu=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(SUPERLU)-525(library.)]TJ 137.4531 -13.5492 Td[(Default:)-525("-lslu")]TJ -137.4531 -13.5492 Td[(--with-superludir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(library)-525(and)]TJ 137.4531 -13.5492 Td[(includes.)]TJ -137.4531 -13.5492 Td[(--with-superludist=LIBNAME)]TJ 137.4531 -13.5492 Td[(Specify)-525(the)-525(libname)-525(for)-525(SUPERLUDIST)-525(library.)]TJ 0 -13.5492 Td[(Requires)-525(you)-525(also)-525(specify)-525(SuperLU.)-525(Default:)-525("-lslud")]TJ -137.4531 -13.5492 Td[(--with-superludistdir=DIR)]TJ 137.4531 -13.5492 Td[(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(library)-525(and)]TJ 0 -13.5492 Td[(includes.)]TJ -148.9075 -27.0984 Td[(Some)-525(influential)-525(environment)-525(variables:)]TJ 11.4544 -13.5492 Td[(FC)-5250(Fortran)-525(compiler)-525(command)]TJ 0 -13.5492 Td[(FCFLAGS)-2625(Fortran)-525(compiler)-525(flags)]TJ 0 -13.5492 Td[(LDFLAGS)-2625(linker)-525(flags,)-525(e.g.)-525(-L)-525(if)-525(you)-525(have)-525(libraries)-525(in)-525(a)]TJ 68.7266 -13.5492 Td[(nonstandard)-525(directory)-525()]TJ -68.7266 -13.5492 Td[(LIBS)-4200(libraries)-525(to)-525(pass)-525(to)-525(the)-525(linker,)-525(e.g.)-525(-l)]TJ 0 -13.5492 Td[(CC)-5250(C)-525(compiler)-525(command)]TJ 0 -13.5492 Td[(CFLAGS)-3150(C)-525(compiler)-525(flags)]TJ 0 -13.5492 Td[(CPPFLAGS)-2100(C/C++/Objective)-525(C)-525(preprocessor)-525(flags,)-525(e.g.)-525(-I)-525(if)]TJ 68.7266 -13.5492 Td[(you)-525(have)-525(headers)-525(in)-525(a)-525(nonstandard)-525(directory)-525()]TJ -68.7266 -13.5492 Td[(CPP)-4725(C)-525(preprocessor)]TJ 0 -13.5492 Td[(MPICC)-3675(MPI)-525(C)-525(compiler)-525(command)]TJ -11.4544 -27.0984 Td[(Use)-525(these)-525(variables)-525(to)-525(override)-525(the)-525(choices)-525(made)-525(by)-525(`configure')-525(or)-525(to)-525(help)]TJ 0 -13.5492 Td[(it)-525(to)-525(find)-525(libraries)-525(and)-525(programs)-525(with)-525(nonstandard)-525(names/locations.)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -235 0 obj << +254 0 obj << /Type /Page -/Contents 236 0 R -/Resources 234 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 238 0 R -/Annots [ 233 0 R ] +/Contents 255 0 R +/Resources 253 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 258 0 R +/Annots [ 257 0 R ] >> endobj -233 0 obj << +257 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.3) >> >> endobj -237 0 obj << -/D [235 0 R /XYZ 93.6 740.002 null] +256 0 obj << +/D [254 0 R /XYZ 93.6002 740.0018 null] >> endobj -234 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F44 200 0 R >> +253 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -241 0 obj << -/Length 4777 +261 0 obj << +/Length 6158 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(8)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(8)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F44 10.9091 Tf -203.265 -49.415 Td [(Report)-525(bugs)-525(to)-525(.)]TJ/F15 10.9091 Tf 0 -22.515 Td [(Th)28(us,)-352(a)-348(sample)-348(build)-348(with)-348(libraries)-348(in)-348(installation)-348(directories)-348(sp)-28(eci\014cs)-348(to)-348(the)-348(GNU)-348(4.3)]TJ 0 -13.55 Td [(compiler)-333(suite)-334(migh)28(t)-333(b)-28(e)-333(as)-334(follo)28(ws,)-333(sp)-28(ecifying)-333(only)-333(the)-334(UMFP)84(A)27(CK)-333(external)-333(pac)28(k)55(age:)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F46 10.9091 Tf 86.3998 690.5871 Td[(Report)-525(bugs)-525(to)-525(.)]TJ/F15 10.9091 Tf 0 -22.5155 Td[(Th)28(us,)-352(a)-348(sample)-348(bu)1(ild)-348(wit)1(h)-348(lib)1(rari)1(e)-1(s)-348(in)-348(in)1(s)-1(t)1(allation)-347(dir)1(e)-1(ctories)-349(sp)-27(e)-1(ci\014cs)-348(to)-348(the)-348(GNU)-348(4.3)]TJ 0 -13.5492 Td[(com)-1(p)1(iler)-333(s)-1(u)1(ite)-334(migh)28(t)-333(b)-27(e)-334(as)-334(f)1(ollo)28(ws)-1(,)-333(sp)-28(ec)-1(i)1(fyi)1(ng)-333(only)-333(th)1(e)-334(UMF)1(P)83(A)28(CK)-333(e)-1(x)1(te)-1(r)1(nal)-333(pac)28(k)55(age:)]TJ +ET +1 0 0 1 80.9452 632.0068 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf 5.727 -22.515 Td [(./configure)-525(--with-psblas=/home/user/psblas-2.3/)-525(\134)]TJ 0 -13.549 Td [(--with-libs="-L/usr/local/BLAS/gnu43)-525(-L/usr/local/BLACS/gnu43")-525(\134)]TJ 0 -13.55 Td [(--with-blacs=-lmpiblacs)-1050(--with-umfpackdir=/usr/local/UMFPACK/gnu43)]TJ/F15 10.9091 Tf -5.727 -22.515 Td [(Once)-529(the)-529(con\014gure)-530(script)-529(has)-529(completed)-529(execution,)-578(it)-530(will)-529(ha)28(v)28(e)-529(ge)-1(n)1(e)-1(r)1(ate)-1(d)-529(the)-529(\014le)]TJ/F44 10.9091 Tf 0 -13.549 Td [(Make.inc)]TJ/F15 10.9091 Tf 49.454 0 Td [(whic)28(h)-333(w)-1(i)1(ll)-334(then)-333(b)-28(e)-333(used)-334(b)28(y)-333(all)-333(Mak)28(e)-1(\014)1(les)-334(in)-333(the)-333(directory)-334(tree.)]TJ -32.518 -13.55 Td [(T)83(o)-333(build)-333(the)-334(li)1(brary)-334(the)-333(user)-333(will)-334(no)28(w)-333(en)28(ter)]TJ +1 0 0 1 -80.9452 -632.0068 cm +BT +/F46 10.9091 Tf 92.127 632.0068 Td[(./configure)-525(--with-psblas=/home/user/psblas-2.3/)-525(\134)]TJ 0 -13.5492 Td[(--with-libs="-L/usr/local/BLAS/gnu43)-525(-L/usr/local/BLACS/gnu43")-525(\134)]TJ 0 -13.5492 Td[(--with-blacs=-lmpiblacs)-1050(--with-umfpackdir=/usr/local/UMFPACK/gnu43)]TJ/F15 10.9091 Tf -5.7272 -22.5156 Td[(On)1(c)-1(e)-529(the)-530(con\014)1(gur)1(e)-530(sc)-1(ri)1(pt)-529(has)-529(c)-1(ompl)1(e)-1(ted)-529(exe)-1(cut)1(ion,)-578(it)-529(wil)1(l)-529(ha)28(v)28(e)-530(generated)-529(the)-529(\014le)]TJ/F46 10.9091 Tf 0 -13.5492 Td[(Make.inc)]TJ/F15 10.9091 Tf 49.454 0 Td[(whic)28(h)-333(will)-333(th)1(e)-1(n)-333(b)-27(e)-334(u)1(s)-1(ed)-333(b)28(y)-333(all)-333(Mak)28(e\014l)1(e)-1(s)-334(i)1(n)-333(the)-334(d)1(irectory)-333(tree)-1(.)]TJ -32.5175 -13.5492 Td[(T)83(o)-333(bu)1(ild)-333(th)1(e)-334(lib)1(rar)1(y)-334(t)1(he)-334(u)1(s)-1(er)-333(will)-333(no)28(w)-333(e)-1(n)28(ter)]TJ +ET +1 0 0 1 80.9452 532.7789 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf -16.936 -22.515 Td [(make)]TJ/F15 10.9091 Tf 0 -22.516 Td [(follo)28(w)28(ed)-334(\050optionally\051)-333(b)28(y)]TJ +1 0 0 1 -80.9452 -532.7789 cm +BT +/F46 10.9091 Tf 86.3998 532.7789 Td[(make)]TJ/F15 10.9091 Tf 0 -22.5156 Td[(fol)1(lo)28(w)27(ed)-333(\050opt)1(ionall)1(y\051)-333(b)28(y)]TJ +ET +1 0 0 1 80.9452 487.7477 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf 0 -22.515 Td [(make)-525(install)]TJ/F17 11.9552 Tf 0 -29.213 Td [(3.4)-1125(Bug)-375(rep)-31(orting)]TJ/F15 10.9091 Tf 0 -20.595 Td [(If)-457(y)28(ou)-456(\014nd)-457(an)28(y)-456(bugs)-457(in)-456(our)-457(co)-28(des,)-487(please)-457(let)-456(us)-457(kno)28(w)-457(at)]TJ/F44 10.9091 Tf 290.642 0 Td [(bugreport@mld2p4.it)]TJ/F15 10.9091 Tf 118.779 0 Td [(;)]TJ -409.421 -13.549 Td [(b)-28(e)-360(a)28(w)28(are)-360(that)-360(the)-361(amoun)28(t)-360(of)-360(information)-360(needed)-360(to)-360(repro)-28(duce)-360(a)-360(problem)-360(in)-360(a)-360(parallel)]TJ 0 -13.549 Td [(program)-333(ma)28(y)-334(v)56(ary)-334(q)1(uite)-334(a)-333(lot.)]TJ/F17 11.9552 Tf 0 -29.213 Td [(3.5)-1125(Example)-375(and)-375(test)-375(programs)]TJ/F15 10.9091 Tf 0 -20.594 Td [(The)-419(pac)28(k)55(age)-418(con)27(tains)-418(the)]TJ/F44 10.9091 Tf 128.338 0 Td [(examples)]TJ/F15 10.9091 Tf 50.387 0 Td [(and)]TJ/F44 10.9091 Tf 22.146 0 Td [(tests)]TJ/F15 10.9091 Tf 33.205 0 Td [(directories;)-462(b)-27(oth)-419(of)-419(them)-419(are)-419(further)]TJ -234.076 -13.55 Td [(divided)-333(in)28(to)]TJ/F44 10.9091 Tf 60.606 0 Td [(fileread)]TJ/F15 10.9091 Tf 49.454 0 Td [(and)]TJ/F44 10.9091 Tf 21.212 0 Td [(pdegen)]TJ/F15 10.9091 Tf 38 0 Td [(sub)-28(directories.)-444(Their)-333(purp)-28(ose)-333(is)-334(as)-333(follo)28(ws:)]TJ +1 0 0 1 -80.9452 -487.7477 cm +BT +/F46 10.9091 Tf 86.3998 487.7477 Td[(make)-525(install)]TJ/F19 11.9552 Tf 0 -29.2128 Td[(3.)-1(4)-1125(Bug)-376(re)-1(p)-31(or)-1(ti)-1(ng)]TJ/F15 10.9091 Tf 0 -20.5946 Td[(If)-456(y)28(ou)-456(\014n)1(d)-457(an)29(y)-457(b)1(ugs)-457(in)-456(ou)1(r)-457(co)-28(d)1(e)-1(s,)-487(pleas)-1(e)-457(l)1(e)-1(t)-456(us)-457(kn)1(o)28(w)-457(at)]TJ/F46 10.9091 Tf 290.6423 0 Td[(bugreport@mld2p4.it)]TJ/F15 10.9091 Tf 118.7785 0 Td[(;)]TJ -409.4208 -13.5492 Td[(b)-27(e)-361(a)28(w)27(ar)1(e)-361(th)1(at)-360(the)-360(amoun)28(t)-360(of)-359(inf)1(ormation)-360(n)1(e)-1(eded)-360(to)-360(r)1(e)-1(p)1(ro)-28(d)1(uce)-361(a)-360(pr)1(oblem)-361(i)1(n)-360(a)-360(par)1(allel)]TJ 0 -13.5492 Td[(pr)1(ogram)-334(ma)28(y)-333(v)56(ary)-333(qui)1(te)-334(a)-333(lot.)]TJ/F19 11.9552 Tf 0 -29.2128 Td[(3.)-1(5)-1125(E)-1(xampl)-1(e)-375(and)-375(te)-1(s)1(t)-376(pro)-1(gr)-1(ams)]TJ/F15 10.9091 Tf 0 -20.5946 Td[(The)-419(pac)28(k)55(age)-419(con)28(tain)1(s)-420(th)1(e)]TJ/F46 10.9091 Tf 128.3385 0 Td[(examples)]TJ/F15 10.9091 Tf 50.3872 0 Td[(and)]TJ/F46 10.9091 Tf 22.1452 0 Td[(tests)]TJ/F15 10.9091 Tf 33.2055 0 Td[(di)1(rec)-1(tor)1(ie)-1(s;)-462(b)-27(oth)-418(of)-419(t)1(he)-1(m)-419(ar)1(e)-420(f)1(ur)1(ther)]TJ -234.0764 -13.5492 Td[(di)1(vid)1(e)-1(d)-333(in)29(to)]TJ/F46 10.9091 Tf 60.6061 0 Td[(fileread)]TJ/F15 10.9091 Tf 49.454 0 Td[(and)]TJ/F46 10.9091 Tf 21.2122 0 Td[(pdegen)]TJ/F15 10.9091 Tf 37.9996 0 Td[(sub)-27(dir)1(e)-1(ctories.)-445(Th)1(e)-1(ir)-333(p)1(ur)1(p)-28(ose)-334(is)-334(as)-333(foll)1(o)27(ws:)]TJ +ET +1 0 0 1 80.9452 324.9697 cm 0 g 0 G -/F44 10.9091 Tf -169.272 -22.515 Td [(examples)]TJ +1 0 0 1 -80.9452 -324.9697 cm +BT +/F46 10.9091 Tf 86.3998 324.9697 Td[(examples)]TJ +ET +1 0 0 1 132.2175 324.9697 cm 0 g 0 G -/F15 10.9091 Tf 51.272 0 Td [(con)28(tains)-245(a)-244(s)-1(et)-244(of)-245(simple)-245(example)-244(programs)-245(with)-244(a)-245(prede\014ned)-245(c)28(hoice)-245(of)-244(precon-)]TJ -23.999 -13.549 Td [(ditioners,)-294(selectable)-284(via)-284(in)28(teger)-284(v)56(alues.)-428(These)-284(are)-284(in)28(tended)-284(to)-284(get)-284(an)-284(acquain)28(tance)]TJ 0 -13.55 Td [(with)-333(the)-334(m)28(ultilev)28(el)-333(preconditioners.)]TJ +1 0 0 1 -132.2175 -324.9697 cm +BT +/F15 10.9091 Tf 137.672 324.9697 Td[(con)28(tain)1(s)-246(a)-244(s)-1(et)-245(of)-244(simple)-245(example)-245(p)1(rograms)-245(with)-244(a)-245(p)1(re)-1(d)1(e)-1(\014)1(ned)-244(c)27(hoi)1(c)-1(e)-245(of)-244(pr)1(e)-1(con-)]TJ -23.9994 -13.5492 Td[(di)1(tioners,)-294(se)-1(l)1(e)-1(ctable)-284(vi)1(a)-284(in)28(tege)-1(r)-283(v)55(al)1(ues)-1(.)-428(Th)1(e)-1(se)-285(ar)1(e)-285(in)29(te)-1(n)1(ded)-284(to)-284(get)-284(an)-283(ac)-1(qu)1(ain)28(tan)1(c)-1(e)]TJ 0 -13.5492 Td[(with)-333(th)1(e)-334(m)27(u)1(ltil)1(e)-1(v)28(el)-333(precondi)1(tioners.)]TJ +ET +1 0 0 1 80.9452 275.3557 cm 0 g 0 G -/F44 10.9091 Tf -27.273 -22.515 Td [(tests)]TJ +1 0 0 1 -80.9452 -275.3557 cm +BT +/F46 10.9091 Tf 86.3998 275.3557 Td[(tests)]TJ +ET +1 0 0 1 115.0358 275.3557 cm 0 g 0 G -/F15 10.9091 Tf 34.09 0 Td [(con)28(tains)-380(a)-380(set)-380(of)-380(more)-380(sophi)1(s)-1(ticated)-379(examples)-380(that)-380(will)-380(allo)28(w)-380(the)-380(user,)-391(via)-380(the)]TJ -6.817 -13.549 Td [(input)-286(\014les)-287(in)-286(the)]TJ/F44 10.9091 Tf 80.438 0 Td [(runs)]TJ/F15 10.9091 Tf 26.034 0 Td [(sub)-28(directories,)-296(t)1(o)-287(exp)-28(erimen)28(t)-286(with)-287(the)-286(full)-286(range)-287(of)-286(precon-)]TJ -106.472 -13.55 Td [(ditioners)-333(implemen)28(te)-1(d)-333(in)-333(the)-333(library)83(.)]TJ -27.273 -22.515 Td [(The)]TJ/F44 10.9091 Tf 24.239 0 Td [(fileread)]TJ/F15 10.9091 Tf 51.269 0 Td [(directories)-500(con)28(tain)-500(sample)-499(programs)-500(that)-500(read)-499(sparse)-500(matrices)-500(from)]TJ -75.508 -13.549 Td [(\014les,)-295(according)-285(to)-285(the)-285(Matrix)-285(Mark)28(et)-285(or)-285(the)-285(Harw)27(ell-Bo)-27(eing)-286(storage)-285(format;)-301(the)]TJ/F44 10.9091 Tf 378.088 0 Td [(pdegen)]TJ/F15 10.9091 Tf -378.088 -13.55 Td [(instead)-272(generate)-272(matrices)-272(in)-272(full)-272(parallel)-272(mo)-28(d)1(e)-273(f)1(rom)-272(the)-272(discretization)-272(of)-272(a)-272(sample)-272(PDE.)]TJ +1 0 0 1 -115.0358 -275.3557 cm +BT +/F15 10.9091 Tf 120.4904 275.3557 Td[(con)28(tain)1(s)-381(a)-380(set)-380(of)-380(more)-380(soph)1(is)-1(ti)1(c)-1(ated)-380(exampl)1(e)-1(s)-380(that)-379(w)-1(i)1(ll)-380(all)1(o)27(w)-380(th)1(e)-380(use)-1(r)1(,)-392(vi)1(a)-380(the)]TJ -6.8178 -13.5492 Td[(in)1(pu)1(t)-287(\014)1(le)-1(s)-286(in)-286(the)]TJ/F46 10.9091 Tf 80.4383 0 Td[(runs)]TJ/F15 10.9091 Tf 26.0336 0 Td[(sub)-27(dir)1(e)-1(ctories,)-296(to)-286(e)-1(xp)-27(erime)-1(n)29(t)-287(with)-286(t)1(he)-287(f)1(ull)-286(ran)1(ge)-287(of)-286(pr)1(e)-1(con-)]TJ -106.4719 -13.5492 Td[(di)1(tioners)-333(im)-1(p)1(lem)-1(en)28(ted)-333(in)-333(th)1(e)-334(lib)1(rar)1(y)83(.)]TJ -27.2728 -22.5155 Td[(The)]TJ/F46 10.9091 Tf 24.2391 0 Td[(fileread)]TJ/F15 10.9091 Tf 51.2688 0 Td[(di)1(rec)-1(tor)1(ie)-1(s)-500(con)28(tain)-499(sam)-1(p)1(le)-500(pr)1(ograms)-501(t)1(hat)-500(r)1(e)-1(ad)-499(sparse)-500(m)-1(at)1(rice)-1(s)-500(f)1(rom)]TJ -75.5079 -13.5492 Td[(\014l)1(e)-1(s,)-295(acc)-1(or)1(din)1(g)-285(to)-285(the)-285(Matri)1(x)-285(Mar)1(k)28(e)-1(t)-285(or)-285(th)1(e)-286(Har)1(w)27(ell-Bo)-28(e)-1(i)1(ng)-285(s)-1(t)1(orage)-286(f)1(ormat;)-301(the)]TJ/F46 10.9091 Tf 378.0878 0 Td[(pdegen)]TJ/F15 10.9091 Tf -378.0878 -13.5492 Td[(in)1(s)-1(tead)-272(generate)-272(matrice)-1(s)-272(in)-271(fu)1(ll)-272(par)1(allel)-272(mo)-28(de)-272(fr)1(om)-273(th)1(e)-273(d)1(isc)-1(r)1(e)-1(tization)-271(of)-272(a)-272(sample)-272(PDE)1(.)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -240 0 obj << +260 0 obj << /Type /Page -/Contents 241 0 R -/Resources 239 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 238 0 R +/Contents 261 0 R +/Resources 259 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 258 0 R >> endobj -242 0 obj << -/D [240 0 R /XYZ 86.4 740.002 null] +262 0 obj << +/D [260 0 R /XYZ 86.3998 740.0018 null] >> endobj 38 0 obj << -/D [240 0 R /XYZ 86.4 472.483 null] +/D [260 0 R /XYZ 86.3998 472.4826 null] >> endobj 42 0 obj << -/D [240 0 R /XYZ 86.4 393.456 null] +/D [260 0 R /XYZ 86.3998 393.4556 null] >> endobj -239 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F44 200 0 R /F17 111 0 R >> +259 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F46 219 0 R /F19 113 0 R >> /ProcSet [ /PDF /Text ] >> endobj -252 0 obj << -/Length 8191 +265 0 obj << +/Length 11558 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(4)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(4)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(Mul)67(ti-level)-378(Domain)-378(Decompo)1(siti)-1(o)1(n)-378(Ba)22(ck)22(gr)22(ound)]TJ/F15 10.9091 Tf 406.997 0 Td [(9)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Mul)66(ti-level)-378(Domain)-378(Decomp)1(osition)-378(Ba)22(ck)23(gr)22(oun)-1(d)]TJ/F15 10.9091 Tf 396.8452 0 Td[(9)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -406.997 -35.866 Td [(4)-1125(Multi-lev)31(el)-375(Domain)-375(Decomp)-31(osition)-375(Bac)31(kground)]TJ/F18 10.9091 Tf 0 -25.25 Td [(Domain)-282(De)51(c)51(omp)51(osition)]TJ/F15 10.9091 Tf 113.171 0 Td [(\050DD\051)-251(preconditioners,)-267(coupled)-251(with)-251(Krylo)28(v)-251(iterativ)28(e)-251(solv)28(ers,)-268(are)]TJ -113.171 -13.549 Td [(widely)-315(used)-316(in)-315(the)-315(parallel)-315(solution)-315(of)-316(large)-315(and)-315(sparse)-316(l)1(inear)-316(systems.)-438(These)-316(precondi-)]TJ 0 -13.549 Td [(tioners)-285(are)-285(based)-285(on)-284(the)-285(divide)-285(and)-285(conquer)-285(tec)28(hnique:)-420(the)-285(matrix)-285(to)-284(b)-28(e)-285(preconditioned)]TJ 0 -13.549 Td [(is)-423(divided)-422(in)28(to)-423(submatrices,)-445(a)-423(\134lo)-27(cal")-423(linear)-423(system)-422(in)27(v)28(olving)-422(eac)27(h)-422(submatrix)-423(is)-422(\050ap-)]TJ 0 -13.549 Td [(pro)28(ximately\051)-356(solv)28(ed,)-362(and)-356(the)-356(lo)-27(cal)-356(solutions)-356(are)-356(used)-356(to)-356(build)-356(a)-356(preconditioner)-356(for)-356(the)]TJ 0 -13.55 Td [(whole)-407(original)-407(matr)1(ix.)-665(This)-407(pro)-28(cess)-407(often)-407(corresp)-27(onds)-407(to)-407(dividing)-407(a)-406(ph)28(ys)-1(i)1(c)-1(al)-406(domain)]TJ 0 -13.549 Td [(asso)-28(ciated)-299(to)-299(the)-299(original)-299(matrix)-299(in)28(to)-299(sub)-28(domains,)-306(e.g.)-433(in)-299(a)-299(PDE)-299(discretization,)-306(to)-299(\050ap-)]TJ 0 -13.549 Td [(pro)28(ximately\051)-276(s)-1(olv)1(ing)-277(the)-276(subproblems)-276(corresp)-28(onding)-276(to)-277(the)-276(sub)-28(domains)-276(and)-276(to)-277(building)]TJ 0 -13.549 Td [(an)-333(appro)28(ximate)-334(solution)-333(of)-333(the)-334(original)-333(problem)-333(from)-333(the)-334(lo)-27(c)-1(al)-333(solutions)-333([)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 14.3462 Tf 93.6002 704.1363 Td[(4)-1125(M)-1(ult)-1(i-l)-1(ev)32(e)-1(l)-375(D)-1(om)-1(a)1(i)-1(n)-375(Deco)-1(mp)-32(osit)-1(io)-1(n)-375(Bac)32(kg)-1(ro)-1(und)]TJ/F20 10.9091 Tf 0 -25.25 Td[(Domain)-282(De)51(c)51(omp)52(o)-1(s)1(ition)]TJ/F15 10.9091 Tf 113.1712 0 Td[(\050DD\051)-250(prec)-1(on)1(di)1(tioners,)-267(c)-1(ou)1(pled)-251(with)-250(Kry)1(lo)28(v)-251(iterativ)28(e)-251(solv)28(e)-1(r)1(s)-1(,)-267(are)]TJ -113.1712 -13.5492 Td[(widely)-315(u)1(s)-1(ed)-315(in)-315(th)1(e)-316(p)1(arallel)-315(s)-1(ol)1(ution)-315(of)-314(large)-316(an)1(d)-315(sparse)-316(li)1(near)-315(s)-1(ystem)-1(s.)-438(T)-1(h)1(e)-1(se)-316(p)1(rec)-1(on)1(di-)]TJ 0 -13.5492 Td[(tion)1(e)-1(r)1(s)-286(ar)1(e)-286(b)1(as)-1(ed)-284(on)-285(th)1(e)-286(d)1(ivid)1(e)-285(and)-284(c)-1(on)1(quer)-285(tec)27(h)1(niq)1(ue:)-420(the)-285(matrix)-284(to)-285(b)-27(e)-286(p)1(rec)-1(on)1(diti)1(oned)]TJ 0 -13.5492 Td[(is)-423(d)1(ivid)1(e)-1(d)-422(in)28(t)1(o)-423(s)-1(u)1(bmatri)1(c)-1(es)-1(,)-444(a)-423(\134lo)-28(cal")-422(linear)-422(s)-1(ystem)-423(in)28(v)28(olv)1(ing)-422(e)-1(ac)27(h)-422(sub)1(m)-1(atr)1(ix)-422(is)-423(\050ap-)]TJ 0 -13.5492 Td[(pr)1(o)28(ximate)-1(l)1(y\051)-356(s)-1(ol)1(v)28(e)-1(d)1(,)-362(an)1(d)-356(th)1(e)-357(l)1(o)-28(c)-1(al)-355(s)-1(olu)1(tion)1(s)-357(ar)1(e)-357(u)1(s)-1(ed)-356(to)-356(b)1(ui)1(ld)-356(a)-356(p)1(rec)-1(on)1(diti)1(oner)-356(for)-355(the)]TJ 0 -13.5492 Td[(whole)-407(or)1(iginal)-406(m)-1(at)1(rix.)-664(T)-1(h)1(is)-407(pr)1(o)-28(c)-1(ess)-408(of)1(te)-1(n)-406(corres)-1(p)-27(ond)1(s)-407(to)-407(di)1(vid)1(ing)-407(a)-406(ph)28(ysical)-407(d)1(om)-1(ai)1(n)]TJ 0 -13.5492 Td[(ass)-1(o)-28(ciated)-299(to)-299(th)1(e)-300(ori)1(ginal)-298(m)-1(atr)1(ix)-299(in)28(t)1(o)-300(sub)-27(d)1(om)-1(ain)1(s)-1(,)-305(e)-1(.g.)-432(in)-299(a)-299(P)1(DE)-299(d)1(is)-1(cretization,)-305(to)-299(\050ap-)]TJ 0 -13.5492 Td[(pr)1(o)28(ximate)-1(l)1(y\051)-276(s)-1(olv)1(ing)-276(the)-276(s)-1(u)1(bpr)1(oblems)-277(c)-1(or)1(res)-1(p)-27(ond)1(ing)-276(to)-276(the)-276(s)-1(u)1(b)-28(d)1(om)-1(ai)1(ns)-277(an)1(d)-276(to)-276(bui)1(ldi)1(ng)]TJ 0 -13.5492 Td[(an)-333(ap)1(pro)28(xi)1(m)-1(ate)-333(s)-1(olu)1(tion)-333(of)-333(th)1(e)-334(ori)1(ginal)-333(p)1(robl)1(e)-1(m)-333(from)-333(the)-334(l)1(o)-28(c)-1(al)-333(solu)1(tions)-333([)]TJ +ET +1 0 0 1 445.1158 570.4927 cm 1 0 0 rg 1 0 0 RG - [(6)]TJ +1 0 0 1 -445.1158 -570.4927 cm +BT +/F15 10.9091 Tf 445.1158 570.4927 Td[(6)]TJ +ET +1 0 0 1 450.5703 570.4927 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -450.5703 -570.4927 cm +BT +/F15 10.9091 Tf 450.5703 570.4927 Td[(,)]TJ +ET +1 0 0 1 457.237 570.4927 cm 1 0 0 rg 1 0 0 RG - [-333(7)]TJ +1 0 0 1 -457.237 -570.4927 cm +BT +/F15 10.9091 Tf 457.237 570.4927 Td[(7)]TJ +ET +1 0 0 1 462.6915 570.4927 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -462.6915 -570.4927 cm +BT +/F15 10.9091 Tf 462.6915 570.4927 Td[(,)]TJ +ET +1 0 0 1 469.3582 570.4927 cm 1 0 0 rg 1 0 0 RG - [-334(20)]TJ +1 0 0 1 -469.3582 -570.4927 cm +BT +/F15 10.9091 Tf 469.3582 570.4927 Td[(20)]TJ +ET +1 0 0 1 480.2673 570.4927 cm 0 g 0 G - [(].)]TJ/F18 10.9091 Tf 16.937 -14.011 Td [(A)51(dditive)-468(Schwarz)]TJ/F15 10.9091 Tf 89.058 0 Td [(preconditioners)-453(are)-453(DD)-454(precondition)1(e)-1(r)1(s)-454(using)-453(o)28(v)28(erlapping)-454(sub-)]TJ -105.995 -13.55 Td [(matrices,)-403(i.e.)-389(with)-389(some)-389(common)-389(ro)27(ws,)-403(to)-389(couple)-389(the)-389(lo)-28(cal)-389(information)-389(related)-389(to)-389(the)]TJ 0 -13.549 Td [(submatrices)-362(\050see,)-369(e.g.,)-369([)]TJ +1 0 0 1 -480.2673 -570.4927 cm +BT +/F15 10.9091 Tf 480.2673 570.4927 Td[(].)]TJ/F20 10.9091 Tf -369.7306 -14.0112 Td[(A)51(dditive)-468(Schw)-1(arz)]TJ/F15 10.9091 Tf 89.0587 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-454(are)-453(DD)-453(prec)-1(on)1(di)1(tioners)-453(using)-453(o)28(v)28(e)-1(r)1(lapp)1(ing)-453(sub)1(-)]TJ -105.9952 -13.5492 Td[(matrice)-1(s,)-403(i.)1(e)-1(.)-389(with)-388(s)-1(ome)-389(c)-1(omm)-1(on)-388(ro)28(ws)-1(,)-403(t)1(o)-389(c)-1(ou)1(ple)-389(the)-389(lo)-28(cal)-389(in)1(formation)-388(relate)-1(d)-388(to)-389(the)]TJ 0 -13.5492 Td[(submatr)1(ic)-1(es)-362(\050s)-1(ee)-1(,)-369(e.g.,)-368([)]TJ +ET +1 0 0 1 205.8126 529.3831 cm 1 0 0 rg 1 0 0 RG - [(20)]TJ +1 0 0 1 -205.8126 -529.3831 cm +BT +/F15 10.9091 Tf 205.8126 529.3831 Td[(20)]TJ +ET +1 0 0 1 216.7217 529.3831 cm 0 g 0 G - [(]\051.)-530(The)-362(main)-362(motiv)55(at)1(ion)-362(for)-362(c)28(ho)-28(osing)-362(Additiv)28(e)-362(Sc)28(h)28(w)27(arz)-362(pre-)]TJ 0 -13.549 Td [(conditioners)-361(is)-361(their)-361(in)28(trinsic)-361(parallelism.)-528(A)-361(dra)28(wbac)28(k)-362(of)-361(these)-361(preconditioners)-361(is)-361(that)]TJ 0 -13.549 Td [(the)-388(n)28(um)27(b)-27(er)-388(of)-389(iterations)-388(of)-388(the)-388(preconditioned)-388(solv)28(ers)-388(generally)-389(gro)28(ws)-388(with)-388(the)-388(n)28(um-)]TJ 0 -13.549 Td [(b)-28(er)-370(of)-370(submatrices.)-555(This)-370(ma)28(y)-370(b)-28(e)-370(a)-370(serious)-370(limitation)-370(on)-370(parallel)-370(computers,)-380(since)-370(the)]TJ 0 -13.55 Td [(n)28(um)28(b)-28(er)-403(of)-404(sub)1(m)-1(atr)1(ic)-1(es)-403(usually)-403(matc)28(hes)-403(the)-404(n)28(um)28(b)-28(er)-403(of)-403(a)28(v)55(ailable)-403(pro)-28(cessors.)-654(Optimal)]TJ 0 -13.549 Td [(con)28(v)28(ergence)-262(rates,)-276(i.e.)-262(iteration)-262(n)28(um)28(b)-28(ers)-262(indep)-27(enden)27(t)-261(of)-262(the)-262(n)28(um)28(b)-28(er)-262(of)-261(submatrices,)-277(can)]TJ 0 -13.549 Td [(b)-28(e)-369(obtained)-370(b)28(y)-369(correcting)-369(the)-370(preconditioner)-369(through)-369(a)-370(suitable)-369(appro)28(ximation)-370(of)-369(the)]TJ 0 -13.549 Td [(original)-323(linear)-323(system)-323(in)-323(a)-323(coarse)-323(space,)-325(whic)28(h)-323(globally)-323(couples)-323(the)-323(infor)1(m)-1(at)1(ion)-323(related)]TJ 0 -13.549 Td [(to)-333(the)-334(single)-333(submatrices.)]TJ/F18 10.9091 Tf 16.937 -14.012 Td [(Two-level)-308(Schwarz)]TJ/F15 10.9091 Tf 91.529 0 Td [(preconditioners)-279(are)-280(obtained)-279(b)27(y)-279(com)27(b)1(ining)-280(basic)-279(\050one-)-1(l)1(e)-1(v)28(el\051)-279(Sc)27(h)1(-)]TJ -108.466 -13.549 Td [(w)28(arz)-363(p)1(rec)-1(on)1(ditioners)-363(with)-362(a)-362(coarse-lev)28(el)-363(correction.)-531(In)-362(this)-362(con)28(text,)-370(the)-362(one-lev)28(el)-363(pre-)]TJ 0 -13.549 Td [(conditioner)-344(is)-345(often)-344(called)-345(`)1(s)-1(mo)-27(other'.)-478(Di\013eren)28(t)-345(t)28(w)28(o-lev)28(el)-345(preconditioners)-344(are)-344(obtained)]TJ 0 -13.549 Td [(b)28(y)-371(v)56(arying)-371(the)-371(c)28(hoice)-371(of)-370(the)-371(smo)-28(other)-371(and)-370(of)-371(the)-371(coarse-lev)28(el)-371(correction,)-380(and)-371(the)-370(w)27(a)28(y)]TJ 0 -13.549 Td [(they)-374(are)-373(com)27(bined)-373([)]TJ +1 0 0 1 -216.7217 -529.3831 cm +BT +/F15 10.9091 Tf 216.7217 529.3831 Td[(]\051.)-530(Th)1(e)-363(main)-361(m)-1(oti)1(v)55(at)1(ion)-362(f)1(or)-362(c)28(ho)-28(osing)-362(Ad)1(di)1(tiv)28(e)-362(Sc)27(h)29(w)27(arz)-362(p)1(re)-1(-)]TJ -123.1215 -13.5492 Td[(condi)1(tioners)-361(is)-362(t)1(heir)-361(in)29(trin)1(s)-1(ic)-361(par)1(allelism)-1(.)-527(A)-361(dr)1(a)27(wb)1(ac)27(k)-361(of)-361(th)1(e)-1(se)-362(p)1(rec)-1(on)1(dit)1(ioners)-361(is)-362(th)1(at)]TJ 0 -13.5492 Td[(th)1(e)-389(n)28(u)1(m)27(b)-27(e)-1(r)-388(of)-387(iteration)1(s)-389(of)-388(th)1(e)-389(p)1(rec)-1(on)1(diti)1(oned)-388(s)-1(ol)1(v)28(e)-1(r)1(s)-389(generally)-388(gr)1(o)27(ws)-388(w)-1(i)1(th)-388(th)1(e)-389(n)28(u)1(m)-1(-)]TJ 0 -13.5492 Td[(b)-27(e)-1(r)-370(of)-369(s)-1(u)1(bmatri)1(c)-1(es)-1(.)-554(T)-1(h)1(is)-370(m)-1(a)28(y)-370(b)-27(e)-371(a)-370(se)-1(r)1(ious)-370(limitation)-369(on)-370(p)1(arallel)-370(com)-1(p)1(uters,)-379(s)-1(in)1(c)-1(e)-370(the)]TJ 0 -13.5492 Td[(n)28(u)1(m)27(b)-27(e)-1(r)-403(of)-402(s)-1(u)1(bmatrices)-404(usual)1(ly)-403(m)-1(at)1(c)27(hes)-404(th)1(e)-404(n)28(u)1(m)27(b)-27(e)-1(r)-402(of)-403(a)28(v)55(ai)1(lable)-403(pr)1(o)-28(c)-1(ess)-1(ors.)-654(Op)1(timal)]TJ 0 -13.5492 Td[(con)28(v)28(e)-1(r)1(ge)-1(n)1(c)-1(e)-262(rates,)-276(i.e.)-262(it)1(e)-1(rati)1(on)-262(n)29(um)28(b)-28(ers)-262(in)1(dep)-28(end)1(e)-1(n)28(t)-261(of)-262(t)1(he)-262(n)28(um)28(b)-27(e)-1(r)-261(of)-262(sub)1(m)-1(at)1(rice)-1(s,)-276(can)]TJ 0 -13.5492 Td[(b)-27(e)-370(obtai)1(ned)-369(b)28(y)-369(c)-1(or)1(re)-1(ctin)1(g)-370(th)1(e)-370(pr)1(e)-1(cond)1(ition)1(e)-1(r)-369(th)1(rou)1(gh)-369(a)-370(suit)1(able)-370(ap)1(pr)1(o)27(x)1(im)-1(at)1(ion)-369(of)-369(the)]TJ 0 -13.5492 Td[(ori)1(ginal)-323(l)1(inear)-323(syste)-1(m)-323(in)-322(a)-323(c)-1(oar)1(s)-1(e)-323(s)-1(p)1(ac)-1(e,)-325(whi)1(c)27(h)-323(gl)1(oball)1(y)-323(c)-1(ou)1(ples)-323(the)-323(inf)1(ormation)-322(related)]TJ 0 -13.5492 Td[(to)-333(the)-333(s)-1(in)1(gle)-334(sub)1(m)-1(atr)1(ice)-1(s.)]TJ/F20 10.9091 Tf 16.9365 -14.0113 Td[(Two-l)1(evel)-308(S)-1(c)1(h)-1(warz)]TJ/F15 10.9091 Tf 91.5293 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-280(are)-280(obt)1(ained)-279(b)28(y)-280(com)27(b)1(in)1(ing)-279(basic)-280(\050one-le)-1(v)28(el\051)-279(Sc)28(h-)]TJ -108.4658 -13.5492 Td[(w)28(arz)-363(p)1(rec)-1(on)1(diti)1(oners)-363(with)-362(a)-362(coarse)-1(-lev)28(e)-1(l)-362(correction.)-531(In)-362(t)1(his)-362(c)-1(on)28(text,)-369(th)1(e)-363(one-le)-1(v)28(el)-362(pr)1(e)-1(-)]TJ 0 -13.5492 Td[(condi)1(tioner)-344(is)-345(of)1(te)-1(n)-344(called)-344(`sm)-1(o)-27(other'.)-477(Di\013e)-1(r)1(e)-1(n)29(t)-345(t)28(w)28(o-)-1(l)1(e)-1(v)28(el)-345(p)1(rec)-1(on)1(dit)1(ioners)-345(ar)1(e)-345(obtai)1(ned)]TJ 0 -13.5492 Td[(b)28(y)-370(v)55(ar)1(yin)1(g)-371(th)1(e)-372(c)28(hoice)-371(of)-371(t)1(he)-371(s)-1(mo)-28(oth)1(e)-1(r)-370(and)-370(of)-370(the)-371(coarse)-1(-lev)28(e)-1(l)-370(c)-1(or)1(re)-1(ction)1(,)-380(and)-370(th)1(e)-372(w)28(a)28(y)]TJ 0 -13.5492 Td[(th)1(e)-1(y)-373(are)-374(c)-1(om)28(bi)1(ned)-374([)]TJ +ET +1 0 0 1 189.4965 352.7814 cm 1 0 0 rg 1 0 0 RG - [(20)]TJ +1 0 0 1 -189.4965 -352.7814 cm +BT +/F15 10.9091 Tf 189.4965 352.7814 Td[(20)]TJ +ET +1 0 0 1 200.4056 352.7814 cm 0 g 0 G - [(].)-566(The)-373(same)-374(reasoning)-374(can)-373(b)-28(e)-374(applied)-373(s)-1(tar)1(ting)-374(from)-374(the)-373(coarse)-1(-)]TJ 0 -13.55 Td [(lev)28(el)-281(system,)-291(i.e.)-281(a)-280(coarse-)-1(space)-280(correction)-281(can)-280(b)-28(e)-281(built)-280(from)-281(this)-280(s)-1(y)1(s)-1(tem,)-291(th)28(us)-281(ob)1(taining)]TJ/F18 10.9091 Tf 0 -13.549 Td [(multi-level)]TJ/F15 10.9091 Tf 53.83 0 Td [(preconditioners.)]TJ -36.893 -14.011 Td [(It)-443(is)-444(w)28(orth)-443(noting)-444(that)-443(optimal)-443(preconditioners)-444(do)-443(not)-444(n)1(e)-1(cessarily)-443(corresp)-28(ond)-443(to)]TJ -16.937 -13.549 Td [(minim)28(um)-480(exec)-1(u)1(tion)-481(times.)-885(Indeed,)-517(to)-480(obtain)-480(e\013ectiv)28(e)-481(m)28(ulti-lev)28(el)-480(preconditioners)-480(a)]TJ 0 -13.549 Td [(tradeo\013)-381(b)-28(et)28(w)28(e)-1(en)-381(optimalit)28(y)-381(of)-381(con)28(v)27(ergence)-381(and)-381(the)-381(cost)-382(of)-381(building)-381(and)-381(applying)-381(the)]TJ 0 -13.55 Td [(coarse-space)-384(corrections)-384(m)28(ust)-384(b)-28(e)-383(ac)27(hiev)28(ed.)-596(The)-383(c)27(hoice)-383(of)-384(the)-384(n)28(um)28(b)-28(er)-384(of)-383(le)-1(v)28(els,)-396(i.e.)-384(of)]TJ 0 -13.549 Td [(the)-379(coarse-space)-379(corrections,)-390(also)-378(a\013ects)-379(the)-379(e\013ectiv)28(eness)-379(of)-378(the)-379(preconditioners.)-580(One)]TJ 0 -13.549 Td [(more)-392(goal)-391(is)-392(to)-392(get)-391(con)27(v)28(ergence)-391(rates)-392(as)-392(less)-392(sensitiv)28(e)-392(as)-391(p)-28(ossible)-392(to)-391(v)55(ariations)-391(in)-392(the)]TJ 0 -13.549 Td [(matrix)-333(co)-28(e\016cien)28(ts.)]TJ 16.937 -14.012 Td [(Tw)28(o)-303(main)-303(approac)28(hes)-303(can)-303(b)-28(e)-303(used)-303(to)-303(build)-303(coarse-space)-303(corrections.)-434(The)-303(geometric)]TJ -16.937 -13.549 Td [(approac)28(h)-412(applies)-413(coarsening)-412(strategies)-413(based)-412(on)-412(the)-413(kn)1(o)27(wledge)-412(of)-412(some)-413(ph)28(ysical)-412(grid)]TJ 0 -13.549 Td [(asso)-28(ciated)-279(to)-280(the)-279(m)-1(atr)1(ix)-280(and)-279(requires)-280(the)-279(use)-1(r)-279(to)-280(de\014n)1(e)-280(grid)-280(t)1(ransfer)-280(op)-28(erators)-279(from)-280(the)]TJ 0 -13.549 Td [(\014ne)-394(to)-393(the)-394(coarse)-393(lev)27(els)-393(and)-394(vice)-393(v)28(ersa.)-626(Thi)1(s)-394(ma)28(y)-394(result)-393(di\016cult)-394(for)-393(complex)-394(geome-)]TJ 0 -13.549 Td [(tries;)-464(furthermore,)-442(suitable)-420(one-lev)27(el)-420(preconditioners)-420(ma)28(y)-421(b)-28(e)-420(required)-420(to)-421(get)-420(e\016cien)28(t)]TJ 0 -13.549 Td [(in)28(terpla)28(y)-381(b)-28(et)28(w)27(een)-381(\014ne)-381(and)-381(coarse)-381(lev)27(els,)-393(e.g.)-381(when)-381(matrices)-381(with)-381(highly)-381(v)55(arying)-381(co)-28(ef-)]TJ 0 -13.55 Td [(\014cien)28(ts)-417(are)-417(considered.)-694(The)-417(al)1(ge)-1(br)1(aic)-417(approac)28(h)-417(builds)-416(coarse-)-1(space)-416(corrections)-417(using)]TJ 0 -13.549 Td [(only)-442(matrix)-442(information.)-770(It)-443(p)-27(erforms)-442(a)-442(fully)-442(automatic)-442(coarsening)-442(and)-442(enforces)-443(th)1(e)]TJ +1 0 0 1 -200.4056 -352.7814 cm +BT +/F15 10.9091 Tf 200.4056 352.7814 Td[(].)-565(The)-374(sam)-1(e)-374(reasonin)1(g)-374(can)-374(b)-27(e)-374(app)1(lied)-373(s)-1(tar)1(ting)-373(from)-374(th)1(e)-374(c)-1(oar)1(s)-1(e-)]TJ -106.8054 -13.5492 Td[(lev)28(e)-1(l)-280(s)-1(y)1(s)-1(tem,)-291(i.e.)-281(a)-280(c)-1(oar)1(s)-1(e-)-1(space)-281(c)-1(or)1(rec)-1(tion)-280(can)-280(b)-28(e)-281(b)1(uil)1(t)-281(f)1(rom)-281(thi)1(s)-281(s)-1(ystem)-1(,)-291(th)29(us)-281(ob)1(taini)1(ng)]TJ/F20 10.9091 Tf 0 -13.5492 Td[(mu)1(lti-l)1(evel)]TJ/F15 10.9091 Tf 53.8299 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-1(.)]TJ -36.8934 -14.0113 Td[(It)-443(is)-444(w)27(or)1(th)-443(noti)1(ng)-443(that)-443(opt)1(im)-1(al)-443(p)1(rec)-1(on)1(diti)1(oners)-444(do)-443(not)-443(n)1(e)-1(ce)-1(ss)-1(ar)1(ily)-443(c)-1(or)1(res)-1(p)-27(ond)-443(to)]TJ -16.9365 -13.5492 Td[(mini)1(m)27(um)-480(e)-1(x)1(e)-1(cuti)1(on)-480(time)-1(s.)-885(Ind)1(e)-1(ed,)-516(to)-480(obtain)-479(e)-1(\013e)-1(ctiv)28(e)-480(m)27(ul)1(ti-le)-1(v)28(el)-480(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-481(a)]TJ 0 -13.5492 Td[(trad)1(e)-1(o\013)-381(b)-27(e)-1(t)28(w)28(e)-1(en)-381(opti)1(m)-1(al)1(it)28(y)-381(of)-381(c)-1(on)29(v)28(e)-1(r)1(ge)-1(n)1(c)-1(e)-382(an)1(d)-381(th)1(e)-382(cos)-1(t)-381(of)-381(b)1(uil)1(din)1(g)-382(an)1(d)-381(ap)1(plyi)1(ng)-381(the)]TJ 0 -13.5492 Td[(coars)-1(e-s)-1(p)1(ac)-1(e)-384(correc)-1(ti)1(ons)-384(m)27(u)1(s)-1(t)-383(b)-28(e)-384(ac)27(h)1(iev)28(e)-1(d)1(.)-596(The)-384(c)28(hoice)-384(of)-384(th)1(e)-384(n)28(um)28(b)-28(er)-384(of)-383(lev)28(e)-1(l)1(s)-1(,)-396(i.)1(e)-1(.)-383(of)]TJ 0 -13.5492 Td[(th)1(e)-380(coarse)-1(-space)-379(c)-1(orr)1(e)-1(ction)1(s)-1(,)-390(al)1(s)-1(o)-378(a\013)-1(ec)-1(ts)-379(th)1(e)-379(e)-1(\013ec)-1(tiv)28(eness)-380(of)-378(th)1(e)-379(pr)1(e)-1(condi)1(tioners.)-580(One)]TJ 0 -13.5492 Td[(more)-392(goal)-392(i)1(s)-392(to)-392(get)-392(con)28(v)28(e)-1(r)1(ge)-1(n)1(c)-1(e)-392(r)1(ate)-1(s)-392(as)-392(les)-1(s)-392(se)-1(n)1(s)-1(i)1(tiv)28(e)-392(as)-392(p)-28(ossible)-392(to)-391(v)56(ariation)1(s)-392(in)-391(the)]TJ 0 -13.5492 Td[(matrix)-333(co)-28(e\016)-1(cien)28(ts)-1(.)]TJ 16.9365 -14.0113 Td[(Tw)27(o)-303(main)-302(app)1(roac)27(h)1(e)-1(s)-303(c)-1(an)-302(b)-27(e)-304(u)1(s)-1(ed)-303(to)-303(b)1(ui)1(ld)-303(coarse)-1(-s)-1(p)1(ac)-1(e)-303(correc)-1(t)1(ions.)-434(T)-1(h)1(e)-304(geome)-1(tr)1(ic)]TJ -16.9365 -13.5492 Td[(app)1(roac)28(h)-412(app)1(lies)-413(c)-1(oar)1(s)-1(enin)1(g)-412(s)-1(tr)1(ate)-1(gies)-413(b)1(as)-1(ed)-412(on)-412(the)-412(kno)28(wledge)-413(of)-412(some)-413(ph)29(ys)-1(i)1(c)-1(al)-412(gri)1(d)]TJ 0 -13.5492 Td[(ass)-1(o)-28(ciated)-279(to)-280(th)1(e)-280(m)-1(at)1(rix)-279(and)-279(r)1(e)-1(qu)1(ires)-280(the)-280(u)1(s)-1(er)-279(to)-280(d)1(e)-1(\014)1(ne)-280(gr)1(id)-279(tran)1(s)-1(f)1(e)-1(r)-279(op)-27(e)-1(rat)1(ors)-280(fr)1(om)-280(the)]TJ 0 -13.5492 Td[(\014n)1(e)-394(to)-394(t)1(he)-394(coars)-1(e)-394(l)1(e)-1(v)28(els)-394(and)-393(v)1(ic)-1(e)-394(v)28(ersa.)-625(This)-394(ma)28(y)-394(r)1(e)-1(sul)1(t)-394(d)1(i\016)-1(cul)1(t)-394(f)1(or)-394(complex)-393(ge)-1(ome)-1(-)]TJ 0 -13.5492 Td[(tri)1(e)-1(s;)-464(f)1(urth)1(e)-1(r)1(m)-1(or)1(e)-1(,)-442(sui)1(table)-420(one-)-1(lev)28(el)-421(p)1(rec)-1(on)1(diti)1(oners)-421(ma)28(y)-420(b)-28(e)-421(r)1(e)-1(qu)1(ired)-420(to)-420(ge)-1(t)-420(e\016)-1(cien)28(t)]TJ 0 -13.5492 Td[(in)28(t)1(e)-1(rp)1(la)28(y)-381(b)-27(e)-1(t)28(w)28(e)-1(en)-381(\014n)1(e)-382(an)1(d)-381(coars)-1(e)-381(lev)28(e)-1(ls,)-393(e.g.)-381(when)-381(matrice)-1(s)-381(with)-381(h)1(ighl)1(y)-381(v)55(ar)1(yin)1(g)-381(c)-1(o)-28(ef-)]TJ 0 -13.5492 Td[(\014cien)28(ts)-417(are)-417(considered.)-694(The)-417(al)1(ge)-1(b)1(raic)-417(ap)1(proac)28(h)-417(b)1(ui)1(lds)-417(coarse)-1(-s)-1(p)1(ac)-1(e)-417(corr)1(e)-1(ctions)-417(u)1(s)-1(i)1(ng)]TJ 0 -13.5492 Td[(onl)1(y)-442(m)-1(at)1(rix)-442(i)1(nfor)1(m)-1(at)1(ion.)-770(It)-442(p)-28(erf)1(orms)-443(a)-442(f)1(ully)-441(automatic)-442(c)-1(oar)1(s)-1(enin)1(g)-442(and)-442(enf)1(orce)-1(s)-442(the)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -251 0 obj << +264 0 obj << /Type /Page -/Contents 252 0 R -/Resources 250 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 238 0 R -/Annots [ 249 0 R 243 0 R 244 0 R 245 0 R 246 0 R 247 0 R ] +/Contents 265 0 R +/Resources 263 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 258 0 R +/Annots [ 267 0 R 268 0 R 269 0 R 270 0 R 271 0 R 272 0 R ] >> endobj -249 0 obj << +267 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -243 0 obj << +268 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [444.119 569.496 451.567 578.519] +/Rect [444.1195 569.4965 451.5666 578.5193] /Subtype /Link /A << /S /GoTo /D (cite.Cai_Widlund_92) >> >> endobj -244 0 obj << +269 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [456.241 569.496 463.688 578.519] +/Rect [456.2407 569.4965 463.6878 578.5193] /Subtype /Link /A << /S /GoTo /D (cite.dd1_94) >> >> endobj -245 0 obj << +270 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [468.362 569.496 481.264 578.519] +/Rect [468.3619 569.4965 481.2636 578.5193] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -246 0 obj << +271 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [204.816 528.387 217.718 537.41] +/Rect [204.8163 528.3868 217.718 537.4096] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -247 0 obj << +272 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [188.5 351.785 201.402 360.808] +/Rect [188.5003 351.7851 201.4019 360.808] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -253 0 obj << -/D [251 0 R /XYZ 93.6 740.002 null] +266 0 obj << +/D [264 0 R /XYZ 93.6002 740.0018 null] >> endobj 46 0 obj << -/D [251 0 R /XYZ 93.6 715.095 null] +/D [264 0 R /XYZ 93.6002 715.0952 null] >> endobj -250 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F18 173 0 R >> +263 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F20 181 0 R >> /ProcSet [ /PDF /Text ] >> endobj -269 0 obj << -/Length 14783 +277 0 obj << +/Length 18740 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(10)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(10)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(in)28(terpla)28(y)-352(b)-28(et)28(w)28(een)-352(the)-352(\014ne)-351(and)-352(coarse)-352(lev)28(els)-352(b)28(y)-351(suitably)-352(c)28(ho)-28(osing)-352(the)-351(coarse)-352(space)-352(and)]TJ 0 -13.549 Td [(the)-333(coarse-to-\014ne)-334(in)28(terp)-28(olation)-333([)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F15 10.9091 Tf 86.3998 704.1363 Td[(in)28(t)1(e)-1(rp)1(la)28(y)-352(b)-27(et)28(w)27(ee)-1(n)-351(th)1(e)-353(\014)1(ne)-352(an)1(d)-352(coarse)-352(le)-1(v)28(els)-352(b)28(y)-351(s)-1(u)1(itab)1(ly)-352(c)28(ho)-28(osin)1(g)-352(the)-352(coarse)-352(s)-1(p)1(ac)-1(e)-352(an)1(d)]TJ 0 -13.5492 Td[(th)1(e)-334(c)-1(oar)1(s)-1(e-)-1(t)1(o-)-1(\014)1(ne)-334(i)1(n)28(te)-1(r)1(p)-28(ol)1(ation)-333([)]TJ +ET +1 0 0 1 239.8545 690.5871 cm 1 0 0 rg 1 0 0 RG - [(22)]TJ +1 0 0 1 -239.8545 -690.5871 cm +BT +/F15 10.9091 Tf 239.8545 690.5871 Td[(22)]TJ +ET +1 0 0 1 250.7636 690.5871 cm 0 g 0 G - [(].)]TJ 16.936 -13.643 Td [(MLD2P4)-255(uses)-255(a)-255(pur)1(e)-255(algebraic)-255(approac)28(h)-255(for)-255(building)-255(the)-254(sequence)-255(of)-255(coarse)-255(matrices)]TJ -16.936 -13.549 Td [(starting)-425(from)-425(the)-425(original)-425(matrix.)-720(The)-426(al)1(ge)-1(b)1(raic)-426(approac)28(h)-425(is)-425(based)-425(on)-425(the)]TJ/F18 10.9091 Tf 369.239 0 Td [(smo)51(othe)51(d)]TJ -369.239 -13.549 Td [(aggr)51(e)51(gation)]TJ/F15 10.9091 Tf 58.612 0 Td [(algorithm)-402([)]TJ +1 0 0 1 -250.7636 -690.5871 cm +BT +/F15 10.9091 Tf 250.7636 690.5871 Td[(].)]TJ -147.4273 -13.6428 Td[(MLD2P)1(4)-255(uses)-256(a)-255(p)1(ur)1(e)-256(al)1(ge)-1(b)1(raic)-255(app)1(roac)27(h)-254(for)-254(bu)1(ild)1(ing)-255(t)1(he)-255(s)-1(equ)1(e)-1(n)1(c)-1(e)-255(of)-255(coarse)-256(matr)1(ic)-1(es)]TJ -16.9365 -13.5492 Td[(startin)1(g)-425(from)-425(the)-425(origi)1(nal)-425(matrix)1(.)-720(The)-426(al)1(ge)-1(b)1(raic)-425(app)1(roac)27(h)-425(i)1(s)-426(based)-425(on)-425(th)1(e)]TJ/F20 10.9091 Tf 369.2393 0 Td[(smo)51(othe)51(d)]TJ -369.2393 -13.5492 Td[(aggr)51(e)51(gation)]TJ/F15 10.9091 Tf 58.6124 0 Td[(algor)1(ithm)-402([)]TJ +ET +1 0 0 1 198.5216 649.8459 cm 1 0 0 rg 1 0 0 RG - [(1)]TJ +1 0 0 1 -198.5216 -649.8459 cm +BT +/F15 10.9091 Tf 198.5216 649.8459 Td[(1)]TJ +ET +1 0 0 1 203.9761 649.8459 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -203.9761 -649.8459 cm +BT +/F15 10.9091 Tf 203.9761 649.8459 Td[(,)]TJ +ET +1 0 0 1 211.3946 649.8459 cm 1 0 0 rg 1 0 0 RG - [-402(24)]TJ +1 0 0 1 -211.3946 -649.8459 cm +BT +/F15 10.9091 Tf 211.3946 649.8459 Td[(24)]TJ +ET +1 0 0 1 222.3037 649.8459 cm 0 g 0 G - [(].)-651(A)-403(decoupled)-402(v)28(ersion)-402(of)-402(this)-403(algorithm)-402(is)-402(implemen)28(ted,)]TJ -58.612 -13.549 Td [(where)-347(the)-346(smo)-28(othed)-347(aggregation)-346(is)-347(applied)-347(l)1(o)-28(cally)-347(to)-347(eac)28(h)-346(submatrix)-347([)]TJ +1 0 0 1 -222.3037 -649.8459 cm +BT +/F15 10.9091 Tf 222.3037 649.8459 Td[(].)-651(A)-402(d)1(e)-1(coup)1(le)-1(d)-401(v)28(e)-1(rsion)-402(of)-401(this)-402(algorit)1(hm)-403(i)1(s)-403(impl)1(e)-1(me)-1(n)29(te)-1(d)1(,)]TJ -135.9039 -13.5492 Td[(where)-347(th)1(e)-348(smo)-28(othed)-346(aggregation)-346(is)-347(app)1(lied)-346(lo)-28(cally)-346(to)-347(eac)27(h)-346(s)-1(u)1(bmatri)1(x)-347([)]TJ +ET +1 0 0 1 422.9733 636.2967 cm 1 0 0 rg 1 0 0 RG - [(23)]TJ +1 0 0 1 -422.9733 -636.2967 cm +BT +/F15 10.9091 Tf 422.9733 636.2967 Td[(23)]TJ +ET +1 0 0 1 433.8824 636.2967 cm 0 g 0 G - [(].)-484(In)-347(the)-347(n)1(e)-1(xt)]TJ 0 -13.549 Td [(t)28(w)28(o)-249(subsections)-249(w)28(e)-249(pro)28(vide)-249(a)-248(brief)-249(description)-249(of)-248(the)-249(m)28(ulti-lev)28(el)-249(Sc)28(h)27(w)28(arz)-249(p)1(rec)-1(on)1(ditioners)]TJ 0 -13.55 Td [(and)-389(of)-390(the)-389(smo)-28(othed)-390(aggregation)-389(tec)28(hnique)-390(as)-389(implemen)27(ted)-389(in)-390(M)1(LD2P4.)-613(F)83(or)-389(further)]TJ 0 -13.549 Td [(details)-333(the)-334(user)-333(is)-333(referred)-334(to)-333([)]TJ +1 0 0 1 -433.8824 -636.2967 cm +BT +/F15 10.9091 Tf 433.8824 636.2967 Td[(].)-484(In)-346(the)-347(n)1(e)-1(xt)]TJ -347.4826 -13.5492 Td[(t)28(w)27(o)-248(s)-1(u)1(bse)-1(ction)1(s)-250(w)28(e)-249(pr)1(o)27(v)1(ide)-249(a)-249(b)1(rief)-248(des)-1(crip)1(tion)-248(of)-248(the)-249(m)28(ulti)1(-)-1(lev)28(el)-249(Sc)28(h)28(w)28(arz)-249(pr)1(e)-1(cond)1(ition)1(e)-1(rs)]TJ 0 -13.5492 Td[(and)-389(of)-389(th)1(e)-390(s)-1(mo)-28(oth)1(e)-1(d)-389(aggr)1(e)-1(gati)1(on)-389(te)-1(c)28(hni)1(que)-390(as)-390(i)1(m)-1(p)1(lem)-1(en)28(ted)-389(in)-389(MLD2P)1(4.)-613(F)83(or)-389(f)1(ur)1(ther)]TJ 0 -13.5492 Td[(detail)1(s)-334(the)-333(use)-1(r)-333(is)-333(re)-1(f)1(e)-1(r)1(red)-333(to)-333([)]TJ +ET +1 0 0 1 230.6423 595.6491 cm 1 0 0 rg 1 0 0 RG - [(2)]TJ +1 0 0 1 -230.6423 -595.6491 cm +BT +/F15 10.9091 Tf 230.6423 595.6491 Td[(2)]TJ +ET +1 0 0 1 236.0969 595.6491 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -236.0969 -595.6491 cm +BT +/F15 10.9091 Tf 236.0969 595.6491 Td[(,)]TJ +ET +1 0 0 1 242.7635 595.6491 cm 1 0 0 rg 1 0 0 RG - [-333(3)]TJ +1 0 0 1 -242.7635 -595.6491 cm +BT +/F15 10.9091 Tf 242.7635 595.6491 Td[(3)]TJ +ET +1 0 0 1 248.2181 595.6491 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -248.2181 -595.6491 cm +BT +/F15 10.9091 Tf 248.2181 595.6491 Td[(,)]TJ +ET +1 0 0 1 254.8848 595.6491 cm 1 0 0 rg 1 0 0 RG - [-334(4)]TJ +1 0 0 1 -254.8848 -595.6491 cm +BT +/F15 10.9091 Tf 254.8848 595.6491 Td[(4)]TJ +ET +1 0 0 1 260.3393 595.6491 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -260.3393 -595.6491 cm +BT +/F15 10.9091 Tf 260.3393 595.6491 Td[(,)]TJ +ET +1 0 0 1 267.006 595.6491 cm 1 0 0 rg 1 0 0 RG - [-333(20)]TJ +1 0 0 1 -267.006 -595.6491 cm +BT +/F15 10.9091 Tf 267.006 595.6491 Td[(20)]TJ +ET +1 0 0 1 277.9151 595.6491 cm 0 g 0 G - [(].)]TJ/F17 11.9552 Tf 0 -29.748 Td [(4.1)-1125(Multi-lev)31(el)-375(Sc)31(h)32(w)31(arz)-375(Preconditioners)]TJ/F15 10.9091 Tf 0 -20.777 Td [(The)-270(Multilev)28(el)-269(prec)-1(on)1(ditioners)-270(implemen)28(ted)-270(in)-270(MLD2P4)-269(are)-270(obtained)-269(b)27(y)-269(com)27(binin)1(g)-270(AS)]TJ 0 -13.549 Td [(preconditioners)-315(with)-315(coarse-space)-315(corrections;)-321(therefore)-315(w)27(e)-315(\014rst)-315(pro)28(vide)-315(a)-315(sk)28(etc)27(h)-315(of)-315(the)]TJ 0 -13.549 Td [(AS)-333(preconditioners.)]TJ 16.936 -13.643 Td [(Giv)28(en)-303(the)-302(linear)-302(system)-303(\050)]TJ +1 0 0 1 -277.9151 -595.6491 cm +BT +/F15 10.9091 Tf 277.9151 595.6491 Td[(].)]TJ/F19 11.9552 Tf -191.5153 -29.7481 Td[(4.)-1(1)-1125(M)-1(ult)-1(i-l)-1(ev)32(e)-1(l)-375(Sc)31(h)31(w)31(arz)-375(Pre)-1(condi)-1(ti)-1(oner)-1(s)]TJ/F15 10.9091 Tf 0 -20.7766 Td[(The)-270(Mu)1(ltil)1(e)-1(v)28(el)-270(p)1(rec)-1(on)1(diti)1(oners)-270(impleme)-1(n)28(ted)-269(in)-269(MLD2P)1(4)-270(are)-270(ob)1(tained)-269(b)28(y)-270(com)27(b)1(in)1(ing)-269(AS)]TJ 0 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-316(with)-314(c)-1(oar)1(s)-1(e-)-1(space)-316(corr)1(e)-1(ctions;)-321(th)1(e)-1(refor)1(e)-316(w)28(e)-316(\014)1(rst)-315(pro)28(vi)1(de)-315(a)-315(s)-1(k)28(etc)27(h)-315(of)-314(the)]TJ 0 -13.5492 Td[(AS)-333(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-1(.)]TJ 16.9365 -13.6429 Td[(Giv)28(en)-302(th)1(e)-303(lin)1(e)-1(ar)-302(syste)-1(m)-302(\050)]TJ +ET +1 0 0 1 223.1205 504.3831 cm 0 0 1 rg 0 0 1 RG - [(1)]TJ +1 0 0 1 -223.1205 -504.3831 cm +BT +/F15 10.9091 Tf 223.1205 504.3831 Td[(1)]TJ +ET +1 0 0 1 228.5751 504.3831 cm 0 g 0 G - [(\051,)-308(where)]TJ/F22 10.9091 Tf 167.085 0 Td [(A)]TJ/F15 10.9091 Tf 11.212 0 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.758 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 -1.636 Td [(ij)]TJ/F15 10.9091 Tf 7.265 1.636 Td [(\051)]TJ/F25 10.9091 Tf 7.273 0 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.182 3.959 Td [(n)]TJ/F26 7.9701 Tf 5.138 0 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F15 10.9091 Tf 8.934 -3.959 Td [(is)-302(a)-303(nonsingular)-302(sparse)-302(matrix)]TJ -270.136 -13.549 Td [(with)-321(a)-321(symmetric)-321(nonzero)-321(pattern,)-324(let)]TJ/F22 10.9091 Tf 184.526 0 Td [(G)]TJ/F15 10.9091 Tf 11.608 0 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.757 0 Td [(W)28(;)-167(E)]TJ/F15 10.9091 Tf 23.531 0 Td [(\051)-321(b)-28(e)-321(the)-321(adjacency)-321(graph)-321(of)]TJ/F22 10.9091 Tf 134.378 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)-324(wh)1(e)-1(re)]TJ/F22 10.9091 Tf -377.982 -13.549 Td [(W)]TJ/F15 10.9091 Tf 15.419 0 Td [(=)]TJ/F25 10.9091 Tf 12.086 0 Td [(f)]TJ/F15 10.9091 Tf 5.455 0 Td [(1)]TJ/F22 10.9091 Tf 5.454 0 Td [(;)]TJ/F15 10.9091 Tf 4.849 0 Td [(2)]TJ/F22 10.9091 Tf 5.454 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(n)]TJ/F25 10.9091 Tf 30.79 0 Td [(g)]TJ/F15 10.9091 Tf 9.434 0 Td [(and)]TJ/F22 10.9091 Tf 21.554 0 Td [(E)]TJ/F15 10.9091 Tf 12.283 0 Td [(=)]TJ/F25 10.9091 Tf 12.086 0 Td [(f)]TJ/F15 10.9091 Tf 5.455 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(i;)-167(j)]TJ/F15 10.9091 Tf 13.724 0 Td [(\051)-330(:)]TJ/F22 10.9091 Tf 14.475 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 -1.637 Td [(ij)]TJ/F25 10.9091 Tf 10.867 1.637 Td [(6)]TJ/F15 10.9091 Tf 0 0 Td [(=)-330(0)]TJ/F25 10.9091 Tf 17.54 0 Td [(g)]TJ/F15 10.9091 Tf 9.434 0 Td [(are)-365(the)-364(v)27(ertex)-364(set)-365(and)-365(the)-365(edge)-364(set)-365(of)]TJ/F22 10.9091 Tf 184.476 0 Td [(G)]TJ/F15 10.9091 Tf 8.578 0 Td [(,)]TJ -409.421 -13.549 Td [(resp)-28(ectiv)28(ely)83(.)-466(Tw)28(o)-341(v)28(ertices)-341(are)-341(called)-340(adjacen)27(t)-340(if)-341(there)-340(is)-341(an)-341(edge)-341(conn)1(e)-1(ctin)1(g)-341(them.)-467(F)84(or)]TJ 0 -13.55 Td [(an)28(y)-238(in)28(te)-1(ger)]TJ/F22 10.9091 Tf 54.621 0 Td [(\016)-316(>)]TJ/F15 10.9091 Tf 19.806 0 Td [(0,)-257(a)]TJ/F22 10.9091 Tf 19.344 0 Td [(\016)]TJ/F15 10.9091 Tf 5.262 0 Td [(-o)28(v)28(erlap)-239(p)1(artition)-239(of)]TJ/F22 10.9091 Tf 96.34 0 Td [(W)]TJ/F15 10.9091 Tf 14.417 0 Td [(can)-238(b)-28(e)-238(de\014ned)-238(recursiv)28(ely)-239(as)-238(follo)28(ws.)-413(Giv)28(en)]TJ -209.79 -13.549 Td [(a)-344(0-o)28(v)28(erlap)-344(\050or)-343(non-o)28(v)27(erlapp)1(ing\051)-344(partition)-343(of)]TJ/F22 10.9091 Tf 216.249 0 Td [(W)]TJ/F15 10.9091 Tf 11.818 0 Td [(,)-346(i.e.)-344(a)-343(se)-1(t)-343(of)]TJ/F22 10.9091 Tf 63.378 0 Td [(m)]TJ/F15 10.9091 Tf 13.327 0 Td [(disjoin)28(t)-344(nonempt)28(y)-343(se)-1(ts)]TJ/F22 10.9091 Tf -304.772 -13.549 Td [(W)]TJ/F20 7.9701 Tf 11.818 3.959 Td [(0)]TJ/F23 7.9701 Tf -1.515 -7.015 Td [(i)]TJ/F25 10.9091 Tf 9.278 3.056 Td [(\032)]TJ/F22 10.9091 Tf 11.515 0 Td [(W)]TJ/F15 10.9091 Tf 14.857 0 Td [(suc)28(h)-279(that)]TJ/F25 10.9091 Tf 47.047 0 Td [([)]TJ/F23 7.9701 Tf 7.272 3.959 Td [(m)]TJ 0 -7.015 Td [(i)]TJ/F20 7.9701 Tf 2.884 0 Td [(=1)]TJ/F22 10.9091 Tf 11.318 3.056 Td [(W)]TJ/F20 7.9701 Tf 11.819 3.959 Td [(0)]TJ/F23 7.9701 Tf -1.516 -7.015 Td [(i)]TJ/F15 10.9091 Tf 9.278 3.056 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(W)]TJ/F15 10.9091 Tf 11.818 0 Td [(,)-290(a)]TJ/F22 10.9091 Tf 14.682 0 Td [(\016)]TJ/F15 10.9091 Tf 5.262 0 Td [(-o)28(v)28(erlap)-279(partition)-278(of)]TJ/F22 10.9091 Tf 97.661 0 Td [(W)]TJ/F15 10.9091 Tf 14.857 0 Td [(is)-279(obtai)1(ned)-279(b)28(y)-279(considering)]TJ -289.85 -13.549 Td [(the)-307(sets)]TJ/F22 10.9091 Tf 39.538 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.959 Td [(\016)]TJ -1.515 -7.015 Td [(i)]TJ/F25 10.9091 Tf 9.089 3.056 Td [(\033)]TJ/F22 10.9091 Tf 11.515 0 Td [(W)]TJ/F23 7.9701 Tf 11.819 4.588 Td [(\016)]TJ/F26 7.9701 Tf 4.046 0 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -12.147 -7.845 Td [(i)]TJ/F15 10.9091 Tf 20.224 3.257 Td [(obtained)-307(b)28(y)-306(including)-307(the)-306(v)28(e)-1(r)1(tice)-1(s)-306(that)-307(are)-306(adjacen)28(t)-307(to)-307(an)28(y)-306(v)27(ertex)]TJ -100.973 -13.549 Td [(in)]TJ/F22 10.9091 Tf 12.727 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 4.587 Td [(\016)]TJ/F26 7.9701 Tf 4.046 0 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -12.148 -7.844 Td [(i)]TJ/F15 10.9091 Tf 16.88 3.257 Td [(.)]TJ -22.974 -15.27 Td [(Let)]TJ/F22 10.9091 Tf 18.79 0 Td [(n)]TJ/F23 7.9701 Tf 6.548 3.959 Td [(\016)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 7.425 3.055 Td [(b)-28(e)-264(the)-264(size)-264(of)]TJ/F22 10.9091 Tf 63.706 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.959 Td [(\016)]TJ -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.94 3.055 Td [(and)]TJ/F22 10.9091 Tf 20.456 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F25 10.9091 Tf 7.658 3.055 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.182 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.813 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F26 7.9701 Tf 4.09 2.582 Td [(\002)]TJ/F23 7.9701 Tf 6.586 0 Td [(n)]TJ/F15 10.9091 Tf 8.517 -3.959 Td [(the)-264(restriction)-264(op)-28(erator)-264(that)-264(maps)-264(a)-264(v)28(ector)]TJ/F22 10.9091 Tf -211.559 -14.974 Td [(v)]TJ/F25 10.9091 Tf 8.993 0 Td [(2)-304(<)]TJ/F23 7.9701 Tf 18.465 3.959 Td [(n)]TJ/F15 10.9091 Tf 9.443 -3.959 Td [(on)28(to)-349(the)-349(v)28(ector)]TJ/F22 10.9091 Tf 76.601 0 Td [(v)]TJ/F23 7.9701 Tf 5.679 3.959 Td [(\016)]TJ -0.392 -7.015 Td [(i)]TJ/F25 10.9091 Tf 8.25 3.056 Td [(2)-304(<)]TJ/F23 7.9701 Tf 18.465 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.812 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F15 10.9091 Tf 8.394 -1.376 Td [(con)28(taining)-349(the)-349(comp)-28(onen)28(ts)-349(of)]TJ/F22 10.9091 Tf 144.983 0 Td [(v)]TJ/F15 10.9091 Tf 9.486 0 Td [(corresp)-28(onding)-349(to)-348(the)]TJ -313.505 -14.975 Td [(v)28(ertices)-369(in)]TJ/F22 10.9091 Tf 52.99 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.959 Td [(\016)]TJ -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.059 3.055 Td [(.)-551(The)-369(transp)-28(ose)-369(of)]TJ/F22 10.9091 Tf 94.001 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.654 3.055 Td [(is)-369(a)-369(prolongation)-369(op)-27(e)-1(rat)1(or)-369(from)]TJ/F25 10.9091 Tf 155.46 0 Td [(<)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.813 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F15 10.9091 Tf 8.613 -1.377 Td [(to)]TJ/F25 10.9091 Tf 13.722 0 Td [(<)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(n)]TJ/F15 10.9091 Tf 5.636 -3.959 Td [(.)-551(The)]TJ -384.617 -14.974 Td [(matrix)]TJ/F22 10.9091 Tf 35.133 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(\016)]TJ 0 -7.015 Td [(i)]TJ/F15 10.9091 Tf 7.574 3.056 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.015 Td [(i)]TJ/F22 10.9091 Tf 4.628 3.056 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.959 Td [(\016)]TJ -0.084 -7.015 Td [(i)]TJ/F15 10.9091 Tf 4.628 3.056 Td [(\051)]TJ/F23 7.9701 Tf 4.242 3.959 Td [(T)]TJ/F25 10.9091 Tf 9.635 -3.959 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.182 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.812 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F26 7.9701 Tf 4.09 2.583 Td [(\002)]TJ/F23 7.9701 Tf 6.586 0 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.812 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F15 10.9091 Tf 7.873 -1.376 Td [(can)-301(b)-28(e)-301(considered)-301(as)-301(a)-301(restriction)-301(of)]TJ/F22 10.9091 Tf 172.963 0 Td [(A)]TJ/F15 10.9091 Tf 11.467 0 Td [(corresp)-28(onding)]TJ -345.966 -13.549 Td [(to)-333(the)-334(set)]TJ/F22 10.9091 Tf 49.151 0 Td [(W)]TJ/F23 7.9701 Tf 11.819 3.958 Td [(\016)]TJ -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.059 3.056 Td [(.)]TJ -48.578 -13.643 Td [(The)]TJ/F18 10.9091 Tf 22.425 0 Td [(classic)51(al)-357(on)-1(e-)1(level)-358(AS)]TJ/F15 10.9091 Tf 106.723 0 Td [(preconditioner)-333(is)-334(de\014n)1(e)-1(d)-333(b)28(y)]TJ/F22 10.9091 Tf -4.792 -32.517 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(AS)]TJ/F15 10.9091 Tf 15.539 3.434 Td [(=)]TJ/F23 7.9701 Tf 15.649 13.637 Td [(m)]TJ/F28 10.9091 Tf -4.134 -3.273 Td [(X)]TJ/F23 7.9701 Tf 1.027 -23.451 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F15 10.9091 Tf 11.848 13.087 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 4.505 Td [(\016)]TJ -0.084 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.629 2.696 Td [(\051)]TJ/F23 7.9701 Tf 4.242 4.505 Td [(T)]TJ/F15 10.9091 Tf 6.604 -4.505 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 4.505 Td [(\016)]TJ 0 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.544 2.696 Td [(\051)]TJ/F26 7.9701 Tf 4.242 4.505 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -4.505 Td [(R)]TJ/F23 7.9701 Tf 8.368 4.505 Td [(\016)]TJ -0.085 -7.201 Td [(i)]TJ/F22 10.9091 Tf 4.629 2.696 Td [(;)]TJ/F15 10.9091 Tf -268.129 -35.907 Td [(where)]TJ/F22 10.9091 Tf 32.336 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(\016)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.971 3.056 Td [(is)-406(assumed)-406(to)-406(b)-27(e)-406(nonsingular.)-662(Its)-406(application)-405(to)-406(a)-406(v)28(ector)]TJ/F22 10.9091 Tf 283.187 0 Td [(v)]TJ/F25 10.9091 Tf 10.027 0 Td [(2)-399(<)]TJ/F23 7.9701 Tf 19.5 3.958 Td [(n)]TJ/F15 10.9091 Tf 10.063 -3.958 Td [(within)-406(a)]TJ -372.266 -13.55 Td [(Krylo)28(v)-333(solv)27(er)-333(requires)-333(the)-334(follo)28(wing)-333(three)-333(steps:)]TJ +1 0 0 1 -228.5751 -504.3831 cm +BT +/F15 10.9091 Tf 228.5751 504.3831 Td[(\051,)-308(where)]TJ/F24 10.9091 Tf 41.846 0 Td[(A)]TJ/F15 10.9091 Tf 11.2121 0 Td[(=)-278(\050)]TJ/F24 10.9091 Tf 15.7576 0 Td[(a)]TJ/F25 7.9701 Tf 5.7664 -1.6364 Td[(ij)]TJ/F15 10.9091 Tf 7.2653 1.6364 Td[(\051)]TJ/F27 10.9091 Tf 7.2727 0 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F28 7.9701 Tf 5.1382 0 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 8.9346 -3.9588 Td[(is)-303(a)-302(n)1(onsingu)1(lar)-302(s)-1(p)1(arse)-303(matrix)]TJ -270.1365 -13.5492 Td[(with)-321(a)-321(symme)-1(tr)1(ic)-322(n)1(onze)-1(r)1(o)-321(pattern)1(,)-324(let)]TJ/F24 10.9091 Tf 184.5267 0 Td[(G)]TJ/F15 10.9091 Tf 11.6075 0 Td[(=)-278(\050)]TJ/F24 10.9091 Tf 15.7575 0 Td[(W)27(;)-166(E)]TJ/F15 10.9091 Tf 23.5303 0 Td[(\051)-321(b)-27(e)-322(th)1(e)-322(ad)1(jace)-1(n)1(c)-1(y)-321(gr)1(aph)-320(of)]TJ/F24 10.9091 Tf 134.3786 0 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(,)-323(w)-1(h)1(e)-1(r)1(e)]TJ/F24 10.9091 Tf -377.9824 -13.5492 Td[(W)]TJ/F15 10.9091 Tf 15.4193 0 Td[(=)]TJ/F27 10.9091 Tf 12.0859 0 Td[(f)]TJ/F15 10.9091 Tf 5.4546 0 Td[(1)]TJ/F24 10.9091 Tf 5.4545 0 Td[(;)]TJ/F15 10.9091 Tf 4.8485 0 Td[(2)]TJ/F24 10.9091 Tf 5.4546 0 Td[(;)-166(:)-167(:)-166(:)-167(;)-166(n)]TJ/F27 10.9091 Tf 30.7903 0 Td[(g)]TJ/F15 10.9091 Tf 9.4334 0 Td[(and)]TJ/F24 10.9091 Tf 21.5546 0 Td[(E)]TJ/F15 10.9091 Tf 12.2829 0 Td[(=)]TJ/F27 10.9091 Tf 12.086 0 Td[(f)]TJ/F15 10.9091 Tf 5.4545 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(i;)-166(j)]TJ/F15 10.9091 Tf 13.7236 0 Td[(\051)-330(:)]TJ/F24 10.9091 Tf 14.4749 0 Td[(a)]TJ/F25 7.9701 Tf 5.7665 -1.6364 Td[(ij)]TJ/F27 10.9091 Tf 10.8664 1.6364 Td[(6)]TJ/F15 10.9091 Tf 0 0 Td[(=)-330(0)]TJ/F27 10.9091 Tf 17.5405 0 Td[(g)]TJ/F15 10.9091 Tf 9.4334 0 Td[(are)-365(th)1(e)-365(v)28(e)-1(rt)1(e)-1(x)-364(s)-1(et)-365(an)1(d)-365(th)1(e)-365(e)-1(d)1(ge)-366(set)-365(of)]TJ/F24 10.9091 Tf 184.4767 0 Td[(G)]TJ/F15 10.9091 Tf 8.5772 0 Td[(,)]TJ -409.4208 -13.5492 Td[(res)-1(p)-27(ec)-1(ti)1(v)28(e)-1(ly)84(.)-466(T)-1(w)28(o)-341(v)28(erti)1(c)-1(es)-341(are)-341(c)-1(al)1(le)-1(d)-340(ad)1(jace)-1(n)28(t)-340(if)-340(there)-341(is)-341(an)-340(edge)-341(c)-1(on)1(nec)-1(t)1(ing)-340(them)-1(.)-466(F)84(or)]TJ 0 -13.5492 Td[(an)28(y)-238(in)29(te)-1(ger)]TJ/F24 10.9091 Tf 54.621 0 Td[(\016)-316(>)]TJ/F15 10.9091 Tf 19.8067 0 Td[(0,)-257(a)]TJ/F24 10.9091 Tf 19.3437 0 Td[(\016)]TJ/F15 10.9091 Tf 5.2614 0 Td[(-o)27(v)28(erl)1(ap)-238(par)1(tition)-237(of)]TJ/F24 10.9091 Tf 96.3406 0 Td[(W)]TJ/F15 10.9091 Tf 14.4165 0 Td[(can)-238(b)-28(e)-238(de\014n)1(e)-1(d)-237(re)-1(cur)1(s)-1(i)1(v)28(e)-1(ly)-238(as)-238(foll)1(o)27(ws.)-413(Gi)1(v)28(e)-1(n)]TJ -209.7899 -13.5492 Td[(a)-344(0-o)28(v)28(e)-1(r)1(lap)-343(\050or)-343(non-o)28(v)28(e)-1(r)1(lapp)1(in)1(g\051)-344(par)1(tition)-343(of)]TJ/F24 10.9091 Tf 216.2495 0 Td[(W)]TJ/F15 10.9091 Tf 11.8182 0 Td[(,)-346(i.e.)-343(a)-344(se)-1(t)-343(of)]TJ/F24 10.9091 Tf 63.3773 0 Td[(m)]TJ/F15 10.9091 Tf 13.3269 0 Td[(di)1(s)-1(j)1(oin)28(t)-343(nonempt)28(y)-343(s)-1(ets)]TJ/F24 10.9091 Tf -304.7719 -13.5492 Td[(W)]TJ/F22 7.9701 Tf 11.8182 3.9588 Td[(0)]TJ/F25 7.9701 Tf -1.5152 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 9.2778 3.0555 Td[(\032)]TJ/F24 10.9091 Tf 11.5151 0 Td[(W)]TJ/F15 10.9091 Tf 14.8569 0 Td[(suc)27(h)-278(th)1(at)]TJ/F27 10.9091 Tf 47.047 0 Td[([)]TJ/F25 7.9701 Tf 7.2728 3.9588 Td[(m)]TJ 0 -7.0143 Td[(i)]TJ/F22 7.9701 Tf 2.8831 0 Td[(=1)]TJ/F24 10.9091 Tf 11.3188 3.0555 Td[(W)]TJ/F22 7.9701 Tf 11.8182 3.9588 Td[(0)]TJ/F25 7.9701 Tf -1.5151 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 9.2777 3.0555 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(W)]TJ/F15 10.9091 Tf 11.8182 0 Td[(,)-289(a)]TJ/F24 10.9091 Tf 14.6817 0 Td[(\016)]TJ/F15 10.9091 Tf 5.2614 0 Td[(-o)27(v)28(erl)1(ap)-279(p)1(arti)1(tion)-278(of)]TJ/F24 10.9091 Tf 97.6615 0 Td[(W)]TJ/F15 10.9091 Tf 14.8569 0 Td[(is)-279(ob)1(tained)-278(b)28(y)-278(c)-1(on)1(s)-1(i)1(derin)1(g)]TJ -289.8501 -13.5492 Td[(th)1(e)-307(s)-1(ets)]TJ/F24 10.9091 Tf 39.5379 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 9.0896 3.0555 Td[(\033)]TJ/F24 10.9091 Tf 11.5151 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 4.5878 Td[(\016)]TJ/F28 7.9701 Tf 4.046 0 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -12.1477 -7.8446 Td[(i)]TJ/F15 10.9091 Tf 20.2247 3.2568 Td[(obt)1(ained)-306(b)28(y)-307(i)1(nclud)1(ing)-306(the)-307(v)28(erti)1(c)-1(es)-307(that)-306(are)-307(adj)1(ac)-1(en)28(t)-306(to)-307(an)28(y)-306(v)28(ertex)]TJ -100.9733 -13.5492 Td[(in)]TJ/F24 10.9091 Tf 12.7273 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 4.5878 Td[(\016)]TJ/F28 7.9701 Tf 4.046 0 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -12.1477 -7.8446 Td[(i)]TJ/F15 10.9091 Tf 16.88 3.2568 Td[(.)]TJ -22.9738 -15.2694 Td[(Let)]TJ/F24 10.9091 Tf 18.79 0 Td[(n)]TJ/F25 7.9701 Tf 6.548 3.9588 Td[(\016)]TJ 0 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 7.425 3.0555 Td[(b)-27(e)-265(th)1(e)-265(size)-265(of)]TJ/F24 10.9091 Tf 63.7053 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 8.9402 3.0555 Td[(and)]TJ/F24 10.9091 Tf 20.4566 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0842 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 7.6586 3.0555 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F28 7.9701 Tf 4.0895 2.5822 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 8.5172 -3.9588 Td[(th)1(e)-265(res)-1(t)1(riction)-264(op)-27(erator)-264(th)1(at)-264(maps)-265(a)-264(v)28(ec)-1(t)1(or)]TJ/F24 10.9091 Tf -211.5596 -14.9745 Td[(v)]TJ/F27 10.9091 Tf 8.9929 0 Td[(2)-303(<)]TJ/F25 7.9701 Tf 18.4651 3.9588 Td[(n)]TJ/F15 10.9091 Tf 9.4427 -3.9588 Td[(on)28(to)-349(t)1(he)-349(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 76.601 0 Td[(v)]TJ/F25 7.9701 Tf 5.6793 3.9588 Td[(\016)]TJ -0.3914 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 8.2491 3.0555 Td[(2)-303(<)]TJ/F25 7.9701 Tf 18.4651 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F15 10.9091 Tf 8.394 -1.3766 Td[(con)28(tain)1(ing)-349(th)1(e)-350(comp)-28(on)1(e)-1(n)29(ts)-350(of)]TJ/F24 10.9091 Tf 144.9832 0 Td[(v)]TJ/F15 10.9091 Tf 9.4857 0 Td[(corres)-1(p)-27(ond)1(in)1(g)-349(to)-349(the)]TJ -313.5049 -14.9745 Td[(v)28(ertice)-1(s)-369(in)]TJ/F24 10.9091 Tf 52.9901 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 6.0593 3.0555 Td[(.)-551(The)-369(transp)-27(os)-1(e)-369(of)]TJ/F24 10.9091 Tf 94.0006 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 8.6538 3.0555 Td[(is)-369(a)-369(pr)1(olongati)1(on)-369(op)-27(e)-1(r)1(ator)-369(fr)1(om)]TJ/F27 10.9091 Tf 155.4601 0 Td[(<)]TJ/F25 7.9701 Tf 7.8788 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F15 10.9091 Tf 8.613 -1.3766 Td[(to)]TJ/F27 10.9091 Tf 13.7223 0 Td[(<)]TJ/F25 7.9701 Tf 7.8788 3.9588 Td[(n)]TJ/F15 10.9091 Tf 5.6363 -3.9588 Td[(.)-551(The)]TJ -384.6175 -14.9745 Td[(matrix)]TJ/F24 10.9091 Tf 35.1334 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 3.9588 Td[(\016)]TJ 0 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 7.5744 3.0555 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F24 10.9091 Tf 4.6284 3.0555 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 4.6284 3.0555 Td[(\051)]TJ/F25 7.9701 Tf 4.2424 3.9588 Td[(T)]TJ/F27 10.9091 Tf 9.6348 -3.9588 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F28 7.9701 Tf 4.0895 2.5822 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F15 10.9091 Tf 7.8725 -1.3766 Td[(can)-301(b)-27(e)-302(considered)-301(as)-302(a)-301(r)1(e)-1(striction)-300(of)]TJ/F24 10.9091 Tf 172.9636 0 Td[(A)]TJ/F15 10.9091 Tf 11.4666 0 Td[(corres)-1(p)-27(ond)1(in)1(g)]TJ -345.9661 -13.5492 Td[(to)-333(the)-333(s)-1(et)]TJ/F24 10.9091 Tf 49.1515 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 6.0593 3.0555 Td[(.)]TJ -48.5774 -13.6429 Td[(The)]TJ/F20 10.9091 Tf 22.4243 0 Td[(class)1(ic)51(al)-357(o)-1(ne-l)1(evel)-357(A)-1(S)]TJ/F15 10.9091 Tf 106.7234 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-333(i)1(s)-334(de\014n)1(e)-1(d)-333(b)29(y)]TJ/F24 10.9091 Tf -4.7921 -32.5163 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5879 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.022 Td[(AS)]TJ/F15 10.9091 Tf 15.5385 3.4341 Td[(=)]TJ/F25 7.9701 Tf 15.6487 13.6364 Td[(m)]TJ/F30 10.9091 Tf -4.1336 -3.2727 Td[(X)]TJ/F25 7.9701 Tf 1.0269 -23.4509 Td[(i)]TJ/F22 7.9701 Tf 2.8831 0 Td[(=1)]TJ/F15 10.9091 Tf 11.8476 13.0872 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(R)]TJ/F25 7.9701 Tf 8.3675 4.5043 Td[(\016)]TJ -0.0843 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.6284 2.6969 Td[(\051)]TJ/F25 7.9701 Tf 4.2424 4.5043 Td[(T)]TJ/F15 10.9091 Tf 6.6045 -4.5043 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 4.5043 Td[(\016)]TJ 0 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.5441 2.6969 Td[(\051)]TJ/F28 7.9701 Tf 4.2424 4.5043 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -4.5043 Td[(R)]TJ/F25 7.9701 Tf 8.3675 4.5043 Td[(\016)]TJ -0.0843 -7.2012 Td[(i)]TJ/F24 10.9091 Tf 4.6284 2.6969 Td[(;)]TJ/F15 10.9091 Tf -268.1287 -35.9079 Td[(where)]TJ/F24 10.9091 Tf 32.3362 0 Td[(A)]TJ/F25 7.9701 Tf 8.1819 3.9588 Td[(\016)]TJ 0 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 8.9712 3.0555 Td[(is)-406(ass)-1(u)1(m)-1(ed)-406(to)-405(b)-28(e)-406(non)1(s)-1(i)1(ngu)1(lar.)-662(Its)-406(ap)1(pli)1(c)-1(ation)-405(to)-406(a)-405(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 283.1864 0 Td[(v)]TJ/F27 10.9091 Tf 10.0275 0 Td[(2)-398(<)]TJ/F25 7.9701 Tf 19.4997 3.9588 Td[(n)]TJ/F15 10.9091 Tf 10.0635 -3.9588 Td[(with)1(in)-406(a)]TJ -372.2664 -13.5492 Td[(Kr)1(ylo)28(v)-333(s)-1(olv)28(er)-333(requ)1(ires)-334(the)-333(foll)1(o)27(win)1(g)-334(t)1(hree)-334(ste)-1(p)1(s)-1(:)]TJ +ET +1 0 0 1 86.3998 203.7409 cm 0 g 0 G - 13.333 -22.89 Td [(1.)]TJ +1 0 0 1 -86.3998 -203.7409 cm +BT +/F15 10.9091 Tf 99.7331 203.7409 Td[(1.)]TJ +ET +1 0 0 1 108.218 203.7409 cm 0 g 0 G - [-500(restriction)-333(of)]TJ/F22 10.9091 Tf 78.606 0 Td [(v)]TJ/F15 10.9091 Tf 9.316 0 Td [(as)]TJ/F22 10.9091 Tf 13.394 0 Td [(v)]TJ/F23 7.9701 Tf 5.288 -1.636 Td [(i)]TJ/F15 10.9091 Tf 6.411 1.636 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F22 10.9091 Tf 4.628 3.055 Td [(v)]TJ/F15 10.9091 Tf 5.679 0 Td [(,)]TJ/F22 10.9091 Tf 6.667 0 Td [(i)]TJ/F15 10.9091 Tf 6.789 0 Td [(=)-278(1)]TJ/F22 10.9091 Tf 16.969 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(m)]TJ/F15 10.9091 Tf 33.821 0 Td [(;)]TJ +1 0 0 1 -108.218 -203.7409 cm +BT +/F15 10.9091 Tf 113.6726 203.7409 Td[(res)-1(t)1(riction)-333(of)]TJ/F24 10.9091 Tf 64.6667 0 Td[(v)]TJ/F15 10.9091 Tf 9.3157 0 Td[(as)]TJ/F24 10.9091 Tf 13.3939 0 Td[(v)]TJ/F25 7.9701 Tf 5.2879 -1.6364 Td[(i)]TJ/F15 10.9091 Tf 6.4115 1.6364 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(R)]TJ/F25 7.9701 Tf 8.3675 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F24 10.9091 Tf 4.6284 3.0555 Td[(v)]TJ/F15 10.9091 Tf 5.6793 0 Td[(,)]TJ/F24 10.9091 Tf 6.6667 0 Td[(i)]TJ/F15 10.9091 Tf 6.7885 0 Td[(=)-278(1)]TJ/F24 10.9091 Tf 16.9697 0 Td[(;)-166(:)-167(:)-166(:)-167(;)-166(m)]TJ/F15 10.9091 Tf 33.8206 0 Td[(;)]TJ +ET +1 0 0 1 86.3998 180.8506 cm 0 g 0 G - -207.367 -22.89 Td [(2.)]TJ +1 0 0 1 -86.3998 -180.8506 cm +BT +/F15 10.9091 Tf 99.7331 180.8506 Td[(2.)]TJ +ET +1 0 0 1 108.218 180.8506 cm 0 g 0 G - [-500(solution)-333(of)-334(th)1(e)-334(linear)-333(systems)]TJ/F22 10.9091 Tf 157.243 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(\016)]TJ 0 -7.015 Td [(i)]TJ/F22 10.9091 Tf 4.544 3.056 Td [(w)]TJ/F23 7.9701 Tf 7.81 -1.637 Td [(i)]TJ/F15 10.9091 Tf 6.411 1.637 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(v)]TJ/F23 7.9701 Tf 5.287 -1.637 Td [(i)]TJ/F15 10.9091 Tf 3.382 1.637 Td [(,)]TJ/F22 10.9091 Tf 6.666 0 Td [(i)]TJ/F15 10.9091 Tf 6.789 0 Td [(=)-278(1)]TJ/F22 10.9091 Tf 16.97 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(m)]TJ/F15 10.9091 Tf 33.82 0 Td [(;)]TJ +1 0 0 1 -108.218 -180.8506 cm +BT +/F15 10.9091 Tf 113.6726 180.8506 Td[(soluti)1(on)-333(of)-333(the)-333(linear)-333(sys)-1(tems)]TJ/F24 10.9091 Tf 143.3032 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 3.9588 Td[(\016)]TJ 0 -7.0143 Td[(i)]TJ/F24 10.9091 Tf 4.5441 3.0555 Td[(w)]TJ/F25 7.9701 Tf 7.81 -1.6364 Td[(i)]TJ/F15 10.9091 Tf 6.4115 1.6364 Td[(=)]TJ/F24 10.9091 Tf 11.5152 0 Td[(v)]TJ/F25 7.9701 Tf 5.2878 -1.6364 Td[(i)]TJ/F15 10.9091 Tf 3.3813 1.6364 Td[(,)]TJ/F24 10.9091 Tf 6.6667 0 Td[(i)]TJ/F15 10.9091 Tf 6.7886 0 Td[(=)-278(1)]TJ/F24 10.9091 Tf 16.9696 0 Td[(;)-166(:)-167(:)-166(:)-167(;)-166(m)]TJ/F15 10.9091 Tf 33.8206 0 Td[(;)]TJ +ET +1 0 0 1 86.3998 157.9603 cm 0 g 0 G - -268.62 -22.89 Td [(3.)]TJ +1 0 0 1 -86.3998 -157.9603 cm +BT +/F15 10.9091 Tf 99.7331 157.9603 Td[(3.)]TJ +ET +1 0 0 1 108.218 157.9603 cm 0 g 0 G - [-500(prolongation)-333(and)-333(sum)-334(of)-333(the)]TJ/F22 10.9091 Tf 153.122 0 Td [(w)]TJ/F23 7.9701 Tf 7.81 -1.637 Td [(i)]TJ/F15 10.9091 Tf 3.381 1.637 Td [('s,)-333(i.e.)]TJ/F22 10.9091 Tf 32.788 0 Td [(w)]TJ/F15 10.9091 Tf 11.134 0 Td [(=)]TJ/F28 10.9091 Tf 11.515 8.181 Td [(P)]TJ/F23 7.9701 Tf 11.515 -3.154 Td [(m)]TJ 0 -8.253 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F15 10.9091 Tf 11.319 3.226 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.958 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 4.628 3.056 Td [(\051)]TJ/F23 7.9701 Tf 4.242 3.958 Td [(T)]TJ/F22 10.9091 Tf 6.605 -3.958 Td [(w)]TJ/F23 7.9701 Tf 7.81 -1.637 Td [(i)]TJ/F15 10.9091 Tf 3.381 1.637 Td [(.)]TJ -297.992 -22.891 Td [(Note)-473(th)1(at)-473(the)-472(linear)-473(systems)-473(at)-472(step)-473(2)-472(are)-473(usually)-472(solv)28(ed)-473(appro)28(ximately)83(,)-507(e.g.)-472(using)]TJ 0 -13.549 Td [(incomplete)-333(LU)-334(factorizations)-333(suc)28(h)-334(as)-333(ILU\050)]TJ/F22 10.9091 Tf 202.637 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-333(MILU\050)]TJ/F22 10.9091 Tf 44.091 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051)-333(and)-334(ILU\050)]TJ/F22 10.9091 Tf 52.273 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-333([)]TJ +1 0 0 1 -108.218 -157.9603 cm +BT +/F15 10.9091 Tf 113.6726 157.9603 Td[(pr)1(olongat)1(ion)-333(and)-333(sum)-333(of)-333(the)]TJ/F24 10.9091 Tf 139.1819 0 Td[(w)]TJ/F25 7.9701 Tf 7.81 -1.6363 Td[(i)]TJ/F15 10.9091 Tf 3.3813 1.6363 Td[('s,)-333(i.e.)]TJ/F24 10.9091 Tf 32.7879 0 Td[(w)]TJ/F15 10.9091 Tf 11.1338 0 Td[(=)]TJ/F30 10.9091 Tf 11.5151 8.1819 Td[(P)]TJ/F25 7.9701 Tf 11.5152 -3.1548 Td[(m)]TJ 0 -8.2525 Td[(i)]TJ/F22 7.9701 Tf 2.8831 0 Td[(=1)]TJ/F15 10.9091 Tf 11.3189 3.2254 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 4.6284 3.0555 Td[(\051)]TJ/F25 7.9701 Tf 4.2425 3.9588 Td[(T)]TJ/F24 10.9091 Tf 6.6044 -3.9588 Td[(w)]TJ/F25 7.9701 Tf 7.81 -1.6364 Td[(i)]TJ/F15 10.9091 Tf 3.3813 1.6364 Td[(.)]TJ -297.9922 -22.8903 Td[(Note)-473(th)1(at)-473(th)1(e)-473(lin)1(e)-1(ar)-472(sys)-1(t)1(e)-1(ms)-473(at)-473(step)-472(2)-473(are)-473(u)1(s)-1(u)1(ally)-472(solv)28(e)-1(d)-472(ap)1(pr)1(o)27(x)1(im)-1(at)1(e)-1(ly)84(,)-507(e)-1(.)1(g.)-473(u)1(s)-1(i)1(ng)]TJ 0 -13.5492 Td[(in)1(c)-1(ompl)1(e)-1(te)-334(LU)-333(f)1(ac)-1(tor)1(iz)-1(ati)1(ons)-334(suc)28(h)-333(as)-334(ILU\050)]TJ/F24 10.9091 Tf 202.6366 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)-333(MILU\050)]TJ/F24 10.9091 Tf 44.091 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051)-333(and)-333(ILU\050)]TJ/F24 10.9091 Tf 52.2728 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051)-333([)]TJ +ET +1 0 0 1 421.563 121.5209 cm 1 0 0 rg 1 0 0 RG - [(19)]TJ +1 0 0 1 -421.563 -121.5209 cm +BT +/F15 10.9091 Tf 421.563 121.5209 Td[(19)]TJ +ET +1 0 0 1 432.4721 121.5209 cm 0 g 0 G - [(,)-334(Chapter)-333(10].)]TJ +1 0 0 1 -432.4721 -121.5209 cm +BT +/F15 10.9091 Tf 432.4721 121.5209 Td[(,)-333(Chap)1(te)-1(r)-333(10].)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -268 0 obj << +276 0 obj << /Type /Page -/Contents 269 0 R -/Resources 267 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 238 0 R -/Annots [ 248 0 R 256 0 R 257 0 R 258 0 R 259 0 R 260 0 R 261 0 R 262 0 R 263 0 R 264 0 R ] +/Contents 277 0 R +/Resources 275 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 258 0 R +/Annots [ 279 0 R 280 0 R 281 0 R 282 0 R 283 0 R 284 0 R 285 0 R 286 0 R 287 0 R 306 0 R ] >> endobj -248 0 obj << +279 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [238.858 689.591 251.76 698.614] +/Rect [238.8582 689.5909 251.7598 698.6137] /Subtype /Link /A << /S /GoTo /D (cite.StubenGMD69_99) >> >> endobj -256 0 obj << +280 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [197.525 648.85 204.972 657.872] +/Rect [197.5253 648.8496 204.9724 657.8724] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -257 0 obj << +281 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [210.398 648.85 223.3 657.872] +/Rect [210.3983 648.8496 223.2999 657.8724] /Subtype /Link /A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> >> endobj -258 0 obj << +282 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [421.977 635.3 434.879 644.323] +/Rect [421.977 635.3004 434.8787 644.3232] /Subtype /Link /A << /S /GoTo /D (cite.TUMINARO_TONG) >> >> endobj -259 0 obj << +283 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [229.646 594.653 237.093 603.676] +/Rect [229.6461 594.6528 237.0931 603.6756] /Subtype /Link /A << /S /GoTo /D (cite.para_04) >> >> endobj -260 0 obj << +284 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [241.767 594.653 249.214 603.676] +/Rect [241.7673 594.6528 249.2144 603.6756] /Subtype /Link /A << /S /GoTo /D (cite.aaecc_07) >> >> endobj -261 0 obj << +285 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [253.888 594.653 261.336 603.676] +/Rect [253.8885 594.6528 261.3356 603.6756] /Subtype /Link /A << /S /GoTo /D (cite.apnum_07) >> >> endobj -262 0 obj << +286 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [266.01 594.653 278.911 603.676] +/Rect [266.0097 594.6528 278.9113 603.6756] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -263 0 obj << +287 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [222.124 500.66 229.571 513.561] +/Rect [222.1242 500.6596 229.5713 513.5612] /Subtype /Link /A << /S /GoTo /D (equation.1) >> >> endobj -264 0 obj << +306 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [420.567 120.525 433.468 129.547] +/Rect [420.5667 120.5246 433.4683 129.5474] /Subtype /Link /A << /S /GoTo /D (cite.Saad_book) >> >> endobj -270 0 obj << -/D [268 0 R /XYZ 86.4 740.002 null] +278 0 obj << +/D [276 0 R /XYZ 86.3998 740.0018 null] >> endobj 50 0 obj << -/D [268 0 R /XYZ 86.4 577.215 null] +/D [276 0 R /XYZ 86.3998 577.2151 null] >> endobj -276 0 obj << -/D [268 0 R /XYZ 86.4 219.839 null] +303 0 obj << +/D [276 0 R /XYZ 86.3998 219.8394 null] >> endobj -277 0 obj << -/D [268 0 R /XYZ 86.4 196.015 null] +304 0 obj << +/D [276 0 R /XYZ 86.3998 196.0148 null] >> endobj -278 0 obj << -/D [268 0 R /XYZ 86.4 173.125 null] +305 0 obj << +/D [276 0 R /XYZ 86.3998 173.1245 null] >> endobj -267 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F18 173 0 R /F17 111 0 R /F22 175 0 R /F23 271 0 R /F25 176 0 R /F26 272 0 R /F20 273 0 R /F24 274 0 R /F28 275 0 R >> +275 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F20 181 0 R /F19 113 0 R /F24 186 0 R /F25 290 0 R /F27 189 0 R /F28 293 0 R /F22 296 0 R /F26 299 0 R /F30 302 0 R >> /ProcSet [ /PDF /Text ] >> endobj -290 0 obj << -/Length 13849 +315 0 obj << +/Length 16183 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(4)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(4)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(Mul)67(ti-level)-378(Domain)-378(Decompo)1(siti)-1(o)1(n)-378(Ba)22(ck)22(gr)22(ound)]TJ/F15 10.9091 Tf 401.542 0 Td [(11)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Mul)66(ti-level)-378(Domain)-378(Decomp)1(osition)-378(Ba)22(ck)23(gr)22(oun)-1(d)]TJ/F15 10.9091 Tf 391.3906 0 Td[(11)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G - -384.605 -35.866 Td [(A)-318(v)56(arian)28(t)-318(of)-318(the)-317(classic)-1(al)-317(AS)-318(preconditioner)-317(that)-318(outp)-28(erforms)-318(it)-317(in)-318(terms)-318(of)-317(con)27(v)28(er-)]TJ -16.937 -13.549 Td [(gence)-265(rate)-266(and)-265(of)-265(computation)-265(and)-265(comm)27(un)1(ic)-1(ati)1(on)-266(time)-265(on)-265(parallel)-265(distributed-memory)]TJ 0 -13.549 Td [(computers)-387(is)-387(the)-387(so-called)]TJ/F18 10.9091 Tf 129.216 0 Td [(R)51(estricte)51(d)-407(AS)-407(\050RAS\051)]TJ/F15 10.9091 Tf 105.994 0 Td [(preconditioner)-387([)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F15 10.9091 Tf 110.5367 704.1363 Td[(A)-318(v)56(ari)1(an)28(t)-318(of)-317(the)-318(class)-1(ical)-318(AS)-317(p)1(rec)-1(on)1(diti)1(oner)-318(th)1(at)-318(out)1(p)-28(erf)1(orms)-319(i)1(t)-318(in)-317(terms)-319(of)-317(con)28(v)28(e)-1(r)1(-)]TJ -16.9365 -13.5492 Td[(gence)-266(rate)-265(and)-265(of)-265(compu)1(tation)-265(an)1(d)-265(c)-1(omm)28(uni)1(c)-1(ati)1(on)-265(time)-266(on)-265(p)1(arallel)-265(di)1(s)-1(tr)1(ibu)1(te)-1(d)1(-m)-1(em)-1(or)1(y)]TJ 0 -13.5492 Td[(com)-1(p)1(uters)-387(is)-387(the)-387(s)-1(o-called)]TJ/F20 10.9091 Tf 129.2159 0 Td[(R)51(estricte)51(d)-407(AS)-408(\050)1(R)-1(AS\051)]TJ/F15 10.9091 Tf 105.9938 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-386([)]TJ +ET +1 0 0 1 404.6064 677.0379 cm 1 0 0 rg 1 0 0 RG - [(5)]TJ +1 0 0 1 -404.6064 -677.0379 cm +BT +/F15 10.9091 Tf 404.6064 677.0379 Td[(5)]TJ +ET +1 0 0 1 410.0609 677.0379 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -410.0609 -677.0379 cm +BT +/F15 10.9091 Tf 410.0609 677.0379 Td[(,)]TJ +ET +1 0 0 1 417.3118 677.0379 cm 1 0 0 rg 1 0 0 RG - [-387(13)]TJ +1 0 0 1 -417.3118 -677.0379 cm +BT +/F15 10.9091 Tf 417.3118 677.0379 Td[(13)]TJ +ET +1 0 0 1 428.2209 677.0379 cm 0 g 0 G - [(].)-605(It)-387(is)-386(obtained)]TJ -235.21 -13.549 Td [(b)28(y)-408(zeroing)-407(the)-408(comp)-28(onen)28(ts)-407(of)]TJ/F22 10.9091 Tf 148.078 0 Td [(w)]TJ/F23 7.9701 Tf 7.81 -1.637 Td [(i)]TJ/F15 10.9091 Tf 7.827 1.637 Td [(corresp)-28(onding)-407(to)-408(the)-407(o)28(v)27(erlapping)-407(v)28(ertices)-408(when)-407(ap-)]TJ -163.715 -13.549 Td [(plying)-349(the)-349(p)1(rolongation.)-491(Therefore,)-353(RAS)-349(di\013ers)-348(from)-349(classical)-349(AS)-349(b)28(y)-349(the)-349(prolongation)]TJ 0 -13.55 Td [(op)-28(erators,)-400(whic)27(h)-387(are)-387(substituted)-387(b)28(y)-387(\050)]TJ 182.692 2.758 Td [(~)]TJ/F22 10.9091 Tf -2.366 -2.758 Td [(R)]TJ/F20 7.9701 Tf 8.367 3.959 Td [(0)]TJ/F23 7.9701 Tf -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 4.817 3.055 Td [(\051)]TJ/F23 7.9701 Tf 4.242 3.959 Td [(T)]TJ/F25 10.9091 Tf 10.614 -3.959 Td [(2)-367(<)]TJ/F23 7.9701 Tf 19.16 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.139 2.813 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F26 7.9701 Tf 4.089 2.582 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F15 10.9091 Tf 5.636 -3.959 Td [(,)-401(where)]TJ 41.899 2.758 Td [(~)]TJ/F22 10.9091 Tf -2.366 -2.758 Td [(R)]TJ/F20 7.9701 Tf 8.368 3.959 Td [(0)]TJ/F23 7.9701 Tf -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 9.04 3.055 Td [(is)-387(obtained)-387(b)28(y)-388(zeroing)]TJ -305.75 -13.549 Td [(the)-333(ro)27(ws)-333(of)]TJ/F22 10.9091 Tf 56.455 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.265 3.055 Td [(corresp)-28(onding)-333(to)-333(the)-334(v)28(ertices)-333(in)]TJ/F22 10.9091 Tf 154.454 0 Td [(W)]TJ/F23 7.9701 Tf 11.819 3.959 Td [(\016)]TJ -1.516 -7.014 Td [(i)]TJ/F25 10.9091 Tf 6.06 3.055 Td [(n)]TJ/F22 10.9091 Tf 5.454 0 Td [(W)]TJ/F20 7.9701 Tf 11.818 3.959 Td [(0)]TJ/F23 7.9701 Tf -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.248 3.055 Td [(:)]TJ/F22 10.9091 Tf -127.805 -29.635 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.775 -8.022 Td [(R)-6(AS)]TJ/F15 10.9091 Tf 21.894 3.434 Td [(=)]TJ/F23 7.9701 Tf 15.649 13.637 Td [(m)]TJ/F28 10.9091 Tf -4.134 -3.273 Td [(X)]TJ/F23 7.9701 Tf 1.027 -23.451 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F15 10.9091 Tf 11.848 13.087 Td [(\050)]TJ 6.608 2.758 Td [(~)]TJ/F22 10.9091 Tf -2.366 -2.758 Td [(R)]TJ/F20 7.9701 Tf 8.368 4.505 Td [(0)]TJ/F23 7.9701 Tf -0.085 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.817 2.696 Td [(\051)]TJ/F23 7.9701 Tf 4.242 4.505 Td [(T)]TJ/F15 10.9091 Tf 6.605 -4.505 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 4.505 Td [(\016)]TJ 0 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.544 2.696 Td [(\051)]TJ/F26 7.9701 Tf 4.243 4.505 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -4.505 Td [(R)]TJ/F23 7.9701 Tf 8.368 4.505 Td [(\016)]TJ -0.084 -7.201 Td [(i)]TJ/F22 10.9091 Tf 4.628 2.696 Td [(:)]TJ/F15 10.9091 Tf -271.401 -30.78 Td [(Analogously)83(,)-333(the)-333(AS)-334(v)56(arian)28(t)-333(called)]TJ/F18 10.9091 Tf 168.576 0 Td [(AS)-358(with)-358(Harmonic)-357(extension)-358(\050ASH\051)]TJ/F15 10.9091 Tf 176.608 0 Td [(is)-333(de\014ned)-334(b)28(y)]TJ/F22 10.9091 Tf -207.735 -29.306 Td [(M)]TJ/F26 7.9701 Tf 11.772 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(AS)-56(H)]TJ/F15 10.9091 Tf 23.037 3.434 Td [(=)]TJ/F23 7.9701 Tf 15.649 13.636 Td [(m)]TJ/F28 10.9091 Tf -4.133 -3.273 Td [(X)]TJ/F23 7.9701 Tf 1.026 -23.451 Td [(i)]TJ/F20 7.9701 Tf 2.884 0 Td [(=1)]TJ/F15 10.9091 Tf 11.847 13.088 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 4.504 Td [(\016)]TJ -0.084 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.628 2.697 Td [(\051)]TJ/F23 7.9701 Tf 4.243 4.504 Td [(T)]TJ/F15 10.9091 Tf 6.604 -4.504 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 4.504 Td [(\016)]TJ 0 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.544 2.697 Td [(\051)]TJ/F26 7.9701 Tf 4.243 4.504 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 7.098 -1.747 Td [(~)]TJ/F22 10.9091 Tf -2.365 -2.757 Td [(R)]TJ/F20 7.9701 Tf 8.367 4.504 Td [(0)]TJ/F23 7.9701 Tf -0.084 -7.201 Td [(i)]TJ/F22 10.9091 Tf 4.816 2.697 Td [(:)]TJ/F15 10.9091 Tf -271.972 -30.174 Td [(W)83(e)-334(note)-335(that)-335(for)]TJ/F22 10.9091 Tf 83.422 0 Td [(\016)]TJ/F15 10.9091 Tf 8.316 0 Td [(=)-280(0)-335(the)-334(three)-335(v)56(arian)28(ts)-335(of)-335(the)-334(AS)-335(preconditioner)-335(are)-334(all)-335(equal)-334(to)-335(the)]TJ -91.738 -13.55 Td [(blo)-28(c)28(k-Jacobi)-333(preconditioner.)]TJ 16.937 -13.549 Td [(As)-358(already)-358(observ)27(ed,)-364(the)-358(con)27(v)28(ergence)-358(rate)-358(of)-359(the)-358(one-lev)28(el)-358(Sc)27(h)28(w)28(arz)-358(preconditioned)]TJ -16.937 -13.549 Td [(iterativ)28(e)-359(solv)28(ers)-358(deteriorates)-358(as)-359(the)-358(n)28(um)28(b)-28(er)]TJ/F22 10.9091 Tf 211.422 0 Td [(m)]TJ/F15 10.9091 Tf 13.487 0 Td [(of)-358(partitions)-358(of)]TJ/F22 10.9091 Tf 75.454 0 Td [(W)]TJ/F15 10.9091 Tf 15.727 0 Td [(increases)-358([)]TJ +1 0 0 1 -428.2209 -677.0379 cm +BT +/F15 10.9091 Tf 428.2209 677.0379 Td[(].)-605(It)-387(i)1(s)-388(ob)1(tain)1(e)-1(d)]TJ -334.6207 -13.5492 Td[(b)28(y)-407(z)-1(eroi)1(ng)-408(t)1(he)-408(com)-1(p)-27(onen)28(ts)-408(of)]TJ/F24 10.9091 Tf 148.0779 0 Td[(w)]TJ/F25 7.9701 Tf 7.8101 -1.6363 Td[(i)]TJ/F15 10.9091 Tf 7.8271 1.6363 Td[(corres)-1(p)-27(ond)1(in)1(g)-408(to)-407(the)-408(o)28(v)28(e)-1(r)1(lapp)1(in)1(g)-408(v)28(ertice)-1(s)-408(wh)1(e)-1(n)-407(ap)1(-)]TJ -163.7151 -13.5492 Td[(pl)1(yin)1(g)-349(the)-349(pr)1(olongat)1(ion.)-490(T)-1(h)1(e)-1(r)1(e)-1(f)1(ore,)-353(RAS)-348(di\013e)-1(r)1(s)-349(from)-349(clas)-1(sical)-349(AS)-348(b)28(y)-349(t)1(he)-349(pr)1(olongati)1(on)]TJ 0 -13.5492 Td[(op)-27(e)-1(r)1(ators,)-401(whi)1(c)27(h)-387(ar)1(e)-388(s)-1(u)1(bstitu)1(te)-1(d)-386(b)28(y)-387(\050)]TJ 182.6914 2.7576 Td[(~)]TJ/F24 10.9091 Tf -2.3655 -2.7576 Td[(R)]TJ/F22 7.9701 Tf 8.3674 3.9588 Td[(0)]TJ/F25 7.9701 Tf -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 4.8166 3.0555 Td[(\051)]TJ/F25 7.9701 Tf 4.2425 3.9588 Td[(T)]TJ/F27 10.9091 Tf 10.6135 -3.9588 Td[(2)-367(<)]TJ/F25 7.9701 Tf 19.1606 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F28 7.9701 Tf 4.0895 2.5822 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 5.6363 -3.9588 Td[(,)-400(w)-1(h)1(e)-1(r)1(e)]TJ 41.8991 2.7576 Td[(~)]TJ/F24 10.9091 Tf -2.3655 -2.7576 Td[(R)]TJ/F22 7.9701 Tf 8.3674 3.9588 Td[(0)]TJ/F25 7.9701 Tf -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 9.0403 3.0555 Td[(is)-387(obtain)1(e)-1(d)-386(b)28(y)-387(z)-1(eroi)1(ng)]TJ -305.7498 -13.5492 Td[(th)1(e)-334(ro)28(ws)-334(of)]TJ/F24 10.9091 Tf 56.4546 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 8.2648 3.0555 Td[(corres)-1(p)-27(ond)1(in)1(g)-334(to)-333(th)1(e)-334(v)28(e)-1(r)1(tice)-1(s)-334(i)1(n)]TJ/F24 10.9091 Tf 154.4547 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 6.0593 3.0555 Td[(n)]TJ/F24 10.9091 Tf 5.4546 0 Td[(W)]TJ/F22 7.9701 Tf 11.8182 3.9588 Td[(0)]TJ/F25 7.9701 Tf -1.5152 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 6.2475 3.0555 Td[(:)]TJ/F24 10.9091 Tf -127.8046 -29.6348 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5879 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7758 -8.022 Td[(R)-6(AS)]TJ/F15 10.9091 Tf 21.8944 3.4341 Td[(=)]TJ/F25 7.9701 Tf 15.6487 13.6364 Td[(m)]TJ/F30 10.9091 Tf -4.1336 -3.2727 Td[(X)]TJ/F25 7.9701 Tf 1.0269 -23.4509 Td[(i)]TJ/F22 7.9701 Tf 2.8831 0 Td[(=1)]TJ/F15 10.9091 Tf 11.8476 13.0872 Td[(\050)]TJ 6.608 2.7576 Td[(~)]TJ/F24 10.9091 Tf -2.3655 -2.7576 Td[(R)]TJ/F22 7.9701 Tf 8.3674 4.5043 Td[(0)]TJ/F25 7.9701 Tf -0.0843 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.8166 2.6969 Td[(\051)]TJ/F25 7.9701 Tf 4.2424 4.5043 Td[(T)]TJ/F15 10.9091 Tf 6.6045 -4.5043 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 4.5043 Td[(\016)]TJ 0 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.5441 2.6969 Td[(\051)]TJ/F28 7.9701 Tf 4.2424 4.5043 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -4.5043 Td[(R)]TJ/F25 7.9701 Tf 8.3675 4.5043 Td[(\016)]TJ -0.0843 -7.2012 Td[(i)]TJ/F24 10.9091 Tf 4.6284 2.6969 Td[(:)]TJ/F15 10.9091 Tf -271.4008 -30.7803 Td[(Anal)1(ogously)83(,)-333(th)1(e)-334(AS)-333(v)56(ari)1(an)28(t)-333(c)-1(all)1(e)-1(d)]TJ/F20 10.9091 Tf 168.5759 0 Td[(AS)-358(w)-1(i)1(t)-1(h)-358(Harm)1(o)-1(ni)1(c)-358(extension)-358(\050AS)-1(H\051)]TJ/F15 10.9091 Tf 176.6079 0 Td[(is)-334(d)1(e)-1(\014)1(ned)-333(b)28(y)]TJ/F24 10.9091 Tf -207.7353 -29.3065 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5879 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.022 Td[(AS)-56(H)]TJ/F15 10.9091 Tf 23.0374 3.4341 Td[(=)]TJ/F25 7.9701 Tf 15.6487 13.6364 Td[(m)]TJ/F30 10.9091 Tf -4.1335 -3.2727 Td[(X)]TJ/F25 7.9701 Tf 1.0268 -23.4509 Td[(i)]TJ/F22 7.9701 Tf 2.8832 0 Td[(=1)]TJ/F15 10.9091 Tf 11.8476 13.0872 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 4.5043 Td[(\016)]TJ -0.0842 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.6283 2.6969 Td[(\051)]TJ/F25 7.9701 Tf 4.2425 4.5043 Td[(T)]TJ/F15 10.9091 Tf 6.6045 -4.5043 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 4.5043 Td[(\016)]TJ 0 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.5441 2.6969 Td[(\051)]TJ/F28 7.9701 Tf 4.2425 4.5043 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 7.0979 -1.7467 Td[(~)]TJ/F24 10.9091 Tf -2.3656 -2.7576 Td[(R)]TJ/F22 7.9701 Tf 8.3674 4.5043 Td[(0)]TJ/F25 7.9701 Tf -0.0842 -7.2012 Td[(i)]TJ/F24 10.9091 Tf 4.8165 2.6969 Td[(:)]TJ/F15 10.9091 Tf -271.9722 -30.1742 Td[(W)84(e)-336(n)1(ote)-335(that)-334(for)]TJ/F24 10.9091 Tf 83.4217 0 Td[(\016)]TJ/F15 10.9091 Tf 8.3157 0 Td[(=)-280(0)-334(the)-335(th)1(re)-1(e)-335(v)56(ari)1(an)28(ts)-335(of)-334(the)-335(AS)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r)-334(are)-335(all)-334(e)-1(q)1(ual)-334(to)-335(th)1(e)]TJ -91.7375 -13.5492 Td[(bl)1(o)-28(c)27(k-Jacobi)-333(p)1(re)-1(cond)1(ition)1(e)-1(r)1(.)]TJ 16.9365 -13.5492 Td[(As)-359(al)1(re)-1(ad)1(y)-358(obse)-1(r)1(v)28(e)-1(d)1(,)-365(t)1(he)-359(con)28(v)28(erge)-1(n)1(c)-1(e)-358(rate)-358(of)-358(the)-358(one-)-1(lev)28(el)-358(Sc)27(h)29(w)27(arz)-358(precondi)1(tioned)]TJ -16.9365 -13.5492 Td[(iterati)1(v)28(e)-359(s)-1(ol)1(v)28(e)-1(rs)-358(dete)-1(r)1(iorates)-359(as)-359(t)1(he)-359(n)28(u)1(m)27(b)-27(er)]TJ/F24 10.9091 Tf 211.4221 0 Td[(m)]TJ/F15 10.9091 Tf 13.487 0 Td[(of)-358(p)1(artiti)1(ons)-359(of)]TJ/F24 10.9091 Tf 75.4535 0 Td[(W)]TJ/F15 10.9091 Tf 15.7269 0 Td[(in)1(c)-1(r)1(e)-1(ase)-1(s)-359([)]TJ +ET +1 0 0 1 458.5984 462.2978 cm 1 0 0 rg 1 0 0 RG - [(7)]TJ +1 0 0 1 -458.5984 -462.2978 cm +BT +/F15 10.9091 Tf 458.5984 462.2978 Td[(7)]TJ +ET +1 0 0 1 464.0529 462.2978 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -464.0529 -462.2978 cm +BT +/F15 10.9091 Tf 464.0529 462.2978 Td[(,)]TJ +ET +1 0 0 1 470.9919 462.2978 cm 1 0 0 rg 1 0 0 RG - [-359(20)]TJ +1 0 0 1 -470.9919 -462.2978 cm +BT +/F15 10.9091 Tf 470.9919 462.2978 Td[(20)]TJ +ET +1 0 0 1 481.901 462.2978 cm 0 g 0 G - [(].)-519(T)83(o)]TJ -316.09 -13.549 Td [(reduce)-308(the)-308(dep)-28(endency)-307(of)-308(the)-308(n)28(um)27(b)-27(er)-308(of)-308(iterations)-308(on)-308(the)-308(degree)-308(of)-308(parallelism)-308(w)28(e)-308(ma)28(y)]TJ 0 -13.549 Td [(in)28(tro)-28(duce)-275(a)-276(global)-275(coupling)-276(among)-275(the)-276(o)28(v)28(erlapping)-275(partitions)-276(b)28(y)-275(de\014ning)-276(a)-275(coarse-space)]TJ 0 -13.55 Td [(appro)28(ximation)]TJ/F22 10.9091 Tf 72.12 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.688 Td [(C)]TJ/F15 10.9091 Tf 10.095 1.688 Td [(of)-275(the)-275(matrix)]TJ/F22 10.9091 Tf 64.783 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(.)-425(In)-275(a)-275(pure)-274(algebraic)-275(setting,)]TJ/F22 10.9091 Tf 137.15 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.688 Td [(C)]TJ/F15 10.9091 Tf 10.095 1.688 Td [(is)-275(usually)-275(built)-274(with)]TJ -318.789 -13.549 Td [(a)-375(Galerkin)-375(appr)1(oac)27(h.)-569(Giv)28(en)-375(a)-374(s)-1(et)]TJ/F22 10.9091 Tf 166.319 0 Td [(W)]TJ/F23 7.9701 Tf 10.303 -1.689 Td [(C)]TJ/F15 10.9091 Tf 11.186 1.689 Td [(of)]TJ/F18 10.9091 Tf 12.876 0 Td [(c)51(o)51(arse)-396(vertic)51(es)]TJ/F15 10.9091 Tf 68.998 0 Td [(,)-385(with)-375(size)]TJ/F22 10.9091 Tf 53.653 0 Td [(n)]TJ/F23 7.9701 Tf 6.548 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.097 1.689 Td [(,)-385(and)-375(a)-375(suitable)]TJ -336.98 -13.549 Td [(restriction)-333(op)-28(erator)]TJ/F22 10.9091 Tf 96.243 0 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F25 10.9091 Tf 10.127 1.689 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.182 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.34 Td [(C)]TJ/F26 7.9701 Tf 6.194 1.34 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F15 10.9091 Tf 5.636 -3.959 Td [(,)]TJ/F22 10.9091 Tf 6.667 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.733 1.689 Td [(is)-333(de\014ned)-334(as)]TJ/F22 10.9091 Tf -10.129 -20.973 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.127 1.689 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F22 10.9091 Tf 7.097 1.689 Td [(AR)]TJ/F23 7.9701 Tf 16.549 4.504 Td [(T)]TJ -0.084 -7.201 Td [(C)]TJ/F15 10.9091 Tf -233.512 -18.277 Td [(and)-496(the)-496(c)-1(oar)1(s)-1(e-lev)28(el)-496(correction)-496(matrix)-497(to)-496(b)-28(e)-496(com)28(bined)-496(with)-497(a)-496(generic)-496(one-lev)28(el)-497(AS)]TJ 0 -13.549 Td [(preconditioner)]TJ/F22 10.9091 Tf 72.182 0 Td [(M)]TJ/F20 7.9701 Tf 10.583 -1.688 Td [(1)]TJ/F23 7.9701 Tf 4.235 0 Td [(L)]TJ/F15 10.9091 Tf 9.893 1.688 Td [(is)-333(obtained)-334(as)]TJ/F22 10.9091 Tf 63.869 -20.973 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 15.539 3.434 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 4.504 Td [(T)]TJ -0.084 -7.201 Td [(C)]TJ/F22 10.9091 Tf 7.097 2.697 Td [(A)]TJ/F26 7.9701 Tf 8.182 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -6.586 -8.022 Td [(C)]TJ/F22 10.9091 Tf 11.318 3.434 Td [(R)]TJ/F23 7.9701 Tf 8.284 -1.689 Td [(C)]TJ/F22 10.9091 Tf 7.096 1.689 Td [(;)]TJ/F15 10.9091 Tf -248.659 -20.973 Td [(where)]TJ/F22 10.9091 Tf 31.91 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 11.097 1.689 Td [(is)-367(assumed)-367(t)1(o)-367(b)-28(e)-367(nonsingular)1(.)-545(The)-367(application)-366(of)]TJ/F22 10.9091 Tf 240.883 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.775 -8.022 Td [(C)]TJ/F15 10.9091 Tf 16.508 3.434 Td [(to)-367(a)-366(v)27(ector)]TJ/F22 10.9091 Tf 56.274 0 Td [(v)]TJ/F15 10.9091 Tf 9.68 0 Td [(corre-)]TJ -385.118 -13.549 Td [(sp)-28(onds)-325(to)-325(a)-325(restriction,)-327(a)-325(solution)-325(and)-325(a)-325(prolongation)-325(step;)-328(the)-325(solution)-325(step,)-327(in)28(v)27(olvi)1(ng)]TJ 0 -13.55 Td [(the)-333(matrix)]TJ/F22 10.9091 Tf 54.273 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.688 Td [(C)]TJ/F15 10.9091 Tf 7.097 1.688 Td [(,)-333(ma)27(y)-333(b)-28(e)-333(carried)-333(out)-334(also)-333(appro)28(ximately)83(.)]TJ -52.615 -13.549 Td [(The)-309(com)28(bination)-309(of)]TJ/F22 10.9091 Tf 96.176 0 Td [(M)]TJ/F23 7.9701 Tf 10.583 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.469 1.689 Td [(and)]TJ/F22 10.9091 Tf 20.948 0 Td [(M)]TJ/F20 7.9701 Tf 10.583 -1.689 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 9.629 1.689 Td [(ma)28(y)-309(b)-28(e)-309(p)-28(erformed)-309(in)-309(either)-309(an)-309(additiv)28(e)-309(or)-309(a)-309(m)27(ul-)]TJ -179.559 -13.549 Td [(tiplicativ)28(e)-275(framew)28(ork.)-425(In)-275(the)-275(former)-275(c)-1(ase,)-286(the)]TJ/F18 10.9091 Tf 217.192 0 Td [(two-level)-304(additive)]TJ/F15 10.9091 Tf 85.198 0 Td [(Sc)28(h)28(w)27(arz)-275(preconditioner)]TJ -302.39 -13.549 Td [(is)-333(obtained:)]TJ/F22 10.9091 Tf 153.971 -13.549 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(2)]TJ/F23 7.9701 Tf 4.234 0 Td [(LA)]TJ/F15 10.9091 Tf 15.631 3.435 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 14.933 3.435 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.435 Td [(:)]TJ/F15 10.9091 Tf -255.45 -18.258 Td [(Applying)]TJ/F22 10.9091 Tf 48.201 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.022 Td [(2)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F26 7.9701 Tf 5.759 0 Td [(\000)]TJ/F23 7.9701 Tf 6.587 0 Td [(A)]TJ/F15 10.9091 Tf 11.405 3.434 Td [(to)-418(a)-419(v)28(ector)]TJ/F22 10.9091 Tf 57.968 0 Td [(v)]TJ/F15 10.9091 Tf 10.244 0 Td [(within)-418(a)-419(Krylo)28(v)-418(solv)27(er)-418(corresp)-28(onds)-418(to)-419(appl)1(ying)]TJ/F22 10.9091 Tf 234.378 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf -399.943 -11.551 Td [(and)]TJ/F22 10.9091 Tf 21.212 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 11.91 3.434 Td [(to)]TJ/F22 10.9091 Tf 13.334 0 Td [(v)]TJ/F15 10.9091 Tf 9.315 0 Td [(indep)-28(enden)28(tly)-333(and)-333(then)-334(summing)-333(up)-333(the)-334(results.)]TJ -53.652 -13.549 Td [(In)-355(the)-355(m)28(ultiplicativ)28(e)-355(case,)-360(the)-355(com)28(bination)-355(can)-355(b)-28(e)-355(p)-27(erformed)-355(b)28(y)-355(\014rst)-355(applying)-355(the)]TJ -16.937 -13.549 Td [(smo)-28(other)]TJ/F22 10.9091 Tf 47.667 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 11.911 3.434 Td [(and)-333(then)-334(th)1(e)-334(coarse-lev)28(el)-334(correction)-333(op)-28(erator)]TJ/F22 10.9091 Tf 217.485 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 12.508 3.434 Td [(:)]TJ/F22 10.9091 Tf -164.465 -21.579 Td [(w)]TJ/F15 10.9091 Tf 11.134 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.434 Td [(v)-36(;)]TJ -45.74 -13.789 Td [(z)]TJ/F15 10.9091 Tf 8.583 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(w)]TJ/F15 10.9091 Tf 10.528 0 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 12.509 3.434 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(v)]TJ/F25 10.9091 Tf 8.103 0 Td [(\000)]TJ/F22 10.9091 Tf 10.91 0 Td [(Aw)]TJ/F15 10.9091 Tf 16.285 0 Td [(\051;)]TJ +1 0 0 1 -481.901 -462.2978 cm +BT +/F15 10.9091 Tf 481.901 462.2978 Td[(].)-519(T)83(o)]TJ -388.3008 -13.5492 Td[(redu)1(c)-1(e)-308(th)1(e)-309(d)1(e)-1(p)-27(e)-1(n)1(dency)-308(of)-307(the)-308(n)28(u)1(m)27(b)-27(e)-1(r)-307(of)-308(iterati)1(ons)-308(on)-308(th)1(e)-308(degre)-1(e)-308(of)-307(paral)1(le)-1(l)1(is)-1(m)-308(w)28(e)-309(ma)28(y)]TJ 0 -13.5492 Td[(in)28(t)1(ro)-28(d)1(uce)-276(a)-276(glob)1(al)-275(c)-1(ou)1(plin)1(g)-276(amon)1(g)-276(th)1(e)-276(o)27(v)28(erl)1(appi)1(ng)-275(part)1(ition)1(s)-276(b)28(y)-275(de\014ni)1(ng)-275(a)-276(coarse)-1(-s)-1(p)1(ac)-1(e)]TJ 0 -13.5492 Td[(app)1(ro)28(ximation)]TJ/F24 10.9091 Tf 72.1198 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.0953 1.6887 Td[(of)-274(the)-275(matrix)]TJ/F24 10.9091 Tf 64.7833 0 Td[(A)]TJ/F15 10.9091 Tf 8.1819 0 Td[(.)-425(In)-274(a)-275(pu)1(re)-275(algebrai)1(c)-276(se)-1(tt)1(ing,)]TJ/F24 10.9091 Tf 137.1498 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.0953 1.6887 Td[(is)-275(usual)1(ly)-275(b)1(uilt)-274(with)]TJ -318.789 -13.5492 Td[(a)-375(Gal)1(e)-1(r)1(kin)-374(appr)1(oac)27(h)1(.)-569(Giv)28(en)-374(a)-375(s)-1(et)]TJ/F24 10.9091 Tf 166.3185 0 Td[(W)]TJ/F25 7.9701 Tf 10.3031 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 11.1858 1.6887 Td[(of)]TJ/F20 10.9091 Tf 12.8769 0 Td[(c)51(o)51(arse)-395(vertic)51(es)]TJ/F15 10.9091 Tf 68.9977 0 Td[(,)-385(with)-374(s)-1(i)1(z)-1(e)]TJ/F24 10.9091 Tf 53.653 0 Td[(n)]TJ/F25 7.9701 Tf 6.5481 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(,)-385(and)-374(a)-375(suit)1(able)]TJ -336.9799 -13.5492 Td[(res)-1(t)1(riction)-333(op)-27(e)-1(r)1(ator)]TJ/F24 10.9091 Tf 96.2426 0 Td[(R)]TJ/F25 7.9701 Tf 8.2831 -1.6887 Td[(C)]TJ/F27 10.9091 Tf 10.1271 1.6887 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 -1.3394 Td[(C)]TJ/F28 7.9701 Tf 6.1942 1.3394 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 5.6363 -3.9588 Td[(,)]TJ/F24 10.9091 Tf 6.6667 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.7332 1.6887 Td[(is)-334(d)1(e)-1(\014)1(ned)-333(as)]TJ/F24 10.9091 Tf -10.1288 -20.9733 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.1271 1.6887 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(R)]TJ/F25 7.9701 Tf 8.2831 -1.6887 Td[(C)]TJ/F24 10.9091 Tf 7.0968 1.6887 Td[(AR)]TJ/F25 7.9701 Tf 16.5493 4.5043 Td[(T)]TJ -0.0843 -7.2012 Td[(C)]TJ/F15 10.9091 Tf -233.5116 -18.2764 Td[(and)-495(the)-497(coarse)-1(-lev)28(e)-1(l)-496(corr)1(e)-1(ction)-496(matri)1(x)-496(to)-497(b)-27(e)-497(com)27(b)1(ined)-496(with)-496(a)-496(generic)-496(one-)-1(lev)28(el)-496(AS)]TJ 0 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)]TJ/F24 10.9091 Tf 72.1819 0 Td[(M)]TJ/F22 7.9701 Tf 10.5833 -1.6887 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 9.8935 1.6887 Td[(is)-334(ob)1(tain)1(e)-1(d)-333(as)]TJ/F24 10.9091 Tf 63.8687 -20.9733 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 15.5384 3.4341 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(R)]TJ/F25 7.9701 Tf 8.3675 4.5043 Td[(T)]TJ -0.0843 -7.2012 Td[(C)]TJ/F24 10.9091 Tf 7.0968 2.6969 Td[(A)]TJ/F28 7.9701 Tf 8.1818 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -6.5865 -8.0219 Td[(C)]TJ/F24 10.9091 Tf 11.3188 3.4341 Td[(R)]TJ/F25 7.9701 Tf 8.2832 -1.6887 Td[(C)]TJ/F24 10.9091 Tf 7.0968 1.6887 Td[(;)]TJ/F15 10.9091 Tf -248.6591 -20.9733 Td[(where)]TJ/F24 10.9091 Tf 31.9095 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 11.0973 1.6887 Td[(is)-367(ass)-1(u)1(m)-1(ed)-366(to)-367(b)-27(e)-367(nonsin)1(gular)1(.)-545(The)-367(ap)1(pli)1(c)-1(ati)1(on)-367(of)]TJ/F24 10.9091 Tf 240.8833 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 16.5086 3.4341 Td[(to)-367(a)-366(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 56.2741 0 Td[(v)]TJ/F15 10.9091 Tf 9.6797 0 Td[(corre-)]TJ -385.1177 -13.5492 Td[(sp)-28(on)1(ds)-325(to)-326(a)-325(r)1(e)-1(striction)1(,)-327(a)-325(soluti)1(on)-325(and)-324(a)-326(p)1(rolon)1(gation)-324(s)-1(tep;)-327(the)-326(solu)1(tion)-325(step,)-327(i)1(n)28(v)28(olvi)1(ng)]TJ 0 -13.5492 Td[(th)1(e)-334(m)-1(at)1(rix)]TJ/F24 10.9091 Tf 54.2728 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(,)-333(ma)27(y)-333(b)-27(e)-334(carri)1(e)-1(d)-333(ou)1(t)-334(al)1(s)-1(o)-333(app)1(ro)28(ximately)83(.)]TJ -52.6149 -13.5492 Td[(The)-309(c)-1(om)28(bin)1(ation)-309(of)]TJ/F24 10.9091 Tf 96.1762 0 Td[(M)]TJ/F25 7.9701 Tf 10.5833 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.4687 1.6887 Td[(and)]TJ/F24 10.9091 Tf 20.9476 0 Td[(M)]TJ/F22 7.9701 Tf 10.5833 -1.6887 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 9.629 1.6887 Td[(ma)27(y)-308(b)-28(e)-309(p)-28(erf)1(orme)-1(d)-308(in)-309(eith)1(e)-1(r)-309(an)-308(add)1(itiv)28(e)-309(or)-309(a)-309(m)27(u)1(l-)]TJ -179.5588 -13.5492 Td[(tip)1(licativ)28(e)-275(framew)27(ork)1(.)-425(In)-275(th)1(e)-276(f)1(orme)-1(r)-274(c)-1(ase)-1(,)-286(the)]TJ/F20 10.9091 Tf 217.1915 0 Td[(tw)-1(o-l)1(evel)-304(additive)]TJ/F15 10.9091 Tf 85.1983 0 Td[(Sc)28(h)28(w)28(arz)-276(p)1(rec)-1(on)1(diti)1(oner)]TJ -302.3899 -13.5492 Td[(is)-334(ob)1(tain)1(e)-1(d)1(:)]TJ/F24 10.9091 Tf 153.9707 -13.5492 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ -7.7759 -8.0219 Td[(2)]TJ/F25 7.9701 Tf 4.2342 0 Td[(LA)]TJ/F15 10.9091 Tf 15.6304 3.4341 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 14.9324 3.4341 Td[(+)]TJ/F24 10.9091 Tf 10.9091 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F24 10.9091 Tf 8.274 3.4341 Td[(:)]TJ/F15 10.9091 Tf -255.4501 -18.2575 Td[(App)1(lyi)1(ng)]TJ/F24 10.9091 Tf 48.2012 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ -7.7759 -8.0219 Td[(2)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F28 7.9701 Tf 5.759 0 Td[(\000)]TJ/F25 7.9701 Tf 6.5865 0 Td[(A)]TJ/F15 10.9091 Tf 11.4059 3.4341 Td[(to)-418(a)-419(v)28(ec)-1(tor)]TJ/F24 10.9091 Tf 57.9672 0 Td[(v)]TJ/F15 10.9091 Tf 10.2441 0 Td[(with)1(in)-418(a)-419(K)1(rylo)28(v)-418(s)-1(ol)1(v)28(e)-1(r)-418(corres)-1(p)-27(on)1(ds)-419(to)-418(app)1(lyin)1(g)]TJ/F24 10.9091 Tf 234.3781 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf -399.9429 -11.5506 Td[(and)]TJ/F24 10.9091 Tf 21.2121 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 11.9103 3.4341 Td[(to)]TJ/F24 10.9091 Tf 13.3334 0 Td[(v)]TJ/F15 10.9091 Tf 9.3156 0 Td[(in)1(dep)-28(end)1(e)-1(n)29(tly)-333(and)-333(th)1(e)-1(n)-332(s)-1(u)1(m)-1(min)1(g)-334(u)1(p)-333(the)-333(re)-1(sul)1(ts)-1(.)]TJ -53.6525 -13.5492 Td[(In)-355(t)1(he)-355(m)27(u)1(ltip)1(licativ)28(e)-355(c)-1(ase)-1(,)-360(th)1(e)-356(com)27(b)1(in)1(ation)-355(can)-354(b)-28(e)-355(p)-27(e)-1(r)1(formed)-355(b)28(y)-354(\014rst)-355(ap)1(ply)1(ing)-355(th)1(e)]TJ -16.9365 -13.5492 Td[(sm)-1(o)-28(ot)1(her)]TJ/F24 10.9091 Tf 47.6667 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7758 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2341 0 Td[(L)]TJ/F15 10.9091 Tf 11.9104 3.4341 Td[(and)-332(then)-333(the)-333(c)-1(oarse-)-1(lev)28(el)-334(corr)1(e)-1(ction)-333(op)-27(e)-1(r)1(ator)]TJ/F24 10.9091 Tf 217.4851 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 12.5082 3.4341 Td[(:)]TJ/F24 10.9091 Tf -164.4656 -21.5786 Td[(w)]TJ/F15 10.9091 Tf 11.1338 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7758 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2341 0 Td[(L)]TJ/F24 10.9091 Tf 8.274 3.4341 Td[(v)-36(;)]TJ -45.7404 -13.7889 Td[(z)]TJ/F15 10.9091 Tf 8.5833 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(w)]TJ/F15 10.9091 Tf 10.5278 0 Td[(+)]TJ/F24 10.9091 Tf 10.909 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7758 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 12.5081 3.4341 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(v)]TJ/F27 10.9091 Tf 8.1035 0 Td[(\000)]TJ/F24 10.9091 Tf 10.9091 0 Td[(Aw)]TJ/F15 10.9091 Tf 16.2854 0 Td[(\051;)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -289 0 obj << +314 0 obj << /Type /Page -/Contents 290 0 R -/Resources 288 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 238 0 R -/Annots [ 287 0 R 265 0 R 266 0 R 285 0 R 286 0 R ] +/Contents 315 0 R +/Resources 313 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 258 0 R +/Annots [ 317 0 R 318 0 R 319 0 R 320 0 R 321 0 R ] >> endobj -287 0 obj << +317 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -265 0 obj << +318 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [403.61 676.042 411.057 685.065] +/Rect [403.6101 676.0417 411.0572 685.0645] /Subtype /Link /A << /S /GoTo /D (cite.CAI_SARKIS) >> >> endobj -266 0 obj << +319 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [416.316 676.042 429.217 685.065] +/Rect [416.3156 676.0417 429.2172 685.0645] /Subtype /Link /A << /S /GoTo /D (cite.EFSTATHIOU) >> >> endobj -285 0 obj << +320 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [457.602 461.302 465.049 470.324] +/Rect [457.6021 461.3016 465.0492 470.3244] /Subtype /Link /A << /S /GoTo /D (cite.dd1_94) >> >> endobj -286 0 obj << +321 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [469.996 461.302 482.897 470.324] +/Rect [469.9956 461.3016 482.8973 470.3244] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -291 0 obj << -/D [289 0 R /XYZ 93.6 740.002 null] +316 0 obj << +/D [314 0 R /XYZ 93.6002 740.0018 null] >> endobj -288 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F18 173 0 R /F22 175 0 R /F23 271 0 R /F20 273 0 R /F25 176 0 R /F24 274 0 R /F26 272 0 R /F28 275 0 R >> +313 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F20 181 0 R /F24 186 0 R /F25 290 0 R /F22 296 0 R /F27 189 0 R /F26 299 0 R /F28 293 0 R /F30 302 0 R >> /ProcSet [ /PDF /Text ] >> endobj -301 0 obj << -/Length 11437 +326 0 obj << +/Length 14322 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(12)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(12)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(this)-278(corresp)-28(onds)-278(to)-278(the)-278(follo)28(wing)]TJ/F18 10.9091 Tf 156.322 0 Td [(two-level)-307(hybrid)-307(pr)51(e-smo)52(o)-1(the)52(d)]TJ/F15 10.9091 Tf 143.004 0 Td [(Sc)28(h)28(w)27(arz)-278(preconditioner:)]TJ/F22 10.9091 Tf -190.113 -24.572 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(2)]TJ/F23 7.9701 Tf 4.234 0 Td [(LH)]TJ/F26 7.9701 Tf 13.33 0 Td [(\000)]TJ/F23 7.9701 Tf 6.586 0 Td [(P)-148(R)-6(E)]TJ/F15 10.9091 Tf 23.154 3.434 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 14.933 3.434 Td [(+)]TJ/F28 10.9091 Tf 10.909 8.836 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.836 Td [(I)]TJ/F25 10.9091 Tf 8.075 0 Td [(\000)]TJ/F22 10.9091 Tf 10.91 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F22 10.9091 Tf 12.508 3.434 Td [(A)]TJ/F28 10.9091 Tf 8.182 8.836 Td [(\001)]TJ/F22 10.9091 Tf 6.818 -8.836 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.235 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.434 Td [(:)]TJ/F15 10.9091 Tf -300.208 -24.572 Td [(On)-368(the)-369(other)-368(hand,)-377(b)27(y)-368(applying)-368(the)-369(smo)-28(other)-368(after)-369(the)-368(coarse-lev)27(el)-368(correction,)-377(i.e.)-369(b)28(y)]TJ 0 -13.55 Td [(computing)]TJ/F22 10.9091 Tf 150.505 -12.905 Td [(w)]TJ/F15 10.9091 Tf 11.134 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.021 Td [(C)]TJ/F22 10.9091 Tf 12.508 3.434 Td [(v)-36(;)]TJ -45.741 -13.789 Td [(z)]TJ/F15 10.9091 Tf 8.584 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(w)]TJ/F15 10.9091 Tf 10.528 0 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 8.274 3.434 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(v)]TJ/F25 10.9091 Tf 8.103 0 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(Aw)]TJ/F15 10.9091 Tf 16.286 0 Td [(\051)]TJ/F22 10.9091 Tf 4.242 0 Td [(;)]TJ/F15 10.9091 Tf -258.915 -19.188 Td [(the)]TJ/F18 10.9091 Tf 18.788 0 Td [(two-level)-358(hybrid)-357(p)51(ost-smo)51(othe)51(d)]TJ/F15 10.9091 Tf 148.756 0 Td [(Sc)28(h)28(w)27(arz)-333(preconditioner)-333(is)-334(ob)1(tained:)]TJ/F22 10.9091 Tf -60.972 -24.572 Td [(M)]TJ/F26 7.9701 Tf 11.772 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.022 Td [(2)]TJ/F23 7.9701 Tf 4.234 0 Td [(LH)]TJ/F26 7.9701 Tf 13.329 0 Td [(\000)]TJ/F23 7.9701 Tf 6.587 0 Td [(P)-148(O)-29(S)-56(T)]TJ/F15 10.9091 Tf 28.436 3.434 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.775 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 10.698 3.434 Td [(+)]TJ/F28 10.9091 Tf 10.909 8.836 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.836 Td [(I)]TJ/F25 10.9091 Tf 8.076 0 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.434 Td [(A)]TJ/F28 10.9091 Tf 8.182 8.836 Td [(\001)]TJ/F22 10.9091 Tf 6.818 -8.836 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F22 10.9091 Tf 12.508 3.434 Td [(:)]TJ/F15 10.9091 Tf -302.849 -24.572 Td [(One)-222(more)-222(v)55(arian)28(t)-222(of)-222(t)27(w)28(o-lev)28(el)-222(h)27(yb)1(rid)-223(precondi)1(tioner)-223(is)-222(obtained)-222(b)28(y)-222(applying)-222(the)-223(smo)-27(other)]TJ 0 -13.55 Td [(b)-28(efore)-239(and)-239(after)-239(the)-240(coarse-lev)28(el)-239(correction.)-413(In)-239(this)-240(case,)-258(the)-239(preconditioner)-239(is)-239(symme)-1(tr)1(ic)]TJ 0 -13.549 Td [(if)]TJ/F22 10.9091 Tf 10 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)]TJ/F22 10.9091 Tf 6.666 0 Td [(M)]TJ/F20 7.9701 Tf 10.584 -1.688 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 9.893 1.688 Td [(and)]TJ/F22 10.9091 Tf 21.213 0 Td [(M)]TJ/F23 7.9701 Tf 10.583 -1.688 Td [(C)]TJ/F15 10.9091 Tf 10.733 1.688 Td [(are)-333(symmetric.)]TJ -75.152 -13.57 Td [(As)-533(previou)1(s)-1(l)1(y)-533(noted,)-582(on)-533(parallel)-532(computers)-533(the)-532(n)28(um)27(b)-27(er)-533(of)-532(submatrices)-533(usually)]TJ -16.936 -13.55 Td [(matc)28(hes)-307(the)-307(n)28(um)28(b)-28(er)-307(of)-307(a)28(v)56(ailable)-307(pro)-28(cessors.)-436(When)-307(t)1(he)-307(size)-307(of)-307(the)-307(system)-307(to)-307(b)-28(e)-306(precon-)]TJ 0 -13.549 Td [(ditioned)-300(is)-300(v)28(ery)-300(large,)-307(the)-300(use)-301(of)-300(man)28(y)-300(pro)-28(cessors,)-307(i.e.)-300(of)-300(man)28(y)-300(small)-300(submatrices,)-307(often)]TJ 0 -13.549 Td [(leads)-314(to)-314(a)-314(large)-314(coarse-lev)28(el)-314(syste)-1(m,)-317(whose)-314(s)-1(olu)1(tion)-314(ma)27(y)-314(b)-27(e)-314(com)-1(p)1(utationally)-314(exp)-28(ensiv)28(e.)]TJ 0 -13.549 Td [(On)-385(the)-384(other)-385(hand,)-397(the)-385(use)-385(of)-384(few)-385(pro)-28(cessors)-385(often)-384(leads)-385(to)-385(lo)-27(cal)-385(sumatrices)-385(that)-384(are)]TJ 0 -13.549 Td [(to)-28(o)-424(exp)-28(ensiv)28(e)-424(to)-424(b)-28(e)-424(pro)-27(cesse)-1(d)-423(on)-424(single)-424(pro)-28(cessors,)-447(b)-28(ecause)-424(of)-424(memory)-424(and/or)-424(com-)]TJ 0 -13.55 Td [(puting)-324(requiremen)28(ts.)-441(Therefore,)-326(it)-324(seems)-324(natural)-324(to)-324(use)-324(a)-323(rec)-1(u)1(rs)-1(i)1(v)27(e)-324(approac)28(h,)-326(i)1(n)-324(whic)27(h)]TJ 0 -13.549 Td [(the)-394(coarse-)-1(l)1(e)-1(v)28(el)-394(correction)-395(is)-394(re-applied)-394(starting)-395(from)-394(the)-394(curren)27(t)-394(coarse-lev)28(el)-395(system.)]TJ 0 -13.549 Td [(The)-321(corresp)-28(onding)-320(preconditioners,)-324(called)]TJ/F18 10.9091 Tf 202.455 0 Td [(multi-level)]TJ/F15 10.9091 Tf 53.694 0 Td [(preconditioners,)-323(can)-321(signi\014can)28(tly)]TJ -256.149 -13.549 Td [(reduce)-282(the)-283(computational)-282(cost)-282(of)-283(preconditioning)-282(with)-282(resp)-28(ect)-283(to)-282(the)-282(t)28(w)27(o-lev)28(el)-282(case)-283(\050see)]TJ 0 -13.549 Td [([)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F15 10.9091 Tf 86.3998 704.1363 Td[(th)1(is)-279(corresp)-28(on)1(ds)-278(to)-279(t)1(he)-279(f)1(ollo)28(win)1(g)]TJ/F20 10.9091 Tf 156.3223 0 Td[(tw)-1(o-l)1(evel)-307(hy)1(brid)-307(pr)52(e-smo)51(othe)51(d)]TJ/F15 10.9091 Tf 143.0037 0 Td[(Sc)28(h)28(w)28(arz)-279(p)1(rec)-1(on)1(diti)1(oner:)]TJ/F24 10.9091 Tf -190.113 -24.5723 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(2)]TJ/F25 7.9701 Tf 4.2342 0 Td[(LH)]TJ/F28 7.9701 Tf 13.3293 0 Td[(\000)]TJ/F25 7.9701 Tf 6.5866 0 Td[(P)-147(R)-7(E)]TJ/F15 10.9091 Tf 23.1536 3.4341 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 14.9324 3.4341 Td[(+)]TJ/F30 10.9091 Tf 10.9091 8.8364 Td[(\000)]TJ/F24 10.9091 Tf 5 -8.8364 Td[(I)]TJ/F27 10.9091 Tf 8.0757 0 Td[(\000)]TJ/F24 10.9091 Tf 10.9091 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F24 10.9091 Tf 12.5082 3.4341 Td[(A)]TJ/F30 10.9091 Tf 8.1818 8.8364 Td[(\001)]TJ/F24 10.9091 Tf 6.8182 -8.8364 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F24 10.9091 Tf 8.274 3.4341 Td[(:)]TJ/F15 10.9091 Tf -300.2078 -24.5724 Td[(On)-368(th)1(e)-369(other)-368(han)1(d,)-377(b)28(y)-368(app)1(lyi)1(ng)-369(t)1(he)-369(sm)-1(o)-27(other)-369(af)1(ter)-369(t)1(he)-369(coars)-1(e-le)-1(v)28(el)-368(c)-1(or)1(rec)-1(tion)1(,)-377(i.e.)-368(b)28(y)]TJ 0 -13.5492 Td[(com)-1(p)1(utin)1(g)]TJ/F24 10.9091 Tf 150.5056 -12.9058 Td[(w)]TJ/F15 10.9091 Tf 11.1338 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7758 -8.0219 Td[(C)]TJ/F24 10.9091 Tf 12.5081 3.4341 Td[(v)-36(;)]TJ -45.7404 -13.7889 Td[(z)]TJ/F15 10.9091 Tf 8.5833 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(w)]TJ/F15 10.9091 Tf 10.5278 0 Td[(+)]TJ/F24 10.9091 Tf 10.909 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 8.274 3.4341 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(v)]TJ/F27 10.9091 Tf 8.1035 0 Td[(\000)]TJ/F24 10.9091 Tf 10.9091 0 Td[(Aw)]TJ/F15 10.9091 Tf 16.2854 0 Td[(\051)]TJ/F24 10.9091 Tf 4.2424 0 Td[(;)]TJ/F15 10.9091 Tf -258.9152 -19.1875 Td[(th)1(e)]TJ/F20 10.9091 Tf 18.7879 0 Td[(tw)-1(o-l)1(evel)-357(h)-1(y)1(bri)1(d)-358(p)51(ost-smo)51(othe)51(d)]TJ/F15 10.9091 Tf 148.7565 0 Td[(Sc)28(h)28(w)28(arz)-334(p)1(re)-1(cond)1(ition)1(e)-1(r)-333(i)1(s)-334(obtai)1(ned:)]TJ/F24 10.9091 Tf -60.9726 -24.5723 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(2)]TJ/F25 7.9701 Tf 4.2342 0 Td[(LH)]TJ/F28 7.9701 Tf 13.3293 0 Td[(\000)]TJ/F25 7.9701 Tf 6.5866 0 Td[(P)-147(O)-30(S)-56(T)]TJ/F15 10.9091 Tf 28.4361 3.4341 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 10.6982 3.4341 Td[(+)]TJ/F30 10.9091 Tf 10.9091 8.8364 Td[(\000)]TJ/F24 10.9091 Tf 5 -8.8364 Td[(I)]TJ/F27 10.9091 Tf 8.0757 0 Td[(\000)]TJ/F24 10.9091 Tf 10.9091 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F24 10.9091 Tf 8.274 3.4341 Td[(A)]TJ/F30 10.9091 Tf 8.1818 8.8364 Td[(\001)]TJ/F24 10.9091 Tf 6.8182 -8.8364 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F24 10.9091 Tf 12.5082 3.4341 Td[(:)]TJ/F15 10.9091 Tf -302.8491 -24.5724 Td[(On)1(e)-223(more)-223(v)56(ari)1(an)28(t)-222(of)-222(t)28(w)27(o-lev)28(e)-1(l)-222(h)29(ybr)1(id)-222(p)1(re)-1(cond)1(ition)1(e)-1(r)-221(is)-223(ob)1(tained)-222(b)28(y)-222(ap)1(ply)1(ing)-222(th)1(e)-223(s)-1(mo)-28(oth)1(e)-1(r)]TJ 0 -13.5492 Td[(b)-27(e)-1(f)1(ore)-240(an)1(d)-239(aft)1(e)-1(r)-239(th)1(e)-240(coars)-1(e-le)-1(v)28(el)-239(correc)-1(ti)1(on.)-413(In)-239(th)1(is)-240(case)-1(,)-258(th)1(e)-240(p)1(re)-1(cond)1(ition)1(e)-1(r)-238(is)-240(symm)-1(etric)]TJ 0 -13.5492 Td[(if)]TJ/F24 10.9091 Tf 10 0 Td[(A)]TJ/F15 10.9091 Tf 8.1819 0 Td[(,)]TJ/F24 10.9091 Tf 6.6666 0 Td[(M)]TJ/F22 7.9701 Tf 10.5834 -1.6887 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 9.8935 1.6887 Td[(and)]TJ/F24 10.9091 Tf 21.2121 0 Td[(M)]TJ/F25 7.9701 Tf 10.5834 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.7331 1.6887 Td[(are)-333(s)-1(ymme)-1(tr)1(ic)-1(.)]TJ -75.1517 -13.5706 Td[(As)-533(pr)1(e)-1(v)1(iously)-532(noted,)-582(on)-532(p)1(arallel)-532(c)-1(ompu)1(te)-1(r)1(s)-533(the)-533(n)29(um)27(b)-27(er)-532(of)-533(sub)1(matrice)-1(s)-533(u)1(s)-1(u)1(ally)]TJ -16.9365 -13.5492 Td[(matc)27(h)1(e)-1(s)-307(the)-307(n)28(u)1(m)27(b)-27(e)-1(r)-306(of)-307(a)28(v)56(ailab)1(le)-307(pr)1(o)-28(c)-1(ess)-1(ors.)-435(When)-307(th)1(e)-307(s)-1(ize)-307(of)-307(th)1(e)-307(s)-1(ystem)-308(to)-306(b)-28(e)-307(pr)1(e)-1(con-)]TJ 0 -13.5492 Td[(di)1(tioned)-300(i)1(s)-301(v)28(e)-1(r)1(y)-300(large,)-307(t)1(he)-301(u)1(s)-1(e)-300(of)-300(man)28(y)-300(p)1(ro)-28(ce)-1(ss)-1(or)1(s)-1(,)-306(i.e.)-300(of)-300(man)28(y)-300(sm)-1(all)-299(s)-1(u)1(bmatrice)-1(s,)-307(of)1(ten)]TJ 0 -13.5492 Td[(leads)-314(to)-314(a)-314(large)-314(coars)-1(e-le)-1(v)28(el)-314(sys)-1(t)1(e)-1(m,)-318(whose)-315(solu)1(tion)-314(ma)28(y)-314(b)-27(e)-315(comput)1(ational)1(ly)-314(exp)-28(ensiv)28(e.)]TJ 0 -13.5492 Td[(On)-384(th)1(e)-386(ot)1(her)-385(h)1(and)1(,)-398(th)1(e)-385(use)-385(of)-385(f)1(e)-1(w)-385(p)1(ro)-28(ces)-1(sors)-385(often)-384(le)-1(ad)1(s)-385(to)-385(lo)-27(c)-1(al)-384(s)-1(u)1(m)-1(at)1(rice)-1(s)-385(th)1(at)-385(are)]TJ 0 -13.5492 Td[(to)-28(o)-424(exp)-27(e)-1(n)1(s)-1(i)1(v)28(e)-425(to)-424(b)-27(e)-425(p)1(ro)-28(ces)-1(se)-1(d)-423(on)-424(single)-424(pr)1(o)-28(ce)-1(ss)-1(or)1(s)-1(,)-446(b)-28(ec)-1(au)1(s)-1(e)-424(of)-424(mem)-1(or)1(y)-424(and)1(/or)-424(com)-1(-)]TJ 0 -13.5492 Td[(pu)1(tin)1(g)-324(requi)1(re)-1(men)28(ts.)-442(Th)1(e)-1(r)1(e)-1(f)1(ore)-1(,)-325(it)-324(se)-1(ems)-325(n)1(atur)1(al)-324(to)-324(u)1(s)-1(e)-324(a)-324(rec)-1(u)1(rsiv)28(e)-324(appr)1(oac)27(h)1(,)-326(in)-323(whic)28(h)]TJ 0 -13.5492 Td[(th)1(e)-395(c)-1(oar)1(s)-1(e-)-1(l)1(e)-1(v)28(el)-394(c)-1(orr)1(e)-1(ction)-394(is)-394(re)-1(-ap)1(plied)-394(startin)1(g)-395(f)1(rom)-395(t)1(he)-395(curr)1(e)-1(n)29(t)-395(coarse)-1(-lev)28(e)-1(l)-394(sys)-1(t)1(e)-1(m.)]TJ 0 -13.5492 Td[(The)-321(c)-1(or)1(res)-1(p)-27(ond)1(ing)-321(p)1(rec)-1(on)1(dit)1(ioners,)-323(c)-1(all)1(e)-1(d)]TJ/F20 10.9091 Tf 202.455 0 Td[(mu)1(lti-l)1(evel)]TJ/F15 10.9091 Tf 53.6944 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-1(,)-323(can)-321(signi)1(\014can)28(tly)]TJ -256.1494 -13.5492 Td[(redu)1(c)-1(e)-282(the)-283(com)-1(p)1(utat)1(ional)-282(cos)-1(t)-282(of)-282(pr)1(e)-1(cond)1(ition)1(ing)-282(with)-282(r)1(e)-1(sp)-28(ec)-1(t)-282(to)-282(the)-282(t)28(w)27(o-lev)28(e)-1(l)-282(c)-1(ase)-283(\050se)-1(e)]TJ 0 -13.5492 Td[([)]TJ +ET +1 0 0 1 89.4301 370.2545 cm 1 0 0 rg 1 0 0 RG - [(20)]TJ +1 0 0 1 -89.4301 -370.2545 cm +BT +/F15 10.9091 Tf 89.4301 370.2545 Td[(20)]TJ +ET +1 0 0 1 100.3392 370.2545 cm 0 g 0 G - [(,)-320(Chapter)-317(3]\051.)-439(Additiv)28(e)-318(and)-317(h)28(ybrid)-317(m)28(ultilev)28(el)-317(preconditioners)-317(are)-317(obtained)-317(as)-318(direct)]TJ 0 -13.549 Td [(extensions)-359(of)-359(the)-359(t)28(w)27(o-lev)28(el)-359(coun)28(terparts.)-522(F)84(or)-359(a)-359(detailed)-359(descrition)-359(of)-359(them,)-366(the)-359(reader)]TJ 0 -13.55 Td [(is)-321(referred)-321(to)-321([)]TJ +1 0 0 1 -100.3392 -370.2545 cm +BT +/F15 10.9091 Tf 100.3392 370.2545 Td[(,)-320(Chap)1(te)-1(r)-317(3])1(\051.)-439(Add)1(itiv)28(e)-317(and)-316(h)28(ybr)1(id)-317(m)28(ult)1(ilev)28(e)-1(l)-317(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-318(ar)1(e)-318(obt)1(ained)-317(as)-317(dir)1(e)-1(ct)]TJ -13.9394 -13.5492 Td[(exte)-1(n)1(s)-1(i)1(ons)-359(of)-359(th)1(e)-360(t)28(w)28(o-)-1(lev)28(el)-359(c)-1(ou)1(n)28(terpar)1(ts)-1(.)-521(F)84(or)-359(a)-359(detailed)-359(d)1(e)-1(sc)-1(r)1(ition)-358(of)-359(th)1(e)-1(m,)-365(the)-359(reader)]TJ 0 -13.5492 Td[(is)-321(referred)-321(to)-321([)]TJ +ET +1 0 0 1 153.7247 343.1561 cm 1 0 0 rg 1 0 0 RG - [(20)]TJ +1 0 0 1 -153.7247 -343.1561 cm +BT +/F15 10.9091 Tf 153.7247 343.1561 Td[(20)]TJ +ET +1 0 0 1 164.6338 343.1561 cm 0 g 0 G - [(,)-324(Ch)1(apter)-321(3].)-441(The)-321(algorithm)-321(for)-321(the)-321(application)-321(of)-321(a)-321(m)28(ulti-lev)28(el)-321(h)28(ybrid)]TJ 0 -13.549 Td [(p)-28(ost-smo)-28(othed)-335(preconditioner)]TJ/F22 10.9091 Tf 145.676 0 Td [(M)]TJ/F15 10.9091 Tf 15.428 0 Td [(to)-335(a)-335(v)28(e)-1(ctor)]TJ/F22 10.9091 Tf 55.241 0 Td [(v)]TJ/F15 10.9091 Tf 5.68 0 Td [(,)-336(i.)1(e)-1(.)-335(for)-335(the)-335(computation)-335(of)]TJ/F22 10.9091 Tf 135.91 0 Td [(w)]TJ/F15 10.9091 Tf 11.167 0 Td [(=)]TJ/F22 10.9091 Tf 11.548 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(v)]TJ/F15 10.9091 Tf 5.68 0 Td [(,)]TJ -409.421 -13.549 Td [(is)-311(rep)-27(orted,)-316(for)-310(example,)-315(in)-311(Figure)]TJ +1 0 0 1 -164.6338 -343.1561 cm +BT +/F15 10.9091 Tf 164.6338 343.1561 Td[(,)-323(C)-1(h)1(apter)-321(3])1(.)-441(Th)1(e)-322(algor)1(ith)1(m)-322(f)1(or)-321(the)-321(app)1(lication)-320(of)-321(a)-321(m)27(u)1(lti-lev)28(e)-1(l)-320(h)28(ybr)1(id)]TJ -78.234 -13.5492 Td[(p)-27(os)-1(t-sm)-1(o)-28(ot)1(hed)-335(pr)1(e)-1(cond)1(ition)1(e)-1(r)]TJ/F24 10.9091 Tf 145.6758 0 Td[(M)]TJ/F15 10.9091 Tf 15.4287 0 Td[(to)-335(a)-335(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 55.2408 0 Td[(v)]TJ/F15 10.9091 Tf 5.6793 0 Td[(,)-335(i.e.)-335(for)-335(th)1(e)-336(comput)1(ation)-335(of)]TJ/F24 10.9091 Tf 135.9109 0 Td[(w)]TJ/F15 10.9091 Tf 11.1665 0 Td[(=)]TJ/F24 10.9091 Tf 11.5479 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(v)]TJ/F15 10.9091 Tf 5.6793 0 Td[(,)]TJ -409.4208 -13.5492 Td[(is)-311(rep)-27(orted,)-315(f)1(or)-311(example,)-315(in)-310(Figu)1(re)]TJ +ET +1 0 0 1 252.6225 316.0577 cm 0 0 1 rg 0 0 1 RG - [-311(1)]TJ +1 0 0 1 -252.6225 -316.0577 cm +BT +/F15 10.9091 Tf 252.6225 316.0577 Td[(1)]TJ +ET +1 0 0 1 258.077 316.0577 cm 0 g 0 G - [(.)-437(Here)-310(the)-311(n)28(um)28(b)-28(er)-311(of)-310(lev)27(els)-310(is)-311(denoted)-311(b)28(y)]TJ/F22 10.9091 Tf 370.709 0 Td [(nl)-20(ev)]TJ/F15 10.9091 Tf 24.166 0 Td [(and)]TJ -394.875 -13.549 Td [(the)-359(lev)27(els)-359(are)-360(n)28(um)28(b)-28(ered)-359(in)-360(i)1(ncreas)-1(in)1(g)-360(order)-359(starting)-360(from)-359(the)-359(\014nest)-360(one,)-366(i.e.)-359(the)-360(\014nest)]TJ 0 -13.549 Td [(lev)28(el)-393(is)-392(lev)28(el)-393(1;)-421(the)-393(coarse)-392(matrix)-393(and)-392(the)-392(corresp)-28(onding)-392(basic)-393(precondit)1(ioner)-393(at)-392(eac)28(h)]TJ 0 -13.55 Td [(lev)28(el)]TJ/F22 10.9091 Tf 24.848 0 Td [(l)]TJ/F15 10.9091 Tf 7.106 0 Td [(are)-333(denoted)-334(b)28(y)]TJ/F22 10.9091 Tf 74.576 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.777 Td [(l)]TJ/F15 10.9091 Tf 6.757 1.777 Td [(and)]TJ/F22 10.9091 Tf 21.212 0 Td [(M)]TJ/F23 7.9701 Tf 10.583 -1.777 Td [(l)]TJ/F15 10.9091 Tf 3.12 1.777 Td [(,)-333(resp)-28(ectiv)28(ely)83(,)-333(with)]TJ/F22 10.9091 Tf 93.122 0 Td [(A)]TJ/F20 7.9701 Tf 8.181 -1.636 Td [(1)]TJ/F15 10.9091 Tf 7.763 1.636 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(.)]TJ/F17 11.9552 Tf -285.147 -29.335 Td [(4.2)-1125(Smo)-31(othed)-375(Aggregation)]TJ/F15 10.9091 Tf 0 -20.636 Td [(In)-411(order)-411(to)-411(de\014ne)-411(the)-411(restriction)-411(op)-27(erator)]TJ/F22 10.9091 Tf 207.99 0 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.097 1.689 Td [(,)-430(whic)27(h)-411(is)-411(u)1(s)-1(ed)-411(to)-411(compu)1(te)-412(t)1(he)-411(c)-1(oar)1(s)-1(e-)]TJ -223.37 -13.549 Td [(lev)28(el)-281(matrix)]TJ/F22 10.9091 Tf 59.188 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.096 1.689 Td [(,)-291(MLD2P4)-281(uses)-281(the)]TJ/F18 10.9091 Tf 93.551 0 Td [(smo)51(othe)51(d)-309(aggr)51(e)51(gation)]TJ/F15 10.9091 Tf 103.876 0 Td [(algorithm)-281(describ)-28(ed)-280(in)-281([)]TJ +1 0 0 1 -258.077 -316.0577 cm +BT +/F15 10.9091 Tf 258.077 316.0577 Td[(.)-437(Here)-311(th)1(e)-311(n)28(um)28(b)-28(er)-311(of)-310(lev)28(els)-311(is)-311(denoted)-310(b)28(y)]TJ/F24 10.9091 Tf 199.0322 0 Td[(nl)-20(ev)]TJ/F15 10.9091 Tf 24.1659 0 Td[(and)]TJ -394.8753 -13.5492 Td[(th)1(e)-360(le)-1(v)28(els)-360(ar)1(e)-360(n)28(um)28(b)-27(e)-1(red)-359(in)-359(i)1(ncre)-1(asin)1(g)-360(or)1(der)-360(start)1(ing)-359(fr)1(om)-360(the)-360(\014)1(nes)-1(t)-359(on)1(e)-1(,)-366(i)1(.e)-1(.)-359(th)1(e)-360(\014n)1(e)-1(st)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)-392(is)-392(le)-1(v)28(el)-392(1;)-422(th)1(e)-393(c)-1(oar)1(s)-1(e)-392(m)-1(atr)1(ix)-392(and)-392(th)1(e)-393(corres)-1(p)-27(ond)1(in)1(g)-393(b)1(as)-1(ic)-392(prec)-1(on)1(di)1(tioner)-392(at)-392(e)-1(ac)28(h)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)]TJ/F24 10.9091 Tf 24.8485 0 Td[(l)]TJ/F15 10.9091 Tf 7.106 0 Td[(are)-333(denoted)-333(b)28(y)]TJ/F24 10.9091 Tf 74.5759 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.7772 Td[(l)]TJ/F15 10.9091 Tf 6.7566 1.7772 Td[(and)]TJ/F24 10.9091 Tf 21.2121 0 Td[(M)]TJ/F25 7.9701 Tf 10.5834 -1.7772 Td[(l)]TJ/F15 10.9091 Tf 3.1202 1.7772 Td[(,)-333(res)-1(p)-27(ec)-1(tiv)28(ely)84(,)-333(w)-1(i)1(th)]TJ/F24 10.9091 Tf 93.1213 0 Td[(A)]TJ/F22 7.9701 Tf 8.1818 -1.6363 Td[(1)]TJ/F15 10.9091 Tf 7.7626 1.6363 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(.)]TJ/F19 11.9552 Tf -285.1472 -29.3352 Td[(4.)-1(2)-1125(Sm)-1(o)-32(ot)-1(hed)-375(Agg)-1(reg)-1(ati)-1(on)]TJ/F15 10.9091 Tf 0 -20.6362 Td[(In)-411(or)1(der)-411(to)-411(d)1(e)-1(\014)1(ne)-411(the)-411(res)-1(tr)1(ic)-1(t)1(ion)-411(op)-27(e)-1(r)1(ator)]TJ/F24 10.9091 Tf 207.9903 0 Td[(R)]TJ/F25 7.9701 Tf 8.2832 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(,)-430(whic)28(h)-411(is)-411(use)-1(d)-410(to)-411(com)-1(p)1(ute)-411(the)-411(c)-1(oar)1(s)-1(e-)]TJ -223.3703 -13.5492 Td[(lev)28(e)-1(l)-280(m)-1(atr)1(ix)]TJ/F24 10.9091 Tf 59.1879 0 Td[(A)]TJ/F25 7.9701 Tf 8.1819 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(,)-291(MLD2P)1(4)-281(use)-1(s)-281(th)1(e)]TJ/F20 10.9091 Tf 93.5509 0 Td[(smo)51(othe)51(d)-310(aggr)52(e)51(gation)]TJ/F15 10.9091 Tf 103.8759 0 Td[(algor)1(ithm)-281(d)1(e)-1(sc)-1(r)1(ib)-28(ed)-280(in)-281([)]TJ +ET +1 0 0 1 470.3327 211.8895 cm 1 0 0 rg 1 0 0 RG - [(1)]TJ +1 0 0 1 -470.3327 -211.8895 cm +BT +/F15 10.9091 Tf 470.3327 211.8895 Td[(1)]TJ +ET +1 0 0 1 475.7872 211.8895 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -475.7872 -211.8895 cm +BT +/F15 10.9091 Tf 475.7872 211.8895 Td[(,)]TJ +ET +1 0 0 1 481.8812 211.8895 cm 1 0 0 rg 1 0 0 RG - [-281(24)]TJ +1 0 0 1 -481.8812 -211.8895 cm +BT +/F15 10.9091 Tf 481.8812 211.8895 Td[(24)]TJ +ET +1 0 0 1 492.7903 211.8895 cm 0 g 0 G - [(].)]TJ -271.893 -13.549 Td [(The)-443(basic)-442(idea)-443(of)-443(thi)1(s)-443(algorithm)-443(is)-442(to)-443(build)-443(a)-442(coarse)-443(set)-443(of)-442(v)27(erti)1(c)-1(es)]TJ/F22 10.9091 Tf 335.939 0 Td [(W)]TJ/F23 7.9701 Tf 10.303 -1.689 Td [(C)]TJ/F15 10.9091 Tf 11.925 1.689 Td [(b)28(y)-443(suitably)]TJ -358.167 -13.55 Td [(grouping)-329(the)-330(v)28(ertices)-330(of)]TJ/F22 10.9091 Tf 116.02 0 Td [(W)]TJ/F15 10.9091 Tf 15.414 0 Td [(in)28(to)-330(disjoin)28(t)-329(subsets)-330(\050aggregates\051,)-331(an)1(d)-330(to)-330(de\014ne)-329(the)-330(coarse-)]TJ -131.434 -13.549 Td [(to-\014ne)-253(space)-254(transfer)-253(op)-28(erator)]TJ/F22 10.9091 Tf 144.031 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(T)]TJ -0.084 -7.192 Td [(C)]TJ/F15 10.9091 Tf 9.862 3.233 Td [(b)28(y)-254(applyin)1(g)-254(a)-253(s)-1(u)1(itable)-254(smo)-28(other)-253(to)-254(a)-253(simple)-254(piecewise)]TJ -162.176 -13.549 Td [(constan)28(t)-334(p)1(rolongation)-334(op)-27(erator,)-334(to)-333(impro)28(v)28(e)-334(the)-333(qualit)28(y)-333(of)-334(the)-333(coarse-space)-334(correction.)]TJ 16.936 -13.571 Td [(Three)-333(main)-334(steps)-333(can)-333(b)-28(e)-334(id)1(e)-1(n)28(ti\014ed)-333(in)-333(the)-334(smo)-27(othed)-334(aggregation)-333(pro)-28(cedure:)]TJ +1 0 0 1 -492.7903 -211.8895 cm +BT +/F15 10.9091 Tf 492.7903 211.8895 Td[(].)]TJ -406.3905 -13.5492 Td[(The)-443(b)1(as)-1(ic)-443(id)1(e)-1(a)-442(of)-442(this)-443(al)1(gorith)1(m)-443(is)-443(to)-443(b)1(uil)1(d)-443(a)-442(c)-1(oar)1(s)-1(e)-443(se)-1(t)-442(of)-443(v)28(erti)1(c)-1(es)]TJ/F24 10.9091 Tf 335.9387 0 Td[(W)]TJ/F25 7.9701 Tf 10.3031 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 11.9257 1.6887 Td[(b)28(y)-442(s)-1(u)1(itab)1(ly)]TJ -358.1675 -13.5492 Td[(grou)1(pin)1(g)-330(th)1(e)-330(v)28(e)-1(r)1(tice)-1(s)-330(of)]TJ/F24 10.9091 Tf 116.0197 0 Td[(W)]TJ/F15 10.9091 Tf 15.414 0 Td[(in)28(t)1(o)-330(di)1(s)-1(j)1(oin)28(t)-329(s)-1(u)1(bse)-1(ts)-330(\050aggr)1(e)-1(gates)-1(\051,)-330(an)1(d)-329(to)-330(d)1(e)-1(\014)1(ne)-330(the)-330(coarse)-1(-)]TJ -131.4337 -13.5492 Td[(to-\014n)1(e)-254(s)-1(p)1(ac)-1(e)-254(tr)1(ansfer)-253(op)-28(erator)]TJ/F24 10.9091 Tf 144.0312 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(T)]TJ -0.0842 -7.1916 Td[(C)]TJ/F15 10.9091 Tf 9.8621 3.2328 Td[(b)28(y)-253(app)1(lyi)1(ng)-254(a)-253(suitab)1(le)-254(sm)-1(o)-28(ot)1(her)-254(t)1(o)-254(a)-253(s)-1(impl)1(e)-254(piec)-1(ewise)]TJ -162.1765 -13.5492 Td[(constan)28(t)-333(prol)1(ongation)-332(op)-28(erator)1(,)-334(t)1(o)-334(imp)1(ro)28(v)28(e)-334(the)-333(qual)1(it)28(y)-333(of)-333(the)-334(coarse)-1(-space)-334(c)-1(or)1(rec)-1(ti)1(on.)]TJ 16.9365 -13.5706 Td[(Thr)1(e)-1(e)-334(main)-333(steps)-334(can)-333(b)-27(e)-334(iden)28(ti)1(\014ed)-333(in)-333(th)1(e)-334(s)-1(mo)-28(oth)1(e)-1(d)-333(aggr)1(e)-1(gati)1(on)-333(pr)1(o)-28(c)-1(edu)1(re:)]TJ +ET +1 0 0 1 86.3998 121.5209 cm 0 g 0 G - -3.603 -22.601 Td [(1.)]TJ +1 0 0 1 -86.3998 -121.5209 cm +BT +/F15 10.9091 Tf 99.7331 121.5209 Td[(1.)]TJ +ET +1 0 0 1 108.218 121.5209 cm 0 g 0 G - [-500(coarsening)-333(of)-334(the)-333(v)28(ertex)-333(s)-1(et)]TJ/F22 10.9091 Tf 148.667 0 Td [(W)]TJ/F15 10.9091 Tf 11.818 0 Td [(,)-333(to)-334(obtain)]TJ/F22 10.9091 Tf 53.94 0 Td [(W)]TJ/F23 7.9701 Tf 10.303 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.096 1.689 Td [(;)]TJ +1 0 0 1 -108.218 -121.5209 cm +BT +/F15 10.9091 Tf 113.6726 121.5209 Td[(coars)-1(eni)1(ng)-333(of)-333(the)-333(v)28(e)-1(r)1(te)-1(x)-333(se)-1(t)]TJ/F24 10.9091 Tf 134.7274 0 Td[(W)]TJ/F15 10.9091 Tf 11.8182 0 Td[(,)-333(to)-333(obtain)]TJ/F24 10.9091 Tf 53.9395 0 Td[(W)]TJ/F25 7.9701 Tf 10.303 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(;)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -300 0 obj << +325 0 obj << /Type /Page -/Contents 301 0 R -/Resources 299 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 238 0 R -/Annots [ 294 0 R 295 0 R 296 0 R 297 0 R 298 0 R ] +/Contents 326 0 R +/Resources 324 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 258 0 R +/Annots [ 328 0 R 329 0 R 330 0 R 331 0 R 332 0 R ] >> endobj -294 0 obj << +328 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [88.434 369.258 101.335 378.281] +/Rect [88.4338 369.2582 101.3354 378.2811] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -295 0 obj << +329 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [152.728 342.16 165.63 351.183] +/Rect [152.7285 342.1598 165.6301 351.1827] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -296 0 obj << +330 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [251.626 312.94 259.073 324.63] +/Rect [251.6262 312.9402 259.0733 324.6297] /Subtype /Link /A << /S /GoTo /D (figure.1) >> >> endobj -297 0 obj << +331 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [469.336 210.893 476.783 219.916] +/Rect [469.3364 210.8932 476.7835 219.9161] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -298 0 obj << +332 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [480.885 210.893 493.787 219.916] +/Rect [480.8849 210.8932 493.7865 219.9161] /Subtype /Link /A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> >> endobj -302 0 obj << -/D [300 0 R /XYZ 86.4 740.002 null] +327 0 obj << +/D [325 0 R /XYZ 86.3998 740.0018 null] >> endobj 54 0 obj << -/D [300 0 R /XYZ 86.4 257.923 null] +/D [325 0 R /XYZ 86.3998 257.9228 null] >> endobj -303 0 obj << -/D [300 0 R /XYZ 86.4 137.475 null] +333 0 obj << +/D [325 0 R /XYZ 86.3998 137.4749 null] >> endobj -299 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F18 173 0 R /F22 175 0 R /F26 272 0 R /F20 273 0 R /F23 271 0 R /F28 275 0 R /F25 176 0 R /F17 111 0 R >> +324 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F20 181 0 R /F24 186 0 R /F28 293 0 R /F22 296 0 R /F25 290 0 R /F30 302 0 R /F27 189 0 R /F19 113 0 R >> /ProcSet [ /PDF /Text ] >> endobj -313 0 obj << -/Length 10156 +337 0 obj << +/Length 12841 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(4)]TJ -0 g 0 G - [-378(Mul)67(ti-level)-378(Domain)-378(Decompo)1(siti)-1(o)1(n)-378(Ba)22(ck)22(gr)22(ound)]TJ/F15 10.9091 Tf 401.542 0 Td [(13)]TJ -0 g 0 G +/F43 10.9091 Tf 93.6002 740.0018 Td[(4)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Mul)66(ti-level)-378(Domain)-378(Decomp)1(osition)-378(Ba)22(ck)23(gr)22(oun)-1(d)]TJ/F15 10.9091 Tf 391.3906 0 Td[(13)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G +1 0 0 1 66.6128 -138.7337 cm 0 g 0 G 0 g 0 G -/F22 9.9626 Tf -322.451 -45.783 Td [(v)]TJ/F7 6.9738 Tf 4.829 -1.495 Td [(1)]TJ/F15 9.9626 Tf 7.237 1.495 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(v)]TJ/F15 9.9626 Tf 5.187 0 Td [(;)]TJ/F43 9.9626 Tf -27.769 -17.625 Td [(for)]TJ/F22 9.9626 Tf 17.767 0 Td [(l)]TJ/F15 9.9626 Tf 5.936 0 Td [(=)-278(2)]TJ/F22 9.9626 Tf 15.497 0 Td [(;)-167(nl)-19(ev)]TJ/F43 9.9626 Tf 27.221 0 Td [(do)]TJ/F15 9.9626 Tf -56.458 -14.789 Td [(!)-444(transfer)]TJ/F22 9.9626 Tf 44.112 0 Td [(v)]TJ/F10 6.9738 Tf 4.829 -1.495 Td [(l)]TJ/F13 6.9738 Tf 2.56 0 Td [(\000)]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F15 9.9626 Tf 7.79 1.495 Td [(to)-333(the)-334(next)-333(coarser)-333(lev)27(el)]TJ/F22 9.9626 Tf -65.518 -11.956 Td [(v)]TJ/F10 6.9738 Tf 4.829 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.825 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(R)]TJ/F10 6.9738 Tf 7.565 -1.494 Td [(l)]TJ/F22 9.9626 Tf 3.058 1.494 Td [(v)]TJ/F10 6.9738 Tf 4.829 -1.494 Td [(l)]TJ/F13 6.9738 Tf 2.56 0 Td [(\000)]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F43 9.9626 Tf -55.372 -13.295 Td [(endfor)]TJ/F15 9.9626 Tf 0 -17.625 Td [(!)-444(apply)-334(the)-333(coarsest-lev)28(el)-334(correction)]TJ/F22 9.9626 Tf 0 -15.177 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(nl)-6(ev)]TJ/F15 9.9626 Tf 18.765 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(A)]TJ/F13 6.9738 Tf 7.472 4.262 Td [(\000)]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F10 6.9738 Tf -6.227 -7.267 Td [(nl)-6(ev)]TJ/F22 9.9626 Tf 15.998 3.005 Td [(v)]TJ/F10 6.9738 Tf 4.829 -1.494 Td [(nl)-6(ev)]TJ/F43 9.9626 Tf -62.465 -16.131 Td [(for)]TJ/F22 9.9626 Tf 17.767 0 Td [(l)]TJ/F15 9.9626 Tf 5.936 0 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(nl)-20(ev)]TJ/F25 9.9626 Tf 21.188 0 Td [(\000)]TJ/F15 9.9626 Tf 9.962 0 Td [(1)]TJ/F22 9.9626 Tf 4.982 0 Td [(;)]TJ/F15 9.9626 Tf 4.428 0 Td [(1)]TJ/F22 9.9626 Tf 4.981 0 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(\000)]TJ/F15 9.9626 Tf 7.749 0 Td [(1)]TJ/F43 9.9626 Tf 8.8 0 Td [(do)]TJ/F15 9.9626 Tf -90.774 -14.789 Td [(!)-444(transfer)]TJ/F22 9.9626 Tf 44.112 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.495 Td [(l)]TJ/F7 6.9738 Tf 2.56 0 Td [(+1)]TJ/F15 9.9626 Tf 13.906 1.495 Td [(to)-333(the)-334(next)-333(\014ner)-333(lev)28(e)-1(l)]TJ/F22 9.9626 Tf -65.463 -11.968 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.826 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(R)]TJ/F10 6.9738 Tf 7.641 3.616 Td [(T)]TJ -0.077 -6.437 Td [(l)]TJ/F7 6.9738 Tf 2.56 0 Td [(+1)]TJ/F22 9.9626 Tf 10.586 2.821 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(l)]TJ/F7 6.9738 Tf 2.56 0 Td [(+1)]TJ/F15 9.9626 Tf 10.585 1.494 Td [(;)]TJ -59.965 -14.855 Td [(!)-444(com)-1(p)1(ute)-334(the)-333(residual)-333(at)-334(the)-333(curren)28(t)-334(lev)28(el)]TJ/F22 9.9626 Tf 0 -12.342 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.495 Td [(l)]TJ/F15 9.9626 Tf 5.825 1.495 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(v)]TJ/F10 6.9738 Tf 4.829 -1.495 Td [(l)]TJ/F25 9.9626 Tf 5.272 1.495 Td [(\000)]TJ/F22 9.9626 Tf 9.963 0 Td [(A)]TJ/F13 6.9738 Tf 7.472 4.262 Td [(\000)]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F10 6.9738 Tf -6.226 -7.268 Td [(l)]TJ/F22 9.9626 Tf 10.696 3.006 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.495 Td [(l)]TJ/F15 9.9626 Tf 3.058 1.495 Td [(;)]TJ -67.01 -14.79 Td [(!)-444(apply)-334(the)-333(basic)-333(Sc)27(h)28(w)28(arz)-333(preconditioner)-334(to)-333(the)-333(residual)]TJ/F22 9.9626 Tf 0 -12.343 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.825 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(M)]TJ/F13 6.9738 Tf 10.751 4.262 Td [(\000)]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F10 6.9738 Tf -7.313 -7.267 Td [(l)]TJ/F22 9.9626 Tf 11.782 3.005 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.494 Td [(l)]TJ/F15 9.9626 Tf -46.778 -13.295 Td [(!)-444(up)-28(date)]TJ/F22 9.9626 Tf 40.681 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.495 Td [(l)]TJ/F22 9.9626 Tf -45.565 -10.461 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.826 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.272 1.494 Td [(+)]TJ/F22 9.9626 Tf 9.963 0 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.494 Td [(l)]TJ/F43 9.9626 Tf -55.803 -10.461 Td [(endfor)]TJ/F22 9.9626 Tf 0 -14.79 Td [(w)]TJ/F15 9.9626 Tf 10.168 0 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(y)]TJ/F7 6.9738 Tf 4.885 -1.494 Td [(1)]TJ/F15 9.9626 Tf 4.469 1.494 Td [(;)]TJ -ET +1 0 0 1 5.4546 138.3352 cm q -1 0 0 1 165.668 714.896 cm -[]0 d 0 J 0.398 w 0 0 m 268.316 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +268.3164 0.1992 l +S Q +1 0 0 1 0 -271.2158 cm q -1 0 0 1 165.867 443.282 cm -[]0 d 0 J 0.398 w 0 0 m 0 271.614 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 271.2158 l +S Q +1 0 0 1 1.5691 259.8584 cm +0 g 0 G +0 g 0 G +1 0 0 1 -167.2367 -703.3393 cm +BT +/F24 9.9626 Tf 172.6912 694.2188 Td[(v)]TJ/F7 6.9738 Tf 4.8291 -1.4944 Td[(1)]TJ/F15 9.9626 Tf 7.2367 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(v)]TJ/F15 9.9626 Tf 5.1866 0 Td[(;)]TJ/F45 9.9626 Tf -27.7685 -17.6244 Td[(for)]TJ/F24 9.9626 Tf 17.7666 0 Td[(l)]TJ/F15 9.9626 Tf 5.936 0 Td[(=)-278(2)]TJ/F24 9.9626 Tf 15.4974 0 Td[(;)-166(n)-1(l)-20(e)1(v)]TJ/F45 9.9626 Tf 27.2209 0 Td[(do)]TJ/F15 9.9626 Tf -56.4583 -14.7898 Td[(!)-444(tran)1(s)-1(f)1(e)-1(r)]TJ/F24 9.9626 Tf 44.1125 0 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(l)]TJ/F13 6.9738 Tf 2.5599 0 Td[(\000)]TJ/F7 6.9738 Tf 6.2266 0 Td[(1)]TJ/F15 9.9626 Tf 7.7903 1.4944 Td[(to)-333(the)-333(next)-333(c)-1(oarser)-333(le)-1(v)28(el)]TJ/F24 9.9626 Tf -65.5183 -11.9552 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(R)]TJ/F10 6.9738 Tf 7.5645 -1.4944 Td[(l)]TJ/F24 9.9626 Tf 3.058 1.4944 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(l)]TJ/F13 6.9738 Tf 2.5599 0 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F45 9.9626 Tf -55.3714 -13.2954 Td[(endfor)]TJ/F15 9.9626 Tf 0 -17.6244 Td[(!)-444(app)1(ly)-333(the)-333(c)-1(oarses)-1(t-lev)28(e)-1(l)-333(correc)-1(ti)1(on)]TJ/F24 9.9626 Tf 0 -15.1773 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(nl)-6(ev)]TJ/F15 9.9626 Tf 18.7654 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(A)]TJ/F13 6.9738 Tf 7.472 4.2618 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F10 6.9738 Tf -6.2267 -7.2671 Td[(nl)-6(ev)]TJ/F24 9.9626 Tf 15.9981 3.0053 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(nl)-6(ev)]TJ/F45 9.9626 Tf -62.4652 -16.13 Td[(for)]TJ/F24 9.9626 Tf 17.7666 0 Td[(l)]TJ/F15 9.9626 Tf 5.936 0 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(nl)-20(ev)]TJ/F27 9.9626 Tf 21.1879 0 Td[(\000)]TJ/F15 9.9626 Tf 9.9626 0 Td[(1)]TJ/F24 9.9626 Tf 4.9813 0 Td[(;)]TJ/F15 9.9626 Tf 4.4278 0 Td[(1)]TJ/F24 9.9626 Tf 4.9814 0 Td[(;)]TJ/F27 9.9626 Tf 4.4278 0 Td[(\000)]TJ/F15 9.9626 Tf 7.7487 0 Td[(1)]TJ/F45 9.9626 Tf 8.8003 0 Td[(do)]TJ/F15 9.9626 Tf -90.7739 -14.7898 Td[(!)-444(tran)1(s)-1(f)1(e)-1(r)]TJ/F24 9.9626 Tf 44.1124 0 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F7 6.9738 Tf 2.5599 0 Td[(+1)]TJ/F15 9.9626 Tf 13.9062 1.4944 Td[(to)-333(the)-333(next)-333(\014ner)-333(lev)28(e)-1(l)]TJ/F24 9.9626 Tf -65.463 -11.9674 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(R)]TJ/F10 6.9738 Tf 7.6415 3.6153 Td[(T)]TJ -0.077 -6.4368 Td[(l)]TJ/F7 6.9738 Tf 2.5599 0 Td[(+1)]TJ/F24 9.9626 Tf 10.5854 2.8215 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F7 6.9738 Tf 2.5598 0 Td[(+1)]TJ/F15 9.9626 Tf 10.5854 1.4944 Td[(;)]TJ -59.9654 -14.855 Td[(!)-444(c)-1(ompu)1(te)-334(th)1(e)-334(res)-1(i)1(du)1(al)-334(at)-333(th)1(e)-334(c)-1(u)1(rr)1(e)-1(n)28(t)-333(lev)28(e)-1(l)]TJ/F24 9.9626 Tf 0 -12.3426 Td[(r)]TJ/F10 6.9738 Tf 4.4947 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(l)]TJ/F27 9.9626 Tf 5.2719 1.4944 Td[(\000)]TJ/F24 9.9626 Tf 9.9626 0 Td[(A)]TJ/F13 6.9738 Tf 7.472 4.2618 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F10 6.9738 Tf -6.2267 -7.2671 Td[(l)]TJ/F24 9.9626 Tf 10.696 3.0053 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 3.058 1.4944 Td[(;)]TJ -67.0102 -14.7898 Td[(!)-444(app)1(ly)-333(the)-333(basic)-334(Sc)28(h)28(w)28(arz)-334(p)1(re)-1(cond)1(ition)1(e)-1(r)-333(to)-333(th)1(e)-334(res)-1(i)1(dual)]TJ/F24 9.9626 Tf 0 -12.3426 Td[(r)]TJ/F10 6.9738 Tf 4.4947 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(M)]TJ/F13 6.9738 Tf 10.7513 4.2618 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F10 6.9738 Tf -7.3128 -7.2671 Td[(l)]TJ/F24 9.9626 Tf 11.7822 3.0053 Td[(r)]TJ/F10 6.9738 Tf 4.4947 -1.4944 Td[(l)]TJ/F15 9.9626 Tf -46.7782 -13.2954 Td[(!)-444(up)-27(date)]TJ/F24 9.9626 Tf 40.6809 0 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F24 9.9626 Tf -45.5654 -10.4608 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.2719 1.4944 Td[(+)]TJ/F24 9.9626 Tf 9.9626 0 Td[(r)]TJ/F10 6.9738 Tf 4.4947 -1.4944 Td[(l)]TJ/F45 9.9626 Tf -55.8022 -10.4608 Td[(endfor)]TJ/F24 9.9626 Tf 0 -14.7898 Td[(w)]TJ/F15 9.9626 Tf 10.1678 0 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(y)]TJ/F7 6.9738 Tf 4.8845 -1.4944 Td[(1)]TJ/F15 9.9626 Tf 4.4694 1.4944 Td[(;)]TJ +ET +1 0 0 1 433.5855 443.4809 cm q -1 0 0 1 433.785 443.282 cm -[]0 d 0 J 0.398 w 0 0 m 0 271.614 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 271.2158 l +S Q +1 0 0 1 -267.9179 -0.3985 cm q -1 0 0 1 165.668 443.282 cm -[]0 d 0 J 0.398 w 0 0 m 268.316 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +268.3164 0.1992 l +S Q +1 0 0 1 -51.4935 -18.5347 cm 0 g 0 G +1 0 0 1 -114.1741 -424.5477 cm BT -/F15 10.9091 Tf 114.174 424.548 Td [(Figure)-333(1:)-445(Application)-333(of)-333(the)-333(m)27(ulti-lev)28(el)-333(h)28(ybrid)-334(p)-27(ost-smo)-28(othed)-334(p)1(re)-1(cond)1(itioner.)]TJ +/F15 10.9091 Tf 114.1741 424.5477 Td[(Figu)1(re)-334(1:)-444(Ap)1(pli)1(c)-1(ation)-332(of)-333(the)-334(m)28(ul)1(ti-le)-1(v)28(el)-333(h)28(yb)1(rid)-333(p)-27(ost-)-1(smo)-28(othed)-333(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ +ET +1 0 0 1 485.4775 424.5477 cm 0 g 0 G +1 0 0 1 -391.8773 -14.0763 cm 0 g 0 G +1 0 0 1 0 -32.1522 cm 0 g 0 G - -7.24 -46.229 Td [(2.)]TJ +1 0 0 1 -93.6002 -378.3192 cm +BT +/F15 10.9091 Tf 106.9336 378.3192 Td[(2.)]TJ +ET +1 0 0 1 115.4185 378.3192 cm 0 g 0 G - [-500(construction)-333(of)-333(the)-334(prolongator)]TJ/F22 10.9091 Tf 166.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(T)]TJ -0.084 -7.192 Td [(C)]TJ/F15 10.9091 Tf 7.097 3.233 Td [(;)]TJ +1 0 0 1 -115.4185 -378.3192 cm +BT +/F15 10.9091 Tf 120.873 378.3192 Td[(construction)-333(of)-332(the)-334(p)1(rolon)1(gator)]TJ/F24 10.9091 Tf 152.5759 0 Td[(R)]TJ/F25 7.9701 Tf 8.3675 3.9588 Td[(T)]TJ -0.0843 -7.1916 Td[(C)]TJ/F15 10.9091 Tf 7.0968 3.2328 Td[(;)]TJ +ET +1 0 0 1 93.6002 353.2676 cm 0 g 0 G - -181.895 -25.051 Td [(3.)]TJ +1 0 0 1 -93.6002 -353.2676 cm +BT +/F15 10.9091 Tf 106.9336 353.2676 Td[(3.)]TJ +ET +1 0 0 1 115.4185 353.2676 cm 0 g 0 G - [-500(application)-333(of)]TJ/F22 10.9091 Tf 82.727 0 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.733 1.689 Td [(and)]TJ/F22 10.9091 Tf 21.212 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.958 Td [(T)]TJ -0.084 -7.191 Td [(C)]TJ/F15 10.9091 Tf 10.733 3.233 Td [(to)-333(build)]TJ/F22 10.9091 Tf 41.212 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.097 1.689 Td [(.)]TJ -194.86 -25.052 Td [(T)83(o)-426(p)-28(erform)-426(the)-426(coarsening)-426(s)-1(tep,)-449(w)28(e)-427(ha)28(v)28(e)-426(implemen)27(ted)-426(the)-426(aggregation)-426(algorithm)]TJ -16.937 -13.549 Td [(sk)28(etc)27(hed)-388(in)-388([)]TJ +1 0 0 1 -115.4185 -353.2676 cm +BT +/F15 10.9091 Tf 120.873 353.2676 Td[(app)1(lication)-333(of)]TJ/F24 10.9091 Tf 68.788 0 Td[(R)]TJ/F25 7.9701 Tf 8.2831 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.7332 1.6887 Td[(and)]TJ/F24 10.9091 Tf 21.2121 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(T)]TJ -0.0842 -7.1916 Td[(C)]TJ/F15 10.9091 Tf 10.7331 3.2328 Td[(to)-333(bu)1(ild)]TJ/F24 10.9091 Tf 41.2122 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(.)]TJ -194.8598 -25.0516 Td[(T)83(o)-426(p)-28(erf)1(orm)-426(the)-427(coarse)-1(n)1(ing)-426(ste)-1(p)1(,)-449(w)27(e)-427(h)1(a)28(v)28(e)-427(impleme)-1(n)28(t)1(e)-1(d)-426(th)1(e)-427(aggregation)-426(al)1(gorith)1(m)]TJ -16.9365 -13.5492 Td[(sk)28(e)-1(tc)28(hed)-389(i)1(n)-388([)]TJ +ET +1 0 0 1 154.5615 314.6668 cm 1 0 0 rg 1 0 0 RG - [(4)]TJ +1 0 0 1 -154.5615 -314.6668 cm +BT +/F15 10.9091 Tf 154.5615 314.6668 Td[(4)]TJ +ET +1 0 0 1 160.016 314.6668 cm 0 g 0 G - [(].)-610(According)-389(to)-388([)]TJ +1 0 0 1 -160.016 -314.6668 cm +BT +/F15 10.9091 Tf 160.016 314.6668 Td[(].)-610(Accordi)1(ng)-388(to)-389([)]TJ +ET +1 0 0 1 242.1465 314.6668 cm 1 0 0 rg 1 0 0 RG - [(24)]TJ +1 0 0 1 -242.1465 -314.6668 cm +BT +/F15 10.9091 Tf 242.1465 314.6668 Td[(24)]TJ +ET +1 0 0 1 253.0556 314.6668 cm 0 g 0 G - [(],)-403(a)-388(mo)-28(di\014cation)-388(of)-389(this)-388(algorithm)-389(h)1(as)-389(b)-28(een)-388(actually)]TJ 0 -13.549 Td [(considered,)-257(in)-237(whic)28(h)-238(eac)28(h)-237(aggregate)]TJ/F22 10.9091 Tf 169.041 0 Td [(N)]TJ/F23 7.9701 Tf 8.765 -1.637 Td [(r)]TJ/F15 10.9091 Tf 7.145 1.637 Td [(is)-237(m)-1(ad)1(e)-238(of)-237(v)27(ertices)-237(of)]TJ/F22 10.9091 Tf 99.164 0 Td [(W)]TJ/F15 10.9091 Tf 14.409 0 Td [(that)-237(are)]TJ/F18 10.9091 Tf 39.757 0 Td [(str)51(ongly)-269(c)51(ouple)51(d)]TJ/F15 10.9091 Tf -338.281 -13.55 Td [(to)-333(a)-334(certain)-333(ro)-28(ot)-333(v)28(ertex)]TJ/F22 10.9091 Tf 115.243 0 Td [(r)]TJ/F25 10.9091 Tf 8.255 0 Td [(2)]TJ/F22 10.9091 Tf 10.303 0 Td [(W)]TJ/F15 10.9091 Tf 11.818 0 Td [(,)-333(i.e.)]TJ/F22 10.9091 Tf -39.684 -28.523 Td [(N)]TJ/F23 7.9701 Tf 8.765 -1.637 Td [(r)]TJ/F15 10.9091 Tf 7.585 1.637 Td [(=)]TJ/F28 10.9091 Tf 11.515 12.109 Td [(n)]TJ/F22 10.9091 Tf 7.273 -12.109 Td [(s)]TJ/F25 10.9091 Tf 8.144 0 Td [(2)]TJ/F22 10.9091 Tf 10.303 0 Td [(W)]TJ/F15 10.9091 Tf 14.848 0 Td [(:)]TJ/F25 10.9091 Tf 6.061 0 Td [(j)]TJ/F22 10.9091 Tf 3.03 0 Td [(a)]TJ/F23 7.9701 Tf 5.767 -1.637 Td [(r)-29(s)]TJ/F25 10.9091 Tf 8.47 1.637 Td [(j)]TJ/F22 10.9091 Tf 6.061 0 Td [(>)-278(\022)]TJ/F28 10.9091 Tf 16.939 9.859 Td [(p)]TJ +1 0 0 1 -253.0556 -314.6668 cm +BT +/F15 10.9091 Tf 253.0556 314.6668 Td[(],)-402(a)-388(m)-1(o)-27(di\014)1(c)-1(ati)1(on)-389(of)-388(t)1(his)-389(algor)1(ith)1(m)-389(has)-389(b)-27(e)-1(en)-388(actuall)1(y)]TJ -159.4554 -13.5492 Td[(considered,)-256(in)-237(whic)28(h)-237(e)-1(ac)28(h)-237(aggre)-1(gat)1(e)]TJ/F24 10.9091 Tf 169.0404 0 Td[(N)]TJ/F25 7.9701 Tf 8.7651 -1.6364 Td[(r)]TJ/F15 10.9091 Tf 7.1452 1.6364 Td[(is)-238(made)-237(of)-237(v)28(e)-1(rt)1(ic)-1(es)-238(of)]TJ/F24 10.9091 Tf 99.1645 0 Td[(W)]TJ/F15 10.9091 Tf 14.4087 0 Td[(th)1(at)-238(ar)1(e)]TJ/F20 10.9091 Tf 39.7567 0 Td[(str)51(ongly)-269(c)51(ou)1(ple)51(d)]TJ/F15 10.9091 Tf -338.2806 -13.5492 Td[(to)-333(a)-334(certain)-333(r)1(o)-28(ot)-333(v)28(e)-1(r)1(te)-1(x)]TJ/F24 10.9091 Tf 115.2426 0 Td[(r)]TJ/F27 10.9091 Tf 8.255 0 Td[(2)]TJ/F24 10.9091 Tf 10.303 0 Td[(W)]TJ/F15 10.9091 Tf 11.8182 0 Td[(,)-333(i.e.)]TJ/F24 10.9091 Tf -39.6838 -28.5239 Td[(N)]TJ/F25 7.9701 Tf 8.7651 -1.6364 Td[(r)]TJ/F15 10.9091 Tf 7.585 1.6364 Td[(=)]TJ/F30 10.9091 Tf 11.5151 12.1092 Td[(n)]TJ/F24 10.9091 Tf 7.2728 -12.1092 Td[(s)]TJ/F27 10.9091 Tf 8.1438 0 Td[(2)]TJ/F24 10.9091 Tf 10.303 0 Td[(W)]TJ/F15 10.9091 Tf 14.8485 0 Td[(:)]TJ/F27 10.9091 Tf 6.0605 0 Td[(j)]TJ/F24 10.9091 Tf 3.0303 0 Td[(a)]TJ/F25 7.9701 Tf 5.7664 -1.6364 Td[(r)-30(s)]TJ/F27 10.9091 Tf 8.4707 1.6364 Td[(j)]TJ/F24 10.9091 Tf 6.0606 0 Td[(>)-278(\022)]TJ/F30 10.9091 Tf 16.9393 9.8599 Td[(p)]TJ ET +1 0 0 1 325.2054 268.9044 cm q -1 0 0 1 325.205 269.123 cm -[]0 d 0 J 0.436 w 0 0 m 34.535 0 l S +[]0 d +0 J +0.4364 w +0 0.2182 m +34.5348 0.2182 l +S Q +1 0 0 1 -325.2054 -268.9044 cm BT -/F25 10.9091 Tf 325.205 259.044 Td [(j)]TJ/F22 10.9091 Tf 3.031 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 -1.636 Td [(r)-29(r)]TJ/F22 10.9091 Tf 8.611 1.636 Td [(a)]TJ/F23 7.9701 Tf 5.767 -1.636 Td [(ss)]TJ/F25 10.9091 Tf 8.33 1.636 Td [(j)]TJ/F28 10.9091 Tf 3.03 12.11 Td [(o)]TJ/F25 10.9091 Tf 9.697 -12.11 Td [([)-222(f)]TJ/F22 10.9091 Tf 15.152 0 Td [(r)]TJ/F25 10.9091 Tf 5.224 0 Td [(g)]TJ/F22 10.9091 Tf 7.273 0 Td [(;)]TJ/F15 10.9091 Tf -303.486 -29.13 Td [(for)-341(a)-341(giv)28(en)]TJ/F22 10.9091 Tf 54.517 0 Td [(\022)]TJ/F25 10.9091 Tf 8.59 0 Td [(2)]TJ/F15 10.9091 Tf 10.439 0 Td [([0)]TJ/F22 10.9091 Tf 8.485 0 Td [(;)]TJ/F15 10.9091 Tf 4.848 0 Td [(1].)-467(Since)-341(th)1(is)-341(algorithm)-341(has)-341(a)-341(sequen)28(tial)-341(natu)1(re,)-343(a)]TJ/F18 10.9091 Tf 242.976 0 Td [(de)51(c)51(ouple)51(d)]TJ/F15 10.9091 Tf 49.172 0 Td [(v)28(ersion)]TJ -379.027 -13.549 Td [(of)-399(it)-399(has)-399(b)-27(ee)-1(n)-398(c)27(hosen,)-415(where)-399(eac)28(h)-399(pro)-28(cessor)]TJ/F22 10.9091 Tf 216.236 0 Td [(i)]TJ/F15 10.9091 Tf 8.111 0 Td [(indep)-28(enden)28(tly)-399(applies)-399(the)-398(algorithm)-399(to)]TJ -224.347 -13.549 Td [(the)-421(set)-421(of)-421(v)28(ertices)]TJ/F22 10.9091 Tf 91.547 0 Td [(W)]TJ/F20 7.9701 Tf 11.818 3.959 Td [(0)]TJ/F23 7.9701 Tf -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 10.839 3.055 Td [(assigned)-421(to)-421(it)-421(in)-420(the)-421(initial)-421(data)-421(distribution.)-707(This)-420(v)27(ersion)-421(i)1(s)]TJ -112.689 -13.549 Td [(em)28(barrassingly)-250(parallel,)-267(since)-250(it)-251(do)-27(es)-251(not)-250(require)-250(an)28(y)-250(data)-251(comm)28(unication.)-416(On)-251(the)-250(other)]TJ 0 -13.549 Td [(hand,)-312(it)-306(ma)28(y)-306(pro)-28(duce)-306(non-uniform)-307(aggr)1(e)-1(gates)-306(near)-306(b)-28(oundary)-306(v)28(ertices,)-312(i.e.)-306(near)-307(v)28(ertices)]TJ 0 -13.55 Td [(adjacen)28(t)-403(to)-403(v)27(ertices)-403(in)-403(other)-403(pro)-28(cessors,)-420(and)-403(is)-404(strongly)-403(dep)-27(enden)27(t)-403(on)-403(the)-403(n)28(um)28(b)-28(er)-403(of)]TJ 0 -13.549 Td [(pro)-28(cessors)-314(and)-314(on)-314(the)-314(initial)-314(partitioning)-314(of)-314(the)-314(matrix)]TJ/F22 10.9091 Tf 263.566 0 Td [(A)]TJ/F15 10.9091 Tf 8.181 0 Td [(.)-438(Nev)28(ertheless,)-318(this)-314(algorithm)]TJ -271.747 -13.549 Td [(has)-260(b)-27(een)-260(c)28(hosen)-260(for)-260(th)1(e)-260(implemen)28(tation)-260(in)-260(MLD)1(2P4,)-275(since)-260(i)1(t)-260(has)-260(b)-27(e)-1(en)-259(sho)28(wn)-260(to)-260(pro)-27(duce)]TJ 0 -13.549 Td [(go)-28(o)-28(d)-333(results)-333(in)-333(practice)-334([)]TJ +/F27 10.9091 Tf 325.2054 259.0445 Td[(j)]TJ/F24 10.9091 Tf 3.0303 0 Td[(a)]TJ/F25 7.9701 Tf 5.7664 -1.6364 Td[(r)-30(r)]TJ/F24 10.9091 Tf 8.6114 1.6364 Td[(a)]TJ/F25 7.9701 Tf 5.7664 -1.6364 Td[(ss)]TJ/F27 10.9091 Tf 8.33 1.6364 Td[(j)]TJ/F30 10.9091 Tf 3.0303 12.1091 Td[(o)]TJ/F27 10.9091 Tf 9.6969 -12.1091 Td[([)-222(f)]TJ/F24 10.9091 Tf 15.1515 0 Td[(r)]TJ/F27 10.9091 Tf 5.2248 0 Td[(g)]TJ/F24 10.9091 Tf 7.2727 0 Td[(;)]TJ/F15 10.9091 Tf -303.4859 -29.1301 Td[(for)-340(a)-341(giv)28(en)]TJ/F24 10.9091 Tf 54.5168 0 Td[(\022)]TJ/F27 10.9091 Tf 8.5901 0 Td[(2)]TJ/F15 10.9091 Tf 10.4386 0 Td[([0)]TJ/F24 10.9091 Tf 8.4849 0 Td[(;)]TJ/F15 10.9091 Tf 4.8484 0 Td[(1].)-466(Sin)1(c)-1(e)-341(th)1(is)-341(algorith)1(m)-341(has)-341(a)-341(se)-1(q)1(uen)28(tial)-340(natu)1(re)-1(,)-342(a)]TJ/F20 10.9091 Tf 242.9761 0 Td[(de)51(c)51(oupl)1(e)51(d)]TJ/F15 10.9091 Tf 49.1719 0 Td[(v)28(ers)-1(i)1(on)]TJ -379.0268 -13.5492 Td[(of)-398(it)-399(has)-399(b)-27(e)-1(en)-399(c)28(hose)-1(n)1(,)-415(w)-1(h)1(e)-1(r)1(e)-400(eac)27(h)-398(pro)-27(c)-1(es)-1(sor)]TJ/F24 10.9091 Tf 216.2363 0 Td[(i)]TJ/F15 10.9091 Tf 8.1102 0 Td[(in)1(dep)-28(end)1(e)-1(n)29(tly)-399(ap)1(pli)1(e)-1(s)-399(the)-399(algori)1(thm)-399(to)]TJ -224.3465 -13.5492 Td[(th)1(e)-422(se)-1(t)-420(of)-421(v)28(ertice)-1(s)]TJ/F24 10.9091 Tf 91.547 0 Td[(W)]TJ/F22 7.9701 Tf 11.8182 3.9589 Td[(0)]TJ/F25 7.9701 Tf -1.5152 -7.0144 Td[(i)]TJ/F15 10.9091 Tf 10.8388 3.0555 Td[(ass)-1(ign)1(e)-1(d)-420(to)-421(it)-420(in)-421(t)1(he)-421(ini)1(tial)-421(d)1(ata)-421(di)1(s)-1(tr)1(ibu)1(tion.)-706(T)-1(h)1(is)-421(v)28(e)-1(r)1(s)-1(ion)-420(is)]TJ -112.6888 -13.5492 Td[(em)27(bar)1(rass)-1(in)1(gly)-250(p)1(arallel,)-267(sin)1(c)-1(e)-250(it)-250(do)-28(es)-251(n)1(ot)-250(re)-1(q)1(uir)1(e)-251(an)28(y)-250(d)1(ata)-250(c)-1(omm)27(u)1(nication)1(.)-417(On)-249(the)-250(other)]TJ 0 -13.5492 Td[(han)1(d,)-311(it)-306(ma)27(y)-306(p)1(ro)-28(d)1(uce)-307(non)1(-)-1(u)1(ni)1(form)-306(aggregate)-1(s)-306(near)-306(b)-28(ou)1(nd)1(ary)-306(v)28(e)-1(r)1(tice)-1(s,)-312(i.)1(e)-1(.)-306(n)1(e)-1(ar)-306(v)28(ertice)-1(s)]TJ 0 -13.5492 Td[(adj)1(ac)-1(en)28(t)-403(to)-403(v)28(ertices)-404(in)-402(other)-403(pr)1(o)-28(c)-1(es)-1(sors,)-420(and)-403(i)1(s)-404(strongl)1(y)-403(dep)-28(end)1(e)-1(n)29(t)-403(on)-403(th)1(e)-404(n)28(u)1(m)27(b)-27(e)-1(r)-402(of)]TJ 0 -13.5492 Td[(pr)1(o)-28(ce)-1(ss)-1(or)1(s)-315(and)-313(on)-314(th)1(e)-315(in)1(itial)-313(parti)1(tioni)1(ng)-314(of)-314(th)1(e)-315(matri)1(x)]TJ/F24 10.9091 Tf 263.5655 0 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(.)-438(Nev)28(e)-1(r)1(theles)-1(s,)-318(thi)1(s)-315(algor)1(ithm)]TJ -271.7473 -13.5492 Td[(has)-260(b)-27(ee)-1(n)-259(c)27(h)1(os)-1(en)-259(for)-259(the)-260(imp)1(le)-1(men)28(tation)-259(in)-259(MLD)1(2P4,)-274(s)-1(i)1(nce)-261(i)1(t)-260(h)1(as)-260(b)-28(ee)-1(n)-259(sho)28(wn)-260(t)1(o)-260(pr)1(o)-28(du)1(c)-1(e)]TJ 0 -13.5492 Td[(go)-28(o)-28(d)-332(re)-1(sul)1(ts)-334(in)-333(p)1(ractice)-334([)]TJ +ET +1 0 0 1 211.964 121.5209 cm 1 0 0 rg 1 0 0 RG - [(3)]TJ +1 0 0 1 -211.964 -121.5209 cm +BT +/F15 10.9091 Tf 211.964 121.5209 Td[(3)]TJ +ET +1 0 0 1 217.4185 121.5209 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -217.4185 -121.5209 cm +BT +/F15 10.9091 Tf 217.4185 121.5209 Td[(,)]TJ +ET +1 0 0 1 224.0852 121.5209 cm 1 0 0 rg 1 0 0 RG - [-333(4)]TJ +1 0 0 1 -224.0852 -121.5209 cm +BT +/F15 10.9091 Tf 224.0852 121.5209 Td[(4)]TJ +ET +1 0 0 1 229.5397 121.5209 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -229.5397 -121.5209 cm +BT +/F15 10.9091 Tf 229.5397 121.5209 Td[(,)]TJ +ET +1 0 0 1 236.2064 121.5209 cm 1 0 0 rg 1 0 0 RG - [-333(23)]TJ +1 0 0 1 -236.2064 -121.5209 cm +BT +/F15 10.9091 Tf 236.2064 121.5209 Td[(23)]TJ +ET +1 0 0 1 247.1155 121.5209 cm 0 g 0 G - [(].)]TJ +1 0 0 1 -247.1155 -121.5209 cm +BT +/F15 10.9091 Tf 247.1155 121.5209 Td[(].)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -312 0 obj << +336 0 obj << /Type /Page -/Contents 313 0 R -/Resources 311 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 320 0 R -/Annots [ 310 0 R 305 0 R 306 0 R 307 0 R 308 0 R 309 0 R ] +/Contents 337 0 R +/Resources 335 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 356 0 R +/Annots [ 339 0 R 351 0 R 352 0 R 353 0 R 354 0 R 355 0 R ] >> endobj -310 0 obj << +339 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -305 0 obj << +351 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [153.565 313.671 161.012 322.693] +/Rect [153.5652 313.6705 161.0123 322.6933] /Subtype /Link /A << /S /GoTo /D (cite.apnum_07) >> >> endobj -306 0 obj << +352 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [241.15 313.671 254.052 322.693] +/Rect [241.1502 313.6705 254.0519 322.6933] /Subtype /Link /A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> >> endobj -307 0 obj << +353 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [210.968 120.525 218.415 129.547] +/Rect [210.9677 120.5246 218.4148 129.5474] /Subtype /Link /A << /S /GoTo /D (cite.aaecc_07) >> >> endobj -308 0 obj << +354 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [223.089 120.525 230.536 129.547] +/Rect [223.0889 120.5246 230.536 129.5474] /Subtype /Link /A << /S /GoTo /D (cite.apnum_07) >> >> endobj -309 0 obj << +355 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [235.21 120.525 248.112 129.547] +/Rect [235.2101 120.5246 248.1118 129.5474] /Subtype /Link /A << /S /GoTo /D (cite.TUMINARO_TONG) >> >> endobj -314 0 obj << -/D [312 0 R /XYZ 93.6 740.002 null] +338 0 obj << +/D [336 0 R /XYZ 93.6002 740.0018 null] >> endobj -304 0 obj << -/D [312 0 R /XYZ 161.932 438.097 null] +334 0 obj << +/D [336 0 R /XYZ 161.9317 438.097 null] >> endobj -318 0 obj << -/D [312 0 R /XYZ 93.6 389.278 null] +349 0 obj << +/D [336 0 R /XYZ 93.6002 389.2781 null] >> endobj -319 0 obj << -/D [312 0 R /XYZ 93.6 369.335 null] +350 0 obj << +/D [336 0 R /XYZ 93.6002 369.3352 null] >> endobj -311 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F22 175 0 R /F7 315 0 R /F43 158 0 R /F10 316 0 R /F13 317 0 R /F25 176 0 R /F23 271 0 R /F18 173 0 R /F28 275 0 R /F20 273 0 R >> +335 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F24 186 0 R /F7 342 0 R /F45 147 0 R /F10 345 0 R /F13 348 0 R /F27 189 0 R /F25 290 0 R /F20 181 0 R /F30 302 0 R /F22 296 0 R >> /ProcSet [ /PDF /Text ] >> endobj -326 0 obj << -/Length 3876 +359 0 obj << +/Length 5350 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(14)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(14)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F15 10.9091 Tf -186.329 -35.866 Td [(The)-277(prolongator)]TJ/F22 10.9091 Tf 80.039 0 Td [(P)]TJ/F23 7.9701 Tf 7.003 -1.688 Td [(C)]TJ/F15 10.9091 Tf 10.127 1.688 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(T)]TJ -0.084 -7.191 Td [(C)]TJ/F15 10.9091 Tf 10.116 3.232 Td [(is)-277(built)-276(starting)-277(from)-277(a)]TJ/F18 10.9091 Tf 109.52 0 Td [(tentative)-306(pr)51(olongator)]TJ/F22 10.9091 Tf 102.594 0 Td [(P)]TJ/F25 10.9091 Tf 11.55 0 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.181 3.959 Td [(n)]TJ/F26 7.9701 Tf 5.138 0 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.339 Td [(C)]TJ/F15 10.9091 Tf 6.693 -2.62 Td [(,)]TJ -409.421 -13.549 Td [(de\014ned)-333(as)]TJ/F22 10.9091 Tf 114.818 -17.818 Td [(P)]TJ/F15 10.9091 Tf 11.549 0 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.758 0 Td [(p)]TJ/F23 7.9701 Tf 5.489 -1.637 Td [(ij)]TJ/F15 10.9091 Tf 7.265 1.637 Td [(\051)]TJ/F22 10.9091 Tf 4.242 0 Td [(;)-1167(p)]TJ/F23 7.9701 Tf 21.247 -1.637 Td [(ij)]TJ/F15 10.9091 Tf 10.295 1.637 Td [(=)]TJ/F28 10.9091 Tf 11.515 15.381 Td [(\032)]TJ/F15 10.9091 Tf 13.163 -9.135 Td [(1)-1913(if)]TJ/F22 10.9091 Tf 35.721 0 Td [(i)]TJ/F25 10.9091 Tf 6.788 0 Td [(2)]TJ/F22 10.9091 Tf 10.303 0 Td [(V)]TJ/F23 7.9701 Tf 8.788 5.307 Td [(j)]TJ -2.424 -8.741 Td [(C)]TJ/F15 10.9091 Tf -59.176 -10.116 Td [(0)-1913(otherwise)]TJ/F22 10.9091 Tf 79.261 7.304 Td [(:)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F15 10.9091 Tf 103.3363 704.1363 Td[(The)-277(pr)1(olongat)1(or)]TJ/F24 10.9091 Tf 80.0384 0 Td[(P)]TJ/F25 7.9701 Tf 7.0037 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.1271 1.6887 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(T)]TJ -0.0842 -7.1916 Td[(C)]TJ/F15 10.9091 Tf 10.1159 3.2328 Td[(is)-277(bu)1(ilt)-276(s)-1(tar)1(ting)-276(from)-277(a)]TJ/F20 10.9091 Tf 109.5201 0 Td[(tent)-1(ative)-305(pr)51(olongator)]TJ/F24 10.9091 Tf 102.5945 0 Td[(P)]TJ/F27 10.9091 Tf 11.5492 0 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F28 7.9701 Tf 5.1382 0 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F26 5.9776 Tf 5.1382 -1.3394 Td[(C)]TJ/F15 10.9091 Tf 6.6924 -2.6194 Td[(,)]TJ -409.4208 -13.5492 Td[(de\014n)1(e)-1(d)-332(as)]TJ/F24 10.9091 Tf 114.8185 -17.8186 Td[(P)]TJ/F15 10.9091 Tf 11.5491 0 Td[(=)-278(\050)]TJ/F24 10.9091 Tf 15.7576 0 Td[(p)]TJ/F25 7.9701 Tf 5.4886 -1.6364 Td[(ij)]TJ/F15 10.9091 Tf 7.2653 1.6364 Td[(\051)]TJ/F24 10.9091 Tf 4.2425 0 Td[(;)-1166(p)]TJ/F25 7.9701 Tf 21.2462 -1.6364 Td[(ij)]TJ/F15 10.9091 Tf 10.2955 1.6364 Td[(=)]TJ/F30 10.9091 Tf 11.5151 15.3819 Td[(\032)]TJ/F15 10.9091 Tf 13.1632 -9.1358 Td[(1)-1913(if)]TJ/F24 10.9091 Tf 35.7202 0 Td[(i)]TJ/F27 10.9091 Tf 6.7886 0 Td[(2)]TJ/F24 10.9091 Tf 10.3029 0 Td[(V)]TJ/F25 7.9701 Tf 8.7879 5.3073 Td[(j)]TJ -2.4242 -8.7414 Td[(C)]TJ/F15 10.9091 Tf -59.1754 -10.1151 Td[(0)-1913(otherwise)]TJ/F24 10.9091 Tf 79.2607 7.3031 Td[(:)]TJ +ET +1 0 0 1 484.9115 672.7685 cm 0 g 0 G -/F15 10.9091 Tf 103.909 0 Td [(\0502\051)]TJ +1 0 0 1 -484.9115 -672.7685 cm +BT +/F15 10.9091 Tf 484.9115 672.7685 Td[(\0502\051)]TJ +ET +1 0 0 1 498.8509 672.7685 cm 0 g 0 G -/F22 10.9091 Tf -398.511 -27.614 Td [(P)]TJ/F23 7.9701 Tf 7.003 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.734 1.689 Td [(is)-333(obtained)-334(b)28(y)-333(applying)-333(to)]TJ/F22 10.9091 Tf 128.848 0 Td [(P)]TJ/F15 10.9091 Tf 12.156 0 Td [(a)-333(smo)-28(other)]TJ/F22 10.9091 Tf 56.757 0 Td [(S)]TJ/F25 10.9091 Tf 10.349 0 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.181 3.958 Td [(n)]TJ/F26 7.9701 Tf 5.139 0 Td [(\002)]TJ/F23 7.9701 Tf 6.586 0 Td [(n)]TJ/F15 10.9091 Tf 5.636 -3.958 Td [(:)]TJ/F22 10.9091 Tf -79.223 -24.508 Td [(P)]TJ/F23 7.9701 Tf 7.003 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.127 1.689 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(S)-58(P)-27(;)]TJ +1 0 0 1 -498.8509 -672.7685 cm +BT +/F24 10.9091 Tf 86.3998 645.1545 Td[(P)]TJ/F25 7.9701 Tf 7.0038 -1.6886 Td[(C)]TJ/F15 10.9091 Tf 10.7331 1.6886 Td[(is)-334(ob)1(tain)1(e)-1(d)-333(b)29(y)-334(ap)1(pl)1(ying)-333(to)]TJ/F24 10.9091 Tf 128.8487 0 Td[(P)]TJ/F15 10.9091 Tf 12.1553 0 Td[(a)-333(s)-1(mo)-28(oth)1(e)-1(r)]TJ/F24 10.9091 Tf 56.7576 0 Td[(S)]TJ/F27 10.9091 Tf 10.3484 0 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F28 7.9701 Tf 5.1382 0 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 5.6363 -3.9588 Td[(:)]TJ/F24 10.9091 Tf -79.2239 -24.5081 Td[(P)]TJ/F25 7.9701 Tf 7.0038 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.127 1.6887 Td[(=)]TJ/F24 10.9091 Tf 11.5152 0 Td[(S)-58(P)-28(;)]TJ +ET +1 0 0 1 484.9115 620.6464 cm 0 g 0 G -/F15 10.9091 Tf 187.699 0 Td [(\0503\051)]TJ +1 0 0 1 -484.9115 -620.6464 cm +BT +/F15 10.9091 Tf 484.9115 620.6464 Td[(\0503\051)]TJ +ET +1 0 0 1 498.8509 620.6464 cm 0 g 0 G - -398.511 -24.509 Td [(in)-303(order)-303(to)-303(remo)27(v)28(e)-303(oscillatory)-303(comp)-28(onen)28(ts)-303(from)-304(th)1(e)-304(range)-303(of)-303(the)-303(prolongator)-303(and)-303(hence)]TJ 0 -13.549 Td [(to)-433(impro)28(v)27(e)-433(the)-433(con)27(v)28(ergence)-433(prop)-28(erties)-433(of)-433(the)-434(m)28(ulti-lev)28(el)-433(Sc)27(h)28(w)28(arz)-433(me)-1(th)1(o)-28(d)-434([)]TJ +1 0 0 1 -498.8509 -620.6464 cm +BT +/F15 10.9091 Tf 86.3998 596.1383 Td[(in)-303(or)1(der)-303(to)-303(rem)-1(o)28(v)28(e)-303(os)-1(cillator)1(y)-303(c)-1(omp)-27(onen)28(ts)-304(f)1(rom)-303(the)-303(range)-303(of)-303(th)1(e)-304(pr)1(olongat)1(or)-303(and)-303(h)1(e)-1(n)1(c)-1(e)]TJ 0 -13.5492 Td[(to)-433(impro)28(v)28(e)-434(t)1(he)-434(con)28(v)28(ergence)-434(pr)1(op)-28(erties)-434(of)-433(th)1(e)-434(m)28(ulti)1(-)-1(lev)28(el)-434(S)1(c)27(h)28(w)28(arz)-433(m)-1(etho)-27(d)-433([)]TJ +ET +1 0 0 1 452.3671 582.5891 cm 1 0 0 rg 1 0 0 RG - [1(1)]TJ +1 0 0 1 -452.3671 -582.5891 cm +BT +/F15 10.9091 Tf 452.3671 582.5891 Td[(1)]TJ +ET +1 0 0 1 457.8216 582.5891 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -457.8216 -582.5891 cm +BT +/F15 10.9091 Tf 457.8216 582.5891 Td[(,)]TJ +ET +1 0 0 1 465.5789 582.5891 cm 1 0 0 rg 1 0 0 RG - [-434(22)]TJ +1 0 0 1 -465.5789 -582.5891 cm +BT +/F15 10.9091 Tf 465.5789 582.5891 Td[(22)]TJ +ET +1 0 0 1 476.488 582.5891 cm 0 g 0 G - [(].)-744(A)]TJ 0 -13.549 Td [(simple)-333(c)27(hoice)-333(for)]TJ/F22 10.9091 Tf 83.121 0 Td [(S)]TJ/F15 10.9091 Tf 10.954 0 Td [(is)-333(the)-334(damp)-27(ed)-334(Jacobi)-333(smo)-28(other:)]TJ/F22 10.9091 Tf 71.293 -24.508 Td [(S)]TJ/F15 10.9091 Tf 10.349 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(I)]TJ/F25 10.9091 Tf 8.075 0 Td [(\000)]TJ/F22 10.9091 Tf 10.91 0 Td [(!)-36(D)]TJ/F26 7.9701 Tf 16.516 4.504 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -4.504 Td [(A;)]TJ +1 0 0 1 -476.488 -582.5891 cm +BT +/F15 10.9091 Tf 476.488 582.5891 Td[(].)-744(A)]TJ -390.0882 -13.5492 Td[(sim)-1(p)1(le)-334(c)28(hoice)-334(f)1(or)]TJ/F24 10.9091 Tf 83.1212 0 Td[(S)]TJ/F15 10.9091 Tf 10.9546 0 Td[(is)-334(t)1(he)-334(d)1(am)-1(p)-27(ed)-333(Jac)-1(ob)1(i)-333(s)-1(mo)-28(oth)1(e)-1(r)1(:)]TJ/F24 10.9091 Tf 71.2927 -24.5081 Td[(S)]TJ/F15 10.9091 Tf 10.3484 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(I)]TJ/F27 10.9091 Tf 8.0757 0 Td[(\000)]TJ/F24 10.9091 Tf 10.9091 0 Td[(!)-36(D)]TJ/F28 7.9701 Tf 16.5167 4.5043 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -4.5043 Td[(A;)]TJ +ET +1 0 0 1 484.9115 544.5318 cm 0 g 0 G -/F15 10.9091 Tf 164.459 0 Td [(\0504\051)]TJ +1 0 0 1 -484.9115 -544.5318 cm +BT +/F15 10.9091 Tf 484.9115 544.5318 Td[(\0504\051)]TJ +ET +1 0 0 1 498.8509 544.5318 cm 0 g 0 G - -398.511 -24.508 Td [(where)-305(the)-305(v)55(alue)-305(of)]TJ/F22 10.9091 Tf 89.707 0 Td [(!)]TJ/F15 10.9091 Tf 10.51 0 Td [(can)-305(b)-28(e)-305(c)28(hosen)-305(using)-305(some)-306(estimate)-305(of)-305(the)-305(sp)-28(ectral)-305(radius)-305(of)]TJ/F22 10.9091 Tf 283.398 0 Td [(D)]TJ/F26 7.9701 Tf 9.335 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(A)]TJ/F15 10.9091 Tf -404.269 -13.549 Td [([)]TJ +1 0 0 1 -498.8509 -544.5318 cm +BT +/F15 10.9091 Tf 86.3998 520.0237 Td[(where)-305(the)-305(v)55(al)1(ue)-305(of)]TJ/F24 10.9091 Tf 89.7069 0 Td[(!)]TJ/F15 10.9091 Tf 10.5101 0 Td[(can)-305(b)-27(e)-306(c)27(h)1(os)-1(en)-305(u)1(s)-1(i)1(ng)-305(s)-1(ome)-305(e)-1(stimate)-306(of)-304(the)-305(s)-1(p)-27(e)-1(ctral)-304(radi)1(us)-306(of)]TJ/F24 10.9091 Tf 283.3986 0 Td[(D)]TJ/F28 7.9701 Tf 9.3349 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(A)]TJ/F15 10.9091 Tf -404.2693 -13.5492 Td[([)]TJ +ET +1 0 0 1 89.4301 506.4745 cm 1 0 0 rg 1 0 0 RG - [(1)]TJ +1 0 0 1 -89.4301 -506.4745 cm +BT +/F15 10.9091 Tf 89.4301 506.4745 Td[(1)]TJ +ET +1 0 0 1 94.8846 506.4745 cm 0 g 0 G - [(].)]TJ +1 0 0 1 -94.8846 -506.4745 cm +BT +/F15 10.9091 Tf 94.8846 506.4745 Td[(].)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -325 0 obj << +358 0 obj << /Type /Page -/Contents 326 0 R -/Resources 324 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 320 0 R -/Annots [ 321 0 R 322 0 R 323 0 R ] +/Contents 359 0 R +/Resources 357 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 356 0 R +/Annots [ 363 0 R 364 0 R 366 0 R ] >> endobj -321 0 obj << +363 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [451.371 581.593 458.818 590.616] +/Rect [451.3708 581.5929 458.8179 590.6157] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -322 0 obj << +364 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [464.583 581.593 477.484 590.616] +/Rect [464.5827 581.5929 477.4843 590.6157] /Subtype /Link /A << /S /GoTo /D (cite.StubenGMD69_99) >> >> endobj -323 0 obj << +366 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [88.434 505.478 95.881 514.501] +/Rect [88.4338 505.4783 95.8809 514.5011] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -327 0 obj << -/D [325 0 R /XYZ 86.4 740.002 null] +360 0 obj << +/D [358 0 R /XYZ 86.3998 740.0018 null] >> endobj -328 0 obj << -/D [325 0 R /XYZ 201.218 686.318 null] +361 0 obj << +/D [358 0 R /XYZ 201.2182 686.3177 null] >> endobj -329 0 obj << -/D [325 0 R /XYZ 268.566 634.196 null] +362 0 obj << +/D [358 0 R /XYZ 268.5656 634.1956 null] >> endobj -330 0 obj << -/D [325 0 R /XYZ 251.768 558.081 null] +365 0 obj << +/D [358 0 R /XYZ 251.7683 558.081 null] >> endobj -324 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F22 175 0 R /F23 271 0 R /F18 173 0 R /F25 176 0 R /F26 272 0 R /F24 274 0 R /F28 275 0 R /F20 273 0 R >> +357 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F24 186 0 R /F25 290 0 R /F20 181 0 R /F27 189 0 R /F28 293 0 R /F26 299 0 R /F30 302 0 R /F22 296 0 R >> /ProcSet [ /PDF /Text ] >> endobj -346 0 obj << -/Length 8885 +369 0 obj << +/Length 13173 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(5)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(5)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(Getting)-378(St)67(ar)67(ted)]TJ/F15 10.9091 Tf 401.542 0 Td [(15)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Getti)-1(ng)-378(St)67(a)-1(r)67(ted)]TJ/F15 10.9091 Tf 391.3906 0 Td[(15)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(5)-1125(Getting)-375(Started)]TJ/F15 10.9091 Tf 0 -24.352 Td [(W)83(e)-441(describ)-28(e)-441(the)-442(basics)-441(for)-441(building)-442(and)-441(applying)-441(MLD2P4)-441(one-lev)27(el)-441(and)-441(m)27(ult)1(i-)-1(l)1(e)-1(v)28(el)]TJ 0 -13.549 Td [(Sc)28(h)28(w)27(arz)-313(preconditioners)-313(with)-313(the)-313(Krylo)28(v)-313(solv)27(ers)-313(included)-313(in)-313(PSBLAS)-313([)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 14.3462 Tf 93.6002 704.1363 Td[(5)-1125(G)-1(et)-1(ti)-1(ng)-375(St)-1(a)1(r)-1(te)-1(d)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(W)84(e)-442(des)-1(crib)-27(e)-442(th)1(e)-442(basics)-442(for)-441(b)1(uil)1(din)1(g)-442(an)1(d)-441(app)1(lyin)1(g)-442(M)1(LD2P4)-441(one-le)-1(v)28(el)-441(and)-441(m)28(ult)1(i-)-1(l)1(e)-1(v)28(el)]TJ 0 -13.5492 Td[(Sc)28(h)28(w)28(arz)-314(p)1(rec)-1(on)1(diti)1(oners)-314(with)-312(the)-313(Kry)1(lo)28(v)-313(s)-1(olv)28(ers)-313(inclu)1(ded)-313(in)-313(P)1(SBLAS)-313([)]TJ +ET +1 0 0 1 430.5874 666.2349 cm 1 0 0 rg 1 0 0 RG - [(14)]TJ +1 0 0 1 -430.5874 -666.2349 cm +BT +/F15 10.9091 Tf 430.5874 666.2349 Td[(14)]TJ +ET +1 0 0 1 441.4965 666.2349 cm 0 g 0 G - [(].)-438(Th)1(e)-314(follo)28(w-)]TJ 0 -13.549 Td [(ing)-333(steps)-334(are)-333(required:)]TJ +1 0 0 1 -441.4965 -666.2349 cm +BT +/F15 10.9091 Tf 441.4965 666.2349 Td[(].)-437(The)-314(f)1(ollo)28(w-)]TJ -347.8963 -13.5492 Td[(in)1(g)-334(steps)-334(ar)1(e)-334(requi)1(re)-1(d)1(:)]TJ +ET +1 0 0 1 93.6002 631.6256 cm 0 g 0 G - 13.334 -21.06 Td [(1.)]TJ +1 0 0 1 -93.6002 -631.6256 cm +BT +/F15 10.9091 Tf 106.9336 631.6256 Td[(1.)]TJ +ET +1 0 0 1 115.4185 631.6256 cm 0 g 0 G -/F18 10.9091 Tf 13.939 0 Td [(De)51(clar)51(e)-370(the)-371(pr)51(e)51(c)51(onditioner)-370(data)-371(structur)51(e)]TJ/F15 10.9091 Tf 195.447 0 Td [(.)-487(It)-347(is)-347(a)-348(deriv)28(ed)-347(data)-348(t)28(yp)-28(e,)]TJ/F44 10.9091 Tf 131.812 0 Td [(mld_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(prec_)]TJ -356.542 -13.55 Td [(type)]TJ/F15 10.9091 Tf 22.909 0 Td [(,)-321(w)-1(h)1(e)-1(r)1(e)]TJ/F18 10.9091 Tf 37.922 0 Td [(x)]TJ/F15 10.9091 Tf 9.849 0 Td [(ma)28(y)-319(b)-28(e)]TJ/F44 10.9091 Tf 38.163 0 Td [(s)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F44 10.9091 Tf 6.538 0 Td [(d)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F44 10.9091 Tf 6.538 0 Td [(c)]TJ/F15 10.9091 Tf 9.202 0 Td [(or)]TJ/F44 10.9091 Tf 13.203 0 Td [(z)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-322(accordi)1(ng)-319(to)-319(the)-318(basic)-319(data)-318(t)28(yp)-28(e)-319(of)-318(the)-319(sparse)]TJ -161.505 -13.549 Td [(matrix)-372(\050)]TJ/F44 10.9091 Tf 40.153 0 Td [(s)]TJ/F15 10.9091 Tf 9.79 0 Td [(=)-372(real)-373(single)-372(precision;)]TJ/F44 10.9091 Tf 114.22 0 Td [(d)]TJ/F15 10.9091 Tf 9.79 0 Td [(=)-372(real)-373(double)-372(precision;)]TJ/F44 10.9091 Tf 119.008 0 Td [(c)]TJ/F15 10.9091 Tf 9.789 0 Td [(=)-372(complex)-373(single)]TJ -302.75 -13.549 Td [(precision;)]TJ/F44 10.9091 Tf 48.807 0 Td [(z)]TJ/F15 10.9091 Tf 9.518 0 Td [(=)-347(c)-1(omplex)-347(double)-347(precision\051.)-487(This)-348(data)-347(structure)-348(is)-347(accessed)-348(b)28(y)-347(the)]TJ -58.325 -13.549 Td [(user)-333(only)-334(throu)1(gh)-334(the)-333(MLD2P4)-333(routines,)-334(foll)1(o)27(wing)-333(an)-333(ob)-56(ject-orien)28(ted)-333(approac)27(h)1(.)]TJ +1 0 0 1 -115.4185 -631.6256 cm +BT +/F20 10.9091 Tf 120.873 631.6256 Td[(De)51(cl)1(a)-1(r)52(e)-371(the)-371(pr)52(e)51(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)-370(data)-371(structu)1(r)51(e)]TJ/F15 10.9091 Tf 195.4474 0 Td[(.)-486(It)-348(is)-347(a)-348(d)1(e)-1(r)1(iv)28(e)-1(d)-347(d)1(ata)-347(t)27(y)1(p)-28(e,)]TJ/F46 10.9091 Tf 131.8118 0 Td[(mld_)]TJ/F20 10.9091 Tf 22.9088 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(prec_)]TJ -356.5422 -13.5492 Td[(type)]TJ/F15 10.9091 Tf 22.9088 0 Td[(,)-321(w)-1(h)1(e)-1(r)1(e)]TJ/F20 10.9091 Tf 37.9221 0 Td[(x)]TJ/F15 10.9091 Tf 9.8494 0 Td[(ma)27(y)-318(b)-27(e)]TJ/F46 10.9091 Tf 38.1627 0 Td[(s)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F46 10.9091 Tf 6.5378 0 Td[(d)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F46 10.9091 Tf 6.5377 0 Td[(c)]TJ/F15 10.9091 Tf 9.2025 0 Td[(or)]TJ/F46 10.9091 Tf 13.2025 0 Td[(z)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)-321(ac)-1(cord)1(ing)-318(to)-319(th)1(e)-319(basic)-319(dat)1(a)-319(t)28(yp)-27(e)-319(of)-318(the)-319(spar)1(s)-1(e)]TJ -161.5051 -13.5492 Td[(matrix)-372(\050)]TJ/F46 10.9091 Tf 40.1533 0 Td[(s)]TJ/F15 10.9091 Tf 9.7896 0 Td[(=)-372(real)-372(s)-1(in)1(gle)-373(p)1(rec)-1(ision)1(;)]TJ/F46 10.9091 Tf 114.2202 0 Td[(d)]TJ/F15 10.9091 Tf 9.7896 0 Td[(=)-372(real)-372(doub)1(le)-373(p)1(rec)-1(ision)1(;)]TJ/F46 10.9091 Tf 119.0081 0 Td[(c)]TJ/F15 10.9091 Tf 9.7896 0 Td[(=)-372(c)-1(omp)1(le)-1(x)-372(singl)1(e)]TJ -302.7504 -13.5492 Td[(pr)1(e)-1(cision;)]TJ/F46 10.9091 Tf 48.8074 0 Td[(z)]TJ/F15 10.9091 Tf 9.5179 0 Td[(=)-347(c)-1(ompl)1(e)-1(x)-347(dou)1(ble)-347(prec)-1(i)1(s)-1(ion)1(\051.)-487(Th)1(is)-348(data)-347(s)-1(t)1(ructur)1(e)-348(is)-348(acc)-1(es)-1(se)-1(d)-347(b)29(y)-348(th)1(e)]TJ -58.3253 -13.5492 Td[(user)-333(only)-333(th)1(rough)-332(the)-334(M)1(LD2P4)-333(rou)1(tines,)-334(f)1(ollo)28(win)1(g)-334(an)-333(ob)-55(j)1(e)-1(ct-orien)28(ted)-333(app)1(roac)27(h)1(.)]TJ +ET +1 0 0 1 93.6002 555.4954 cm 0 g 0 G - -13.939 -21.934 Td [(2.)]TJ +1 0 0 1 -93.6002 -555.4954 cm +BT +/F15 10.9091 Tf 106.9336 555.4954 Td[(2.)]TJ +ET +1 0 0 1 115.4185 555.4954 cm 0 g 0 G -/F18 10.9091 Tf 13.939 0 Td [(A)26(l)-52(l)1(o)51(c)51(ate)-364(and)-365(ini)1(t)-1(i)1(alize)-364(t)-1(he)-364(pr)52(e)51(c)51(onditioner)-364(data)-364(structur)51(e,)-366(ac)51(c)51(or)51(ding)-364(to)-364(a)-364(pr)51(e)51(c)51(ondi-)]TJ 0 -13.549 Td [(tioner)-376(typ)51(e)-376(chosen)-375(by)-376(the)-376(user)]TJ/F15 10.9091 Tf 144.005 0 Td [(.)-503(This)-353(is)-353(p)-28(erformed)-353(b)28(y)-353(the)-353(routine)]TJ/F44 10.9091 Tf 169.416 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 68.727 0 Td [(,)]TJ -382.148 -13.549 Td [(whic)28(h)-406(also)-406(sets)-406(d)1(e)-1(f)1(aults)-406(for)-406(eac)28(h)-406(preconditioner)-405(t)27(yp)-27(e)-406(selected)-406(b)28(y)-406(the)-406(user.)-661(The)]TJ 0 -13.549 Td [(defaults)-404(asso)-28(ciated)-403(to)-404(eac)27(h)-403(preconditioner)-404(t)28(yp)-28(e)-404(are)-404(giv)28(en)-404(in)-403(T)83(able)]TJ +1 0 0 1 -115.4185 -555.4954 cm +BT +/F20 10.9091 Tf 120.873 555.4954 Td[(A)25(l)-50(lo)51(c)51(ate)-364(an)-1(d)-364(ini)1(t)-1(i)1(aliz)1(e)-365(the)-364(pr)51(e)51(c)52(o)-1(nditi)1(o)-1(ner)-364(data)-364(structur)52(e,)-365(a)-1(c)52(c)51(or)51(ding)-364(to)-364(a)-365(pr)52(e)51(c)51(ond)-1(i)1(-)]TJ 0 -13.5492 Td[(tioner)-376(typ)51(e)-375(cho)-1(s)1(en)-377(by)-375(the)-376(user)]TJ/F15 10.9091 Tf 144.0045 0 Td[(.)-503(This)-353(is)-354(p)-27(erfor)1(m)-1(ed)-353(b)29(y)-353(the)-353(rou)1(tin)1(e)]TJ/F46 10.9091 Tf 169.417 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 68.7265 0 Td[(,)]TJ -382.148 -13.5492 Td[(whic)28(h)-406(al)1(s)-1(o)-405(s)-1(ets)-406(defaul)1(ts)-406(for)-405(e)-1(ac)28(h)-406(p)1(rec)-1(on)1(diti)1(oner)-406(t)28(yp)-27(e)-406(s)-1(elec)-1(ted)-405(b)28(y)-406(th)1(e)-406(use)-1(r)1(.)-662(The)]TJ 0 -13.5492 Td[(defau)1(lts)-404(ass)-1(o)-28(ciated)-404(to)-403(e)-1(ac)28(h)-404(p)1(re)-1(cond)1(ition)1(e)-1(r)-403(t)28(yp)-27(e)-405(ar)1(e)-404(giv)28(e)-1(n)-403(in)-403(T)83(abl)1(e)]TJ +ET +1 0 0 1 445.5028 514.8478 cm 0 0 1 rg 0 0 1 RG - [-404(1)]TJ +1 0 0 1 -445.5028 -514.8478 cm +BT +/F15 10.9091 Tf 445.5028 514.8478 Td[(1)]TJ +ET +1 0 0 1 450.9574 514.8478 cm 0 g 0 G - [(,)-421(where)-404(the)]TJ 0 -13.549 Td [(strings)-305(used)-306(b)28(y)]TJ/F44 10.9091 Tf 74.446 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 72.056 0 Td [(to)-305(iden)28(tify)-306(the)-305(preconditioner)-305(t)28(yp)-28(es)-305(are)-306(also)-305(giv)28(en.)]TJ -146.502 -13.55 Td [(Note)-352(that)-353(these)-352(strings)-352(are)-353(v)56(alid)-352(also)-353(if)-352(upp)-28(ercase)-352(letters)-352(are)-353(substituted)-352(b)28(y)-352(c)-1(or)1(-)]TJ 0 -13.549 Td [(resp)-28(onding)-333(lo)28(w)28(ercas)-1(e)-333(ones.)]TJ +1 0 0 1 -450.9574 -514.8478 cm +BT +/F15 10.9091 Tf 450.9574 514.8478 Td[(,)-421(where)-404(the)]TJ -330.0844 -13.5492 Td[(strin)1(gs)-306(use)-1(d)-304(b)28(y)]TJ/F46 10.9091 Tf 74.4455 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 72.0568 0 Td[(to)-305(iden)28(ti)1(fy)-305(th)1(e)-306(pr)1(e)-1(cond)1(ition)1(e)-1(r)-305(t)28(yp)-27(es)-306(are)-306(al)1(s)-1(o)-305(giv)28(en.)]TJ -146.5023 -13.5492 Td[(Note)-353(th)1(at)-352(thes)-1(e)-352(s)-1(tr)1(ings)-353(ar)1(e)-353(v)56(alid)-352(al)1(s)-1(o)-352(if)-352(u)1(pp)-27(e)-1(r)1(c)-1(ase)-353(letters)-353(are)-352(s)-1(u)1(bstitu)1(te)-1(d)-352(b)29(y)-353(cor-)]TJ 0 -13.5492 Td[(res)-1(p)-27(on)1(din)1(g)-334(l)1(o)27(w)28(e)-1(r)1(c)-1(ase)-334(on)1(e)-1(s.)]TJ +ET +1 0 0 1 93.6002 452.2668 cm 0 g 0 G - -13.939 -21.933 Td [(3.)]TJ +1 0 0 1 -93.6002 -452.2668 cm +BT +/F15 10.9091 Tf 106.9336 452.2668 Td[(3.)]TJ +ET +1 0 0 1 115.4185 452.2668 cm 0 g 0 G -/F18 10.9091 Tf 13.939 0 Td [(Mo)51(dify)-340(the)-341(sele)51(cte)52(d)-341(pr)51(e)51(c)51(onditioner)-340(typ)51(e,)-344(by)-340(pr)51(op)51(erly)-340(setting)-341(pr)51(e)52(c)51(onditioner)-341(p)51(ar)51(am-)]TJ 0 -13.549 Td [(eters.)]TJ/F15 10.9091 Tf 30.668 0 Td [(This)-266(is)-265(p)-28(erformed)-265(b)27(y)-265(the)-266(routine)]TJ/F44 10.9091 Tf 155.17 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 62.999 0 Td [(.)-422(This)-265(routine)-266(m)28(ust)-266(b)-27(e)-266(called)]TJ -248.837 -13.55 Td [(only)-364(if)-365(the)-364(user)-365(w)28(an)28(ts)-365(to)-364(mo)-28(dify)-365(t)1(he)-365(default)-364(v)55(alues)-364(of)-365(the)-364(parameters)-365(asso)-28(ciated)]TJ 0 -13.549 Td [(to)-468(the)-467(selected)-468(preconditioner)-467(t)27(yp)-27(e,)-502(to)-467(obtain)-468(a)-467(v)55(arian)28(t)-468(of)-467(the)-468(preconditioner.)]TJ 0 -13.549 Td [(Examples)-395(of)-394(use)-395(of)]TJ/F44 10.9091 Tf 95.977 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 67.304 0 Td [(are)-395(giv)28(en)-394(in)-395(Section)]TJ +1 0 0 1 -115.4185 -452.2668 cm +BT +/F20 10.9091 Tf 120.873 452.2668 Td[(Mo)51(di)1(fy)-340(the)-341(sel)1(e)51(cte)51(d)-341(pr)51(e)52(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)-340(typ)51(e,)-343(by)-340(pr)51(op)51(erl)1(y)-340(setting)-341(pr)51(e)52(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)-340(p)51(ar)52(am-)]TJ 0 -13.5492 Td[(eters.)]TJ/F15 10.9091 Tf 30.6685 0 Td[(This)-266(i)1(s)-266(p)-28(erf)1(orme)-1(d)-265(b)28(y)-265(th)1(e)-266(routi)1(ne)]TJ/F46 10.9091 Tf 155.1693 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)-422(Th)1(is)-266(rou)1(tine)-266(m)28(ust)-266(b)-27(e)-266(called)]TJ -248.8371 -13.5492 Td[(onl)1(y)-365(i)1(f)-364(the)-365(u)1(s)-1(er)-364(w)27(an)28(ts)-365(t)1(o)-365(mo)-28(di)1(fy)-364(the)-365(d)1(e)-1(f)1(aul)1(t)-365(v)56(alu)1(e)-1(s)-365(of)-364(th)1(e)-365(paramete)-1(r)1(s)-365(as)-1(so)-28(ciated)]TJ 0 -13.5492 Td[(to)-468(t)1(he)-468(se)-1(lec)-1(t)1(e)-1(d)-467(pr)1(e)-1(cond)1(ition)1(e)-1(r)-467(t)28(yp)-27(e)-1(,)-501(to)-467(obtai)1(n)-468(a)-467(v)56(arian)28(t)-467(of)-467(the)-468(p)1(re)-1(cond)1(ition)1(e)-1(r)1(.)]TJ 0 -13.5492 Td[(Ex)1(am)-1(p)1(les)-396(of)-394(u)1(s)-1(e)-395(of)]TJ/F46 10.9091 Tf 95.9773 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 67.3042 0 Td[(are)-395(giv)28(en)-394(in)-394(Sec)-1(t)1(ion)]TJ +ET +1 0 0 1 384.4348 398.07 cm 0 0 1 rg 0 0 1 RG - [-395(5.1)]TJ +1 0 0 1 -384.4348 -398.07 cm +BT +/F15 10.9091 Tf 384.4348 398.07 Td[(5.1)]TJ +ET +1 0 0 1 398.3742 398.07 cm 0 g 0 G - [(;)-425(a)-394(com)-1(p)1(le)-1(t)1(e)-395(list)-395(of)-394(all)]TJ -163.281 -13.549 Td [(the)-303(preconditioner)-302(parameters)-303(and)-303(their)-302(allo)27(w)28(ed)-303(and)-302(default)-303(v)56(alues)-303(is)-303(pro)28(vided)-303(in)]TJ 0 -13.549 Td [(Section)]TJ +1 0 0 1 -398.3742 -398.07 cm +BT +/F15 10.9091 Tf 398.3742 398.07 Td[(;)-425(a)-395(complete)-395(list)-395(of)-394(all)]TJ -277.5012 -13.5492 Td[(th)1(e)-304(p)1(rec)-1(on)1(diti)1(oner)-303(p)1(arame)-1(ters)-303(an)1(d)-303(th)1(e)-1(i)1(r)-303(all)1(o)27(w)28(e)-1(d)-302(an)1(d)-303(d)1(e)-1(f)1(ault)-302(v)56(alues)-303(is)-303(pro)28(vi)1(ded)-303(i)1(n)]TJ 0 -13.5492 Td[(Section)]TJ +ET +1 0 0 1 159.0549 370.9716 cm 0 0 1 rg 0 0 1 RG - [-333(6)]TJ +1 0 0 1 -159.0549 -370.9716 cm +BT +/F15 10.9091 Tf 159.0549 370.9716 Td[(6)]TJ +ET +1 0 0 1 164.5094 370.9716 cm 0 g 0 G - [(,)-334(T)84(ables)]TJ +1 0 0 1 -164.5094 -370.9716 cm +BT +/F15 10.9091 Tf 164.5094 370.9716 Td[(,)-333(T)83(abl)1(e)-1(s)]TJ +ET +1 0 0 1 205.4791 370.9716 cm 0 0 1 rg 0 0 1 RG - [-334(2)]TJ +1 0 0 1 -205.4791 -370.9716 cm +BT +/F15 10.9091 Tf 205.4791 370.9716 Td[(2)]TJ +ET +1 0 0 1 210.9337 370.9716 cm 0 g 0 G - [(-)]TJ +1 0 0 1 -210.9337 -370.9716 cm +BT +/F15 10.9091 Tf 210.9337 370.9716 Td[(-)]TJ +ET +1 0 0 1 214.57 370.9716 cm 0 0 1 rg 0 0 1 RG - [(5)]TJ +1 0 0 1 -214.57 -370.9716 cm +BT +/F15 10.9091 Tf 214.57 370.9716 Td[(5)]TJ +ET +1 0 0 1 220.0246 370.9716 cm 0 g 0 G - [(.)]TJ +1 0 0 1 -220.0246 -370.9716 cm +BT +/F15 10.9091 Tf 220.0246 370.9716 Td[(.)]TJ +ET +1 0 0 1 93.6002 349.0382 cm 0 g 0 G - -13.939 -21.934 Td [(4.)]TJ +1 0 0 1 -93.6002 -349.0382 cm +BT +/F15 10.9091 Tf 106.9336 349.0382 Td[(4.)]TJ +ET +1 0 0 1 115.4185 349.0382 cm 0 g 0 G -/F18 10.9091 Tf 13.939 0 Td [(Build)-457(the)-457(pr)51(e)51(c)51(onditioner)-457(for)-457(a)-457(given)-457(matrix.)]TJ/F15 10.9091 Tf 223.323 0 Td [(This)-441(is)-442(p)-27(erformed)-441(b)27(y)-441(the)-441(routine)]TJ/F44 10.9091 Tf -223.323 -13.549 Td [(mld_precbld)]TJ/F15 10.9091 Tf 62.999 0 Td [(.)]TJ +1 0 0 1 -115.4185 -349.0382 cm +BT +/F20 10.9091 Tf 120.873 349.0382 Td[(Bui)1(ld)-457(the)-457(pr)51(e)51(c)51(onditioner)-457(f)1(or)-457(a)-457(given)-457(matrix.)]TJ/F15 10.9091 Tf 223.3234 0 Td[(This)-441(is)-442(p)-27(erfor)1(m)-1(ed)-441(b)28(y)-441(th)1(e)-442(r)1(outin)1(e)]TJ/F46 10.9091 Tf -223.3234 -13.5492 Td[(mld_precbld)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)]TJ +ET +1 0 0 1 93.6002 313.5556 cm 0 g 0 G - -76.938 -21.933 Td [(5.)]TJ +1 0 0 1 -93.6002 -313.5556 cm +BT +/F15 10.9091 Tf 106.9336 313.5556 Td[(5.)]TJ +ET +1 0 0 1 115.4185 313.5556 cm 0 g 0 G -/F18 10.9091 Tf 13.939 0 Td [(Apply)-282(the)-281(pr)51(e)51(c)51(onditioner)-281(at)-282(e)51(ach)-282(iter)52(ation)-282(of)-282(a)-281(Krylov)-282(solver.)]TJ/F15 10.9091 Tf 288.311 0 Td [(This)-251(is)-250(p)-28(erformed)-250(b)27(y)]TJ -288.311 -13.55 Td [(the)-340(routine)]TJ/F44 10.9091 Tf 56.544 0 Td [(mld_precaply)]TJ/F15 10.9091 Tf 68.727 0 Td [(.)-465(When)-340(using)-340(the)-341(PSBLAS)-340(Krylo)28(v)-340(solv)28(ers,)-342(this)-341(step)-340(is)]TJ -125.271 -13.549 Td [(completely)-302(transparen)28(t)-301(to)-302(the)-302(user,)-308(since)]TJ/F44 10.9091 Tf 196.451 0 Td [(mld_precaply)]TJ/F15 10.9091 Tf 72.018 0 Td [(is)-302(called)-301(b)27(y)-301(the)-302(PSBLAS)]TJ -268.469 -13.549 Td [(routine)-333(implemen)28(ting)-334(the)-333(Krylo)28(v)-334(solv)28(er)-333(\050)]TJ/F44 10.9091 Tf 195.909 0 Td [(psb_krylov)]TJ/F15 10.9091 Tf 57.272 0 Td [(\051.)]TJ +1 0 0 1 -115.4185 -313.5556 cm +BT +/F20 10.9091 Tf 120.873 313.5556 Td[(App)-1(l)1(y)-281(th)-1(e)-281(pr)51(e)51(c)51(onditioner)-281(at)-282(e)51(ach)-282(iter)52(at)-1(i)1(on)-282(of)-282(a)-281(Kryl)1(ov)-282(sol)1(ver.)]TJ/F15 10.9091 Tf 288.3113 0 Td[(This)-251(i)1(s)-251(p)-28(erf)1(orme)-1(d)-250(b)28(y)]TJ -288.3113 -13.5492 Td[(th)1(e)-341(rou)1(tine)]TJ/F46 10.9091 Tf 56.5445 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 68.7265 0 Td[(.)-465(Wh)1(e)-1(n)-339(using)-340(th)1(e)-341(PS)1(B)-1(LAS)-339(Kryl)1(o)27(v)-340(solv)28(ers,)-342(thi)1(s)-341(s)-1(t)1(e)-1(p)-340(i)1(s)]TJ -125.271 -13.5492 Td[(com)-1(p)1(le)-1(t)1(e)-1(ly)-301(tran)1(s)-1(p)1(aren)28(t)-302(to)-301(the)-302(u)1(s)-1(er,)-308(sin)1(c)-1(e)]TJ/F46 10.9091 Tf 196.4514 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 72.0175 0 Td[(is)-302(called)-302(b)29(y)-302(th)1(e)-302(PS)1(B)-1(LAS)]TJ -268.4689 -13.5492 Td[(rou)1(tin)1(e)-334(impleme)-1(n)28(ti)1(ng)-333(the)-333(Kryl)1(o)27(v)-333(solv)28(er)-333(\050)]TJ/F46 10.9091 Tf 195.9093 0 Td[(psb_krylov)]TJ/F15 10.9091 Tf 57.2721 0 Td[(\051.)]TJ +ET +1 0 0 1 93.6002 250.9746 cm 0 g 0 G - -267.12 -21.933 Td [(6.)]TJ +1 0 0 1 -93.6002 -250.9746 cm +BT +/F15 10.9091 Tf 106.9336 250.9746 Td[(6.)]TJ +ET +1 0 0 1 115.4185 250.9746 cm 0 g 0 G -/F18 10.9091 Tf 13.939 0 Td [(F)77(r)51(e)51(e)-459(the)-459(pr)51(e)51(c)51(onditioner)-459(data)-459(structur)51(e)]TJ/F15 10.9091 Tf 183.971 0 Td [(.)-775(This)-443(is)-444(p)-28(erfor)1(m)-1(ed)-443(b)28(y)-444(the)-443(routine)]TJ/F44 10.9091 Tf 178.298 0 Td [(mld_)]TJ -362.269 -13.55 Td [(precfree)]TJ/F15 10.9091 Tf 45.818 0 Td [(.)-501(This)-353(step)-352(is)-353(complemen)28(tary)-352(to)-353(step)-352(1)-352(and)-353(should)-352(b)-28(e)-352(p)-28(erformed)-352(when)]TJ -45.818 -13.549 Td [(the)-333(preconditioner)-334(i)1(s)-334(no)-333(more)-334(u)1(s)-1(ed.)]TJ -27.273 -21.06 Td [(A)-384(detailed)-384(description)-384(of)-384(the)-384(ab)-28(o)28(v)28(e)-384(routines)-384(is)-384(giv)27(en)-384(in)-384(Section)]TJ +1 0 0 1 -115.4185 -250.9746 cm +BT +/F20 10.9091 Tf 120.873 250.9746 Td[(F)77(r)51(e)51(e)-459(the)-459(pr)51(e)51(c)52(o)-1(nditi)1(o)-1(ner)-459(data)-459(structur)52(e)]TJ/F15 10.9091 Tf 183.9714 0 Td[(.)-775(Th)1(is)-444(is)-444(p)-27(e)-1(r)1(for)1(m)-1(ed)-443(b)28(y)-443(the)-444(r)1(outin)1(e)]TJ/F46 10.9091 Tf 178.2981 0 Td[(mld_)]TJ -362.2695 -13.5492 Td[(precfree)]TJ/F15 10.9091 Tf 45.8177 0 Td[(.)-501(T)-1(h)1(is)-353(step)-352(is)-353(com)-1(p)1(lem)-1(en)28(tary)-352(to)-352(ste)-1(p)-352(1)-352(and)-352(shou)1(ld)-352(b)-27(e)-353(p)-27(e)-1(r)1(formed)-352(w)-1(h)1(e)-1(n)]TJ -45.8177 -13.5492 Td[(th)1(e)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r)-333(is)-333(no)-333(m)-1(or)1(e)-334(use)-1(d)1(.)]TJ -27.2728 -21.0602 Td[(A)-384(detail)1(e)-1(d)-384(d)1(e)-1(scrip)1(tion)-384(of)-383(the)-384(ab)-28(o)28(v)28(e)-384(rout)1(ines)-385(i)1(s)-385(giv)28(en)-384(in)-383(Sec)-1(ti)1(on)]TJ +ET +1 0 0 1 402.9592 202.8161 cm 0 0 1 rg 0 0 1 RG - [-384(6)]TJ +1 0 0 1 -402.9592 -202.8161 cm +BT +/F15 10.9091 Tf 402.9592 202.8161 Td[(6)]TJ +ET +1 0 0 1 408.4137 202.8161 cm 0 g 0 G - [(.)-596(Examples)-384(sho)28(w)-1(i)1(ng)]TJ 0 -13.549 Td [(the)-333(basic)-334(use)-333(of)-333(MLD2P4)-334(are)-333(rep)-28(orted)-333(in)-333(Section)]TJ +1 0 0 1 -408.4137 -202.8161 cm +BT +/F15 10.9091 Tf 408.4137 202.8161 Td[(.)-596(Exampl)1(e)-1(s)-384(s)-1(h)1(o)27(win)1(g)]TJ -314.8135 -13.5492 Td[(th)1(e)-334(basic)-334(u)1(s)-1(e)-334(of)-332(MLD2P4)-333(are)-333(rep)-28(or)1(te)-1(d)-333(i)1(n)-333(Sec)-1(ti)1(on)]TJ +ET +1 0 0 1 331.2368 189.2669 cm 0 0 1 rg 0 0 1 RG - [-334(5.1)]TJ +1 0 0 1 -331.2368 -189.2669 cm +BT +/F15 10.9091 Tf 331.2368 189.2669 Td[(5.1)]TJ +ET +1 0 0 1 345.1762 189.2669 cm 0 g 0 G - [(.)]TJ 16.937 -13.549 Td [(Note)-421(that)-422(the)-421(F)83(ortran)-421(95)-422(mo)-28(dule)]TJ/F44 10.9091 Tf 167.194 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)-444(con)28(taining)-421(the)-422(de\014n)1(ition)-422(of)-421(the)]TJ -252.857 -13.549 Td [(preconditioner)-351(data)-351(t)28(yp)-28(e)-351(an)1(d)-351(the)-351(in)28(terfaces)-351(to)-351(the)-351(routines)-351(of)-351(MLD2P4,)-355(m)28(ust)-351(b)-28(e)-351(used)]TJ 0 -13.55 Td [(in)-245(an)28(y)-246(progr)1(am)-246(calling)-245(suc)28(h)-245(routines.)-415(The)-246(mo)-27(dules)]TJ/F44 10.9091 Tf 240.498 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)-263(for)-245(the)-245(sparse)-246(matrix)]TJ -309.224 -13.549 Td [(and)-405(c)-1(omm)28(unication)-405(descriptor)-406(data)-405(t)28(yp)-28(es,)-424(and)]TJ/F44 10.9091 Tf 231.165 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 80.181 0 Td [(,)-424(for)-405(in)28(terfacing)-406(with)]TJ -311.346 -13.549 Td [(the)-333(Krylo)28(v)-334(solv)28(ers,)-333(m)27(ust)-333(b)-28(e)-333(also)-333(used)-334(\050see)-333(Section)]TJ +1 0 0 1 -345.1762 -189.2669 cm +BT +/F15 10.9091 Tf 345.1762 189.2669 Td[(.)]TJ -234.6395 -13.5492 Td[(Note)-422(th)1(at)-422(th)1(e)-422(F)84(ortran)-421(95)-421(m)-1(o)-27(du)1(le)]TJ/F46 10.9091 Tf 167.1941 0 Td[(mld_prec_mod)]TJ/F15 10.9091 Tf 68.7265 0 Td[(,)-443(c)-1(on)28(t)1(ainin)1(g)-422(t)1(he)-422(d)1(e)-1(\014)1(niti)1(on)-422(of)-421(t)1(he)]TJ -252.8571 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-350(data)-351(t)28(yp)-27(e)-351(and)-350(the)-351(in)28(terf)1(ac)-1(es)-351(to)-351(the)-351(rou)1(tin)1(e)-1(s)-351(of)-351(M)1(LD2P4,)-355(m)27(u)1(s)-1(t)-350(b)-28(e)-351(used)]TJ 0 -13.5492 Td[(in)-245(an)29(y)-245(progr)1(am)-246(callin)1(g)-245(s)-1(u)1(c)27(h)-245(rou)1(tin)1(e)-1(s.)-415(The)-246(mo)-28(d)1(ules)]TJ/F46 10.9091 Tf 240.4978 0 Td[(psb_base_mod)]TJ/F15 10.9091 Tf 68.7265 0 Td[(,)-263(f)1(or)-245(the)-245(s)-1(p)1(arse)-246(matrix)]TJ -309.2243 -13.5492 Td[(and)-405(comm)27(un)1(ication)-405(des)-1(cri)1(ptor)-405(dat)1(a)-406(t)28(yp)-27(e)-1(s,)-423(and)]TJ/F46 10.9091 Tf 231.165 0 Td[(psb_krylov_mod)]TJ/F15 10.9091 Tf 80.1809 0 Td[(,)-423(for)-405(in)28(terf)1(ac)-1(i)1(ng)-406(wit)1(h)]TJ -311.3459 -13.5492 Td[(th)1(e)-334(Kry)1(lo)28(v)-334(solv)28(ers,)-333(m)27(ust)-333(b)-28(e)-333(als)-1(o)-333(u)1(s)-1(ed)-333(\050s)-1(ee)-334(S)1(e)-1(ction)]TJ +ET +1 0 0 1 335.5398 121.5209 cm 0 0 1 rg 0 0 1 RG - [-334(5.)1(1)]TJ +1 0 0 1 -335.5398 -121.5209 cm +BT +/F15 10.9091 Tf 335.5398 121.5209 Td[(5.1)]TJ +ET +1 0 0 1 349.4792 121.5209 cm 0 g 0 G - [(\051.)]TJ +1 0 0 1 -349.4792 -121.5209 cm +BT +/F15 10.9091 Tf 349.4792 121.5209 Td[(\051.)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -345 0 obj << +368 0 obj << /Type /Page -/Contents 346 0 R -/Resources 344 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 320 0 R -/Annots [ 343 0 R 331 0 R 332 0 R 333 0 R 334 0 R 335 0 R 336 0 R 337 0 R 338 0 R 339 0 R ] +/Contents 369 0 R +/Resources 367 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 356 0 R +/Annots [ 371 0 R 372 0 R 375 0 R 377 0 R 378 0 R 379 0 R 380 0 R 384 0 R 385 0 R 386 0 R ] >> endobj -343 0 obj << +371 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -331 0 obj << +372 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [429.591 665.239 442.493 674.261] +/Rect [429.5912 665.2387 442.4928 674.2615] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -332 0 obj << +375 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [444.507 511.73 451.954 523.42] +/Rect [444.5065 511.7303 451.9536 523.4198] /Subtype /Link /A << /S /GoTo /D (table.1) >> >> endobj -333 0 obj << +377 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [383.439 394.65 399.37 406.642] +/Rect [383.4386 394.6495 399.3705 406.642] /Subtype /Link /A << /S /GoTo /D (subsection.5.1) >> >> endobj -334 0 obj << +378 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [158.059 367.854 165.506 379.544] +/Rect [158.0586 367.8541 165.5057 379.5436] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -335 0 obj << +379 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [204.483 367.854 211.93 379.544] +/Rect [204.4829 367.8541 211.9299 379.5436] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -336 0 obj << +380 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [213.574 367.854 221.021 379.544] +/Rect [213.5738 367.8541 221.0208 379.5436] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -337 0 obj << +384 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [401.963 199.699 409.41 211.388] +/Rect [401.9629 199.6986 409.41 211.3881] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -338 0 obj << +385 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [330.241 186.149 346.172 197.839] +/Rect [330.2405 186.1494 346.1725 197.8389] /Subtype /Link /A << /S /GoTo /D (subsection.5.1) >> >> endobj -339 0 obj << +386 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [334.544 117.797 350.475 130.699] +/Rect [334.5436 117.7973 350.4755 130.699] /Subtype /Link /A << /S /GoTo /D (subsection.5.1) >> >> endobj -347 0 obj << -/D [345 0 R /XYZ 93.6 740.002 null] +370 0 obj << +/D [368 0 R /XYZ 93.6002 740.0018 null] >> endobj 58 0 obj << -/D [345 0 R /XYZ 93.6 715.095 null] +/D [368 0 R /XYZ 93.6002 715.0952 null] >> endobj -348 0 obj << -/D [345 0 R /XYZ 93.6 647.246 null] +373 0 obj << +/D [368 0 R /XYZ 93.6002 647.2457 null] >> endobj -349 0 obj << -/D [345 0 R /XYZ 93.6 571.115 null] +374 0 obj << +/D [368 0 R /XYZ 93.6002 571.1155 null] >> endobj -350 0 obj << -/D [345 0 R /XYZ 93.6 467.887 null] +376 0 obj << +/D [368 0 R /XYZ 93.6002 467.8869 null] >> endobj -351 0 obj << -/D [345 0 R /XYZ 93.6 364.658 null] +381 0 obj << +/D [368 0 R /XYZ 93.6002 364.6583 null] >> endobj -352 0 obj << -/D [345 0 R /XYZ 93.6 328.873 null] +382 0 obj << +/D [368 0 R /XYZ 93.6002 328.8727 null] >> endobj -353 0 obj << -/D [345 0 R /XYZ 93.6 265.989 null] +383 0 obj << +/D [368 0 R /XYZ 93.6002 265.9886 null] >> endobj -344 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F18 173 0 R /F44 200 0 R >> +367 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F20 181 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -361 0 obj << -/Length 8623 +392 0 obj << +/Length 12248 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(16)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(16)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F43 10.9091 Tf -203.265 -49.415 Td [(Remark)-396(1.)]TJ/F15 10.9091 Tf 62.779 0 Td [(The)-344(coarsest-lev)27(el)-344(solv)28(er)-344(used)-344(b)27(y)-344(the)-344(default)-344(t)28(w)28(o-le)-1(v)28(el)-344(preconditioner)-344(has)]TJ -62.779 -13.549 Td [(b)-28(een)-432(c)28(hosen)-432(b)28(y)-432(tak)1(ing)-432(in)28(to)-432(accoun)28(t)-432(that,)-456(on)-432(parallel)-432(mac)28(hines,)-456(it)-432(often)-432(leads)-432(to)-432(th)1(e)]TJ 0 -13.549 Td [(smallest)-422(execution)-421(time)-422(when)-422(applied)-421(to)-422(linear)-421(systems)-422(coming)-422(from)-421(\014nite-di\013erence)]TJ 0 -13.549 Td [(discretizations)-376(of)-376(basic)-376(elliptic)-376(PDE)-376(problems,)-387(considered)-376(as)-376(standard)-376(tests)-376(for)-376(m)28(ulti-)]TJ 0 -13.55 Td [(lev)28(el)-224(Sc)28(h)28(w)28(arz)-224(precondition)1(e)-1(r)1(s)-224([)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F45 10.9091 Tf 86.3998 690.5871 Td[(Re)-1(mark)-395(1.)]TJ/F15 10.9091 Tf 62.7789 0 Td[(The)-344(c)-1(oarses)-1(t-lev)28(e)-1(l)-344(solv)28(er)-344(use)-1(d)-343(b)28(y)-344(the)-344(defau)1(lt)-344(t)28(w)27(o-lev)28(e)-1(l)-344(p)1(rec)-1(on)1(diti)1(oner)-344(has)]TJ -62.7789 -13.5492 Td[(b)-27(e)-1(en)-432(c)28(hose)-1(n)-431(b)28(y)-431(takin)1(g)-432(in)28(to)-431(ac)-1(coun)28(t)-431(that,)-456(on)-431(par)1(allel)-432(mac)27(h)1(ines)-1(,)-456(it)-431(often)-431(le)-1(ad)1(s)-432(to)-432(the)]TJ 0 -13.5492 Td[(sm)-1(all)1(e)-1(st)-422(exec)-1(u)1(tion)-421(time)-422(w)-1(h)1(e)-1(n)-421(ap)1(pli)1(e)-1(d)-421(to)-422(l)1(inear)-421(s)-1(ystem)-1(s)-422(com)-1(i)1(ng)-422(f)1(rom)-422(\014)1(nite-di\013ere)-1(n)1(c)-1(e)]TJ 0 -13.5492 Td[(di)1(s)-1(cretizations)-376(of)-376(b)1(as)-1(ic)-376(ellip)1(tic)-376(PDE)-375(prob)1(lem)-1(s,)-387(consid)1(e)-1(red)-376(as)-376(s)-1(t)1(andar)1(d)-376(tes)-1(t)1(s)-377(f)1(or)-376(m)27(u)1(lti-)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)-223(S)1(c)27(h)28(w)28(arz)-224(p)1(rec)-1(on)1(diti)1(oners)-224([)]TJ +ET +1 0 0 1 229.3164 636.3903 cm 1 0 0 rg 1 0 0 RG - [(3)]TJ +1 0 0 1 -229.3164 -636.3903 cm +BT +/F15 10.9091 Tf 229.3164 636.3903 Td[(3)]TJ +ET +1 0 0 1 234.771 636.3903 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -234.771 -636.3903 cm +BT +/F15 10.9091 Tf 234.771 636.3903 Td[(,)]TJ +ET +1 0 0 1 240.2381 636.3903 cm 1 0 0 rg 1 0 0 RG - [-223(4)]TJ +1 0 0 1 -240.2381 -636.3903 cm +BT +/F15 10.9091 Tf 240.2381 636.3903 Td[(4)]TJ +ET +1 0 0 1 245.6927 636.3903 cm 0 g 0 G - [(].)-408(Ho)28(w)28(ev)27(er,)-245(this)-223(solv)27(er)-223(do)-28(es)-223(not)-224(n)1(e)-1(cessarily)-223(corresp)-28(ond)]TJ 0 -13.549 Td [(to)-446(the)-447(smallest)-446(n)27(um)28(b)-28(er)-446(of)-446(iterations)-447(of)-446(the)-447(preconditioned)-446(Krylo)28(v)-447(metho)-27(d,)-475(whic)28(h)-447(is)]TJ 0 -13.549 Td [(usually)-334(obtained)-334(b)28(y)-334(applying)-334(a)-334(direct)-335(solv)28(er)-334(to)-334(the)-334(coarsest-lev)27(el)-334(system,)-334(e.g.)-334(based)-335(on)]TJ 0 -13.549 Td [(the)-312(LU)-312(f)1(ac)-1(t)1(orization)-312(\050see)-312(Section)]TJ +1 0 0 1 -245.6927 -636.3903 cm +BT +/F15 10.9091 Tf 245.6927 636.3903 Td[(].)-407(Ho)27(w)28(ev)28(e)-1(r,)-245(th)1(is)-224(solv)28(er)-223(do)-28(es)-224(not)-223(n)1(e)-1(ce)-1(ss)-1(ar)1(ily)-223(c)-1(or)1(res)-1(p)-27(ond)]TJ -159.2929 -13.5492 Td[(to)-446(the)-447(smalles)-1(t)-446(n)28(um)28(b)-27(e)-1(r)-446(of)-446(iteration)1(s)-447(of)-446(th)1(e)-447(precondi)1(tioned)-446(Kr)1(ylo)28(v)-446(m)-1(etho)-27(d,)-475(wh)1(ic)27(h)-446(is)]TJ 0 -13.5492 Td[(usual)1(ly)-334(obt)1(ained)-334(b)28(y)-334(ap)1(ply)1(ing)-334(a)-334(di)1(rec)-1(t)-334(solv)28(e)-1(r)-333(to)-334(the)-334(c)-1(oarses)-1(t-lev)28(e)-1(l)-334(syste)-1(m,)-334(e)-1(.)1(g.)-334(base)-1(d)-333(on)]TJ 0 -13.5492 Td[(th)1(e)-313(LU)-311(factorization)-311(\050s)-1(ee)-312(Sec)-1(ti)1(on)]TJ +ET +1 0 0 1 246.0725 595.7428 cm 0 0 1 rg 0 0 1 RG - [-312(6)]TJ +1 0 0 1 -246.0725 -595.7428 cm +BT +/F15 10.9091 Tf 246.0725 595.7428 Td[(6)]TJ +ET +1 0 0 1 251.527 595.7428 cm 0 g 0 G - [-312(for)-311(the)-312(coarsest-lev)28(e)-1(l)-311(solv)27(ers)-311(a)27(v)56(ailable)-312(in)-311(MLD2P4\051.)]TJ/F43 10.9091 Tf 0 -27.099 Td [(Remark)-421(2.)]TJ/F15 10.9091 Tf 63.76 0 Td [(The)-366(include)-366(path)-365(for)-366(MLD2P4)-366(m)28(ust)-366(o)28(v)28(e)-1(r)1(ride)-366(those)-366(for)-366(PSBLAS,)-366(i.e.)-366(the)]TJ -63.76 -13.549 Td [(former)-311(m)28(ust)-310(come)-311(\014rst)-311(in)-310(the)-311(sequence)-310(passed)-311(to)-310(the)-311(compiler,)-315(as)-311(the)-310(MLD2P4)-311(v)28(ersion)]TJ 0 -13.549 Td [(of)-483(the)-484(Krylo)28(v)-484(solv)28(er)-483(in)27(terf)1(ac)-1(es)-483(m)28(ust)-484(o)28(v)28(erride)-484(that)-483(of)-484(PSBLAS.)-483(This)-484(will)-483(c)28(hange)-484(in)]TJ 0 -13.549 Td [(the)-384(f)1(uture)-384(when)-383(the)-384(supp)-28(ort)-383(for)-384(the)]TJ/F44 10.9091 Tf 178.228 0 Td [(class)]TJ/F15 10.9091 Tf 32.82 0 Td [(statemen)28(t)-384(b)-28(ecomes)-383(widespread)-384(in)-383(F)83(ortran)]TJ -211.048 -13.549 Td [(compilers.)]TJ +1 0 0 1 -251.527 -595.7428 cm +BT +/F15 10.9091 Tf 254.9282 595.7428 Td[(for)-311(th)1(e)-313(coarse)-1(st-le)-1(v)28(el)-312(solv)28(ers)-312(a)28(v)55(ai)1(labl)1(e)-313(i)1(n)-312(M)1(LD2P4\051.)]TJ/F45 10.9091 Tf -168.5284 -27.0984 Td[(Re)-1(mark)-420(2.)]TJ/F15 10.9091 Tf 63.7599 0 Td[(The)-366(in)1(c)-1(lu)1(de)-366(path)-365(f)1(or)-366(MLD2P)1(4)-366(m)27(u)1(s)-1(t)-365(o)27(v)28(err)1(ide)-366(th)1(os)-1(e)-366(for)-365(PS)1(B)-1(LAS)1(,)-366(i.)1(e)-1(.)-365(the)]TJ -63.7599 -13.5492 Td[(for)1(m)-1(er)-310(m)27(u)1(s)-1(t)-310(c)-1(ome)-311(\014r)1(s)-1(t)-310(in)-310(th)1(e)-312(sequence)-311(pass)-1(ed)-310(to)-311(th)1(e)-311(c)-1(omp)1(iler,)-315(as)-311(th)1(e)-311(MLD2P4)-310(v)28(e)-1(r)1(s)-1(i)1(on)]TJ 0 -13.5492 Td[(of)-483(the)-483(Kryl)1(o)27(v)-483(solv)28(e)-1(r)-483(in)29(te)-1(r)1(face)-1(s)-484(m)28(ust)-484(o)28(v)28(errid)1(e)-484(that)-483(of)-483(PS)1(B)-1(LAS)1(.)-483(T)-1(h)1(is)-484(will)-483(c)27(h)1(ange)-484(i)1(n)]TJ 0 -13.5492 Td[(th)1(e)-384(fut)1(ure)-384(wh)1(e)-1(n)-383(th)1(e)-384(s)-1(u)1(pp)-27(ort)-383(for)-383(the)]TJ/F46 10.9091 Tf 178.2279 0 Td[(class)]TJ/F15 10.9091 Tf 32.8201 0 Td[(state)-1(men)28(t)-384(b)-27(ec)-1(ome)-1(s)-384(wid)1(e)-1(spr)1(e)-1(ad)-383(in)-383(F)84(ortr)1(an)]TJ -211.048 -13.5492 Td[(com)-1(p)1(ilers.)]TJ +ET +1 0 0 1 86.3998 500.6644 cm 0 g 0 G +1 0 0 1 6.469 -139.6139 cm 0 g 0 G 0 g 0 G -ET +1 0 0 1 5.4546 139.2154 cm q -1 0 0 1 98.323 500.465 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +388.604 0.1992 l +S Q +1 0 0 1 -0.1993 -13.5492 cm q -1 0 0 1 98.323 486.717 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -98.1241 -486.7167 cm BT -/F41 10.9091 Tf 104.301 490.782 Td [(type)]TJ +/F43 10.9091 Tf 104.3009 490.7815 Td[(type)]TJ ET +1 0 0 1 195.8976 486.7167 cm q -1 0 0 1 196.097 486.717 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -195.8976 -486.7167 cm BT -/F41 10.9091 Tf 202.074 490.782 Td [(string)]TJ +/F43 10.9091 Tf 202.0744 490.7815 Td[(strin)-1(g)]TJ ET +1 0 0 1 253.6704 486.7167 cm q -1 0 0 1 253.87 486.717 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -253.6704 -486.7167 cm BT -/F41 10.9091 Tf 259.847 490.782 Td [(def)89(a)22(ul)67(t)-378(preconditioner)]TJ +/F43 10.9091 Tf 259.8473 490.7815 Td[(def)89(a)22(ul)66(t)-378(preco)1(n)-1(diti)-1(o)1(n)-1(e)1(r)]TJ ET +1 0 0 1 486.7281 486.7167 cm q -1 0 0 1 486.927 486.717 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -388.4047 -0.3985 cm q -1 0 0 1 98.323 486.517 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +388.604 0.1992 l +S Q +1 0 0 1 -0.1993 -27.0984 cm q -1 0 0 1 98.323 459.22 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -98.1241 -459.2198 cm BT -/F15 10.9091 Tf 104.301 476.834 Td [(No)-333(preconditioner)]TJ +/F15 10.9091 Tf 104.3009 476.8338 Td[(No)-333(precondi)1(tioner)]TJ ET +1 0 0 1 195.8976 459.2198 cm q -1 0 0 1 196.097 459.22 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -195.8976 -459.2198 cm BT -/F44 10.9091 Tf 202.074 476.834 Td [('NOPREC')]TJ +/F46 10.9091 Tf 202.0744 476.8338 Td[('NOPREC')]TJ ET +1 0 0 1 253.6704 459.2198 cm q -1 0 0 1 253.87 459.22 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -253.6704 -459.2198 cm BT -/F15 10.9091 Tf 259.847 476.834 Td [(Considered)-507(only)-507(to)-507(use)-508(th)1(e)-508(PSBLAS)-507(Kr)1(ylo)27(v)]TJ 0 -13.549 Td [(solv)28(ers)-334(with)-333(no)-333(preconditioner.)]TJ +/F15 10.9091 Tf 259.8473 476.8338 Td[(Considered)-507(on)1(ly)-507(to)-507(use)-508(th)1(e)-508(P)1(SBLAS)-507(Kr)1(ylo)28(v)]TJ 0 -13.5492 Td[(solv)28(e)-1(r)1(s)-334(with)-333(n)1(o)-334(p)1(rec)-1(on)1(diti)1(oner.)]TJ ET +1 0 0 1 486.7281 459.2198 cm q -1 0 0 1 486.927 459.22 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -388.4047 -0.3985 cm q -1 0 0 1 98.323 459.021 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +388.604 0.1992 l +S Q +1 0 0 1 -0.1993 -13.5492 cm q -1 0 0 1 98.323 445.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -98.1241 -445.2721 cm BT -/F15 10.9091 Tf 104.301 449.337 Td [(Diagonal)]TJ +/F15 10.9091 Tf 104.3009 449.3369 Td[(Diagon)1(al)]TJ ET +1 0 0 1 195.8976 445.2721 cm q -1 0 0 1 196.097 445.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -195.8976 -445.2721 cm BT -/F44 10.9091 Tf 202.074 449.337 Td [('DIAG')]TJ +/F46 10.9091 Tf 202.0744 449.3369 Td[('DIAG')]TJ ET +1 0 0 1 253.6704 445.2721 cm q -1 0 0 1 253.87 445.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -253.6704 -445.2721 cm BT -/F15 10.9091 Tf 259.847 449.337 Td [(|)]TJ +/F15 10.9091 Tf 259.8473 449.3369 Td[(|)]TJ ET +1 0 0 1 486.7281 445.2721 cm q -1 0 0 1 486.927 445.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -388.4047 -0.3985 cm q -1 0 0 1 98.323 445.073 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +388.604 0.1992 l +S Q +1 0 0 1 -0.1993 -13.5492 cm q -1 0 0 1 98.323 431.324 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -98.1241 -431.3244 cm BT -/F15 10.9091 Tf 104.301 435.389 Td [(Blo)-28(c)28(k)-333(Jacobi)]TJ +/F15 10.9091 Tf 104.3009 435.3892 Td[(Blo)-28(c)27(k)-333(Jacobi)]TJ ET +1 0 0 1 195.8976 431.3245 cm q -1 0 0 1 196.097 431.324 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -195.8976 -431.3245 cm BT -/F44 10.9091 Tf 202.074 435.389 Td [('BJAC')]TJ +/F46 10.9091 Tf 202.0744 435.3893 Td[('BJAC')]TJ ET +1 0 0 1 253.6704 431.3245 cm q -1 0 0 1 253.87 431.324 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -253.6704 -431.3245 cm BT -/F15 10.9091 Tf 259.847 435.389 Td [(Blo)-28(c)28(k)-333(Jacobi)-334(with)-333(ILU\0500\051)-333(on)-334(the)-333(lo)-28(cal)-333(blo)-28(c)28(ks.)]TJ +/F15 10.9091 Tf 259.8473 435.3893 Td[(Blo)-28(c)27(k)-333(Jacobi)-333(with)-332(I)-1(LU\050)1(0\051)-334(on)-333(t)1(he)-334(lo)-27(c)-1(al)-333(b)1(lo)-28(c)27(k)1(s)-1(.)]TJ ET +1 0 0 1 486.7281 431.3245 cm q -1 0 0 1 486.927 431.324 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -388.4047 -0.3985 cm q -1 0 0 1 98.323 431.125 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +388.604 0.1992 l +S Q +1 0 0 1 -0.1993 -27.0984 cm q -1 0 0 1 98.323 403.828 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -98.1241 -403.8276 cm BT -/F15 10.9091 Tf 104.301 421.442 Td [(Additiv)28(e)-333(Sc)27(h)28(w)28(arz)]TJ +/F15 10.9091 Tf 104.3009 421.4416 Td[(Add)1(itiv)28(e)-333(Sc)27(h)29(w)27(ar)1(z)]TJ ET +1 0 0 1 195.8976 403.8276 cm q -1 0 0 1 196.097 403.828 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -195.8976 -403.8276 cm BT -/F44 10.9091 Tf 202.074 421.442 Td [('AS')]TJ +/F46 10.9091 Tf 202.0744 421.4416 Td[('AS')]TJ ET +1 0 0 1 253.6704 403.8276 cm q -1 0 0 1 253.87 403.828 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -253.6704 -403.8276 cm BT -/F15 10.9091 Tf 259.847 421.442 Td [(Restricted)-268(Ad)1(ditiv)27(e)-267(Sc)28(h)28(w)27(arz)-267(\050RAS\051,)-268(wit)1(h)-268(o)28(v)28(er-)]TJ 0 -13.55 Td [(lap)-333(1)-334(and)-333(ILU\0500\051)-333(on)-333(the)-334(lo)-28(cal)-333(blo)-28(c)28(ks.)]TJ +/F15 10.9091 Tf 259.8473 421.4416 Td[(Re)-1(stri)1(c)-1(ted)-267(Add)1(itiv)28(e)-268(S)1(c)27(h)28(w)28(arz)-268(\050)1(R)-1(AS)1(\051,)-267(with)-267(o)28(v)28(e)-1(r)1(-)]TJ 0 -13.5492 Td[(lap)-333(1)-333(and)-332(I)-1(LU\050)1(0\051)-334(on)-333(t)1(he)-334(lo)-27(c)-1(al)-333(b)1(lo)-28(c)27(k)1(s)-1(.)]TJ ET +1 0 0 1 486.7281 403.8276 cm q -1 0 0 1 486.927 403.828 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -388.4047 -0.3985 cm q -1 0 0 1 98.323 403.628 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +388.604 0.1992 l +S Q +1 0 0 1 -0.1993 -176.1395 cm q -1 0 0 1 98.323 227.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 176.14 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 176.1395 l +S Q +1 0 0 1 -98.1241 -227.2896 cm BT -/F15 10.9091 Tf 104.301 393.945 Td [(Multilev)28(el)]TJ +/F15 10.9091 Tf 104.3009 393.9447 Td[(Mu)1(ltil)1(e)-1(v)28(el)]TJ ET +1 0 0 1 195.8976 227.2896 cm q -1 0 0 1 196.097 227.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 176.14 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 176.1395 l +S Q +1 0 0 1 -195.8976 -227.2896 cm BT -/F44 10.9091 Tf 202.074 393.945 Td [('ML')]TJ +/F46 10.9091 Tf 202.0744 393.9447 Td[('ML')]TJ ET +1 0 0 1 253.6704 227.2896 cm q -1 0 0 1 253.87 227.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 176.14 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 176.1395 l +S Q +1 0 0 1 -253.6704 -227.2896 cm BT -/F15 10.9091 Tf 259.847 393.945 Td [(Multi-lev)28(el)-378(h)28(ybrid)-377(preconditioner)-377(\050additiv)28(e)-378(on)]TJ 0 -13.549 Td [(the)-390(s)-1(ame)-390(lev)28(el)-391(and)-390(m)28(ultiplicativ)28(e)-391(through)-390(the)]TJ 0 -13.55 Td [(lev)28(els\051,)-405(with)-391(p)-27(ost-s)-1(mo)-27(othing)-391(only)84(.)-616(Num)27(b)-27(er)-391(of)]TJ 0 -13.549 Td [(lev)28(els:)-511(2.)-543(P)28(ost-smo)-28(other:)-510(RAS)-366(with)-366(o)28(v)27(erlap)-366(1)]TJ 0 -13.549 Td [(and)-395(ILU\0500\051)-395(on)-396(the)-395(lo)-28(cal)-395(blo)-28(c)28(ks.)-630(Aggregation:)]TJ 0 -13.549 Td [(decoupled)-417(smo)-28(othed)-417(aggregation)-416(w)-1(i)1(th)-417(thresh-)]TJ 0 -13.549 Td [(old)]TJ/F22 10.9091 Tf 17.695 0 Td [(\022)]TJ/F15 10.9091 Tf 8.454 0 Td [(=)-278(0.)-429(Coarsest)-289(matrix:)-422(distributed)-289(among)]TJ -26.149 -13.55 Td [(the)-339(pro)-28(cessors.)-461(Coarses)-1(t-lev)28(el)-339(solv)28(er:)-456(4)-339(sw)28(eeps)]TJ 0 -13.549 Td [(of)-443(the)-444(blo)-28(c)28(k-Jacobi)-443(solv)27(er,)-470(w)-1(i)1(th)-444(LU)-443(\050or)-444(ILU\051)]TJ 0 -13.549 Td [(factorization)-297(of)-298(the)-297(blo)-28(c)28(ks)-297(\050UMFP)83(A)28(CK)-298(for)-297(the)]TJ 0 -13.549 Td [(double)-329(precision)-330(v)28(ersions)-329(and)-329(Sup)-28(erLU)-329(for)-330(the)]TJ 0 -13.549 Td [(single)-291(precision)-292(ones,)-300(if)-291(the)-291(pac)27(k)56(ages)-292(h)1(a)27(v)28(e)-291(b)-28(een)]TJ 0 -13.55 Td [(installed;)-333(ILU\0500\051,)-334(otherwise\051.)]TJ +/F15 10.9091 Tf 259.8473 393.9447 Td[(Mu)1(lti-lev)28(e)-1(l)-377(h)28(y)1(bri)1(d)-377(pr)1(e)-1(cond)1(ition)1(e)-1(r)-377(\050ad)1(diti)1(v)28(e)-378(on)]TJ 0 -13.5492 Td[(th)1(e)-391(s)-1(ame)-391(lev)28(e)-1(l)-390(an)1(d)-390(m)27(ul)1(tipl)1(ic)-1(at)1(iv)28(e)-391(thr)1(ough)-390(th)1(e)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)1(s)-1(\051,)-404(w)-1(i)1(th)-390(p)-28(ost-s)-1(mo)-28(oth)1(ing)-390(only)84(.)-616(Num)28(b)-27(e)-1(r)-390(of)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)1(s)-1(:)-510(2.)-543(P)28(ost-s)-1(mo)-28(oth)1(e)-1(r)1(:)-510(RAS)-366(with)-366(o)28(v)28(e)-1(r)1(lap)-366(1)]TJ 0 -13.5492 Td[(and)-394(ILU\0500\051)-396(on)-394(the)-396(l)1(o)-28(c)-1(al)-395(b)1(lo)-28(c)28(ks)-1(.)-630(Aggr)1(e)-1(gati)1(on:)]TJ 0 -13.5492 Td[(decoupl)1(e)-1(d)-416(s)-1(mo)-28(oth)1(e)-1(d)-416(aggregation)-416(w)-1(i)1(th)-417(th)1(res)-1(h)1(-)]TJ 0 -13.5492 Td[(old)]TJ/F24 10.9091 Tf 17.6947 0 Td[(\022)]TJ/F15 10.9091 Tf 8.4545 0 Td[(=)-278(0.)-429(Coarse)-1(st)-289(matri)1(x:)-422(di)1(s)-1(tr)1(ibu)1(te)-1(d)-288(among)]TJ -26.1492 -13.5492 Td[(th)1(e)-340(p)1(ro)-28(ce)-1(ss)-1(or)1(s)-1(.)-461(Coarse)-1(st-)-1(l)1(e)-1(v)28(el)-339(solv)28(e)-1(r)1(:)-456(4)-339(sw)27(ee)-1(p)1(s)]TJ 0 -13.5492 Td[(of)-443(th)1(e)-444(blo)-27(c)27(k-Jac)-1(ob)1(i)-443(s)-1(olv)28(er,)-470(w)-1(i)1(th)-443(LU)-444(\050or)-443(ILU\051)]TJ 0 -13.5492 Td[(factori)1(z)-1(ati)1(on)-297(of)-297(the)-298(b)1(lo)-28(c)28(ks)-298(\050UMF)1(P)83(A)28(CK)-297(for)-297(th)1(e)]TJ 0 -13.5492 Td[(dou)1(bl)1(e)-330(pr)1(e)-1(cis)-1(i)1(on)-329(v)28(e)-1(r)1(s)-1(ion)1(s)-330(an)1(d)-329(Su)1(p)-28(erLU)-329(for)-329(th)1(e)]TJ 0 -13.5492 Td[(single)-291(prec)-1(i)1(s)-1(ion)-290(ones)-1(,)-300(i)1(f)-291(the)-292(p)1(ac)27(k)56(ages)-292(ha)28(v)28(e)-292(b)-27(e)-1(en)]TJ 0 -13.5492 Td[(in)1(s)-1(tal)1(le)-1(d)1(;)-333(ILU\0500\051,)-333(otherwise)-1(\051.)]TJ ET +1 0 0 1 486.7281 227.2896 cm q -1 0 0 1 486.927 227.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 176.14 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 176.1395 l +S Q +1 0 0 1 -388.4047 -0.3985 cm q -1 0 0 1 98.323 227.09 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +388.604 0.1992 l +S Q +1 0 0 1 17.7866 -30.4898 cm 0 g 0 G +1 0 0 1 -116.11 -196.4013 cm BT -/F15 10.9091 Tf 116.11 196.401 Td [(T)83(able)-333(1:)-444(Preconditioner)-334(t)28(yp)-28(es,)-333(corresp)-28(onding)-333(strings)-333(and)-333(default)-334(c)28(hoices.)]TJ +/F15 10.9091 Tf 116.11 196.4013 Td[(T)83(ab)1(le)-334(1:)-444(Pr)1(e)-1(cond)1(ition)1(e)-1(r)-333(t)28(yp)-27(e)-1(s,)-333(c)-1(or)1(res)-1(p)-27(ond)1(ing)-333(strin)1(gs)-334(and)-332(defaul)1(t)-334(c)28(hoices)-1(.)]TJ +ET +1 0 0 1 469.1406 196.4013 cm 0 g 0 G +1 0 0 1 -382.7408 -2.1212 cm 0 g 0 G -/F17 11.9552 Tf -29.71 -40.736 Td [(5.1)-1125(Examples)]TJ/F15 10.9091 Tf 0 -20.595 Td [(The)-340(co)-28(de)-340(rep)-28(or)1(te)-1(d)-339(in)-340(Figure)]TJ +1 0 0 1 -86.3998 -194.2801 cm +BT +/F19 11.9552 Tf 86.3998 155.6647 Td[(5.)-1(1)-1125(E)-1(xampl)-1(es)]TJ/F15 10.9091 Tf 0 -20.5946 Td[(The)-340(c)-1(o)-27(de)-340(re)-1(p)-27(ort)1(e)-1(d)-339(in)-340(F)1(igur)1(e)]TJ +ET +1 0 0 1 225.4896 135.0701 cm 0 0 1 rg 0 0 1 RG - [-340(2)]TJ +1 0 0 1 -225.4896 -135.0701 cm +BT +/F15 10.9091 Tf 225.4896 135.0701 Td[(2)]TJ +ET +1 0 0 1 230.9441 135.0701 cm 0 g 0 G - [-340(sho)28(ws)-341(h)1(o)27(w)-340(to)-340(set)-340(and)-340(apply)-339(the)-340(default)-340(m)27(u)1(lti-le)-1(v)28(el)-340(pre-)]TJ 0 -13.549 Td [(conditioner)-257(a)27(v)56(ailable)-258(in)-257(the)-258(real)-258(d)1(ouble)-258(precision)-258(v)28(ersion)-257(of)-258(MLD2P4)-258(\050see)-257(T)83(able)]TJ +1 0 0 1 -230.9441 -135.0701 cm +BT +/F15 10.9091 Tf 234.6529 135.0701 Td[(sho)28(ws)-341(h)1(o)27(w)-340(to)-340(se)-1(t)-339(and)-340(ap)1(pl)1(y)-340(the)-340(defau)1(lt)-340(m)28(ulti)1(-)-1(lev)28(el)-340(pr)1(e)-1(-)]TJ -148.2531 -13.5492 Td[(condi)1(tioner)-257(a)27(v)56(ail)1(able)-258(i)1(n)-258(th)1(e)-258(real)-258(d)1(oub)1(le)-258(pr)1(e)-1(cis)-1(i)1(on)-258(v)28(ersion)-257(of)-257(MLD2P)1(4)-258(\050se)-1(e)-258(T)83(ab)1(le)]TJ +ET +1 0 0 1 460.2777 121.5209 cm 0 0 1 rg 0 0 1 RG - [-258(1)]TJ +1 0 0 1 -460.2777 -121.5209 cm +BT +/F15 10.9091 Tf 460.2777 121.5209 Td[(1)]TJ +ET +1 0 0 1 465.7322 121.5209 cm 0 g 0 G - [(\051.)-419(This)]TJ +1 0 0 1 -465.7322 -121.5209 cm +BT +/F15 10.9091 Tf 465.7322 121.5209 Td[(\051.)-419(Thi)1(s)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -360 0 obj << +391 0 obj << /Type /Page -/Contents 361 0 R -/Resources 359 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 320 0 R -/Annots [ 340 0 R 341 0 R 342 0 R 357 0 R 358 0 R ] +/Contents 392 0 R +/Resources 390 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 356 0 R +/Annots [ 394 0 R 395 0 R 396 0 R 397 0 R 398 0 R ] >> endobj -340 0 obj << +394 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [228.32 635.394 235.767 644.417] +/Rect [228.3202 635.3941 235.7672 644.4169] /Subtype /Link /A << /S /GoTo /D (cite.aaecc_07) >> >> endobj -341 0 obj << +395 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [239.242 635.394 246.689 644.417] +/Rect [239.2418 635.3941 246.6889 644.4169] /Subtype /Link /A << /S /GoTo /D (cite.apnum_07) >> >> endobj -342 0 obj << +396 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [245.076 592.019 252.523 604.921] +/Rect [245.0762 592.0192 252.5233 604.9208] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -357 0 obj << +397 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [224.493 131.953 231.94 143.642] +/Rect [224.4933 131.9526 231.9404 143.6421] /Subtype /Link /A << /S /GoTo /D (figure.2) >> >> endobj -358 0 obj << +398 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [459.281 117.797 466.728 130.699] +/Rect [459.2814 117.7973 466.7285 130.699] /Subtype /Link /A << /S /GoTo /D (table.1) >> >> endobj -362 0 obj << -/D [360 0 R /XYZ 86.4 740.002 null] +393 0 obj << +/D [391 0 R /XYZ 86.3998 740.0018 null] >> endobj -354 0 obj << -/D [360 0 R /XYZ 159.443 209.95 null] +387 0 obj << +/D [391 0 R /XYZ 159.4434 209.9504 null] >> endobj 62 0 obj << -/D [360 0 R /XYZ 86.4 167.491 null] +/D [391 0 R /XYZ 86.3998 167.4912 null] >> endobj -359 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F43 158 0 R /F44 200 0 R /F22 175 0 R /F17 111 0 R >> +390 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F45 147 0 R /F46 219 0 R /F24 186 0 R /F19 113 0 R >> /ProcSet [ /PDF /Text ] >> endobj -378 0 obj << -/Length 8948 +402 0 obj << +/Length 13038 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(5)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(5)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(Getting)-378(St)67(ar)67(ted)]TJ/F15 10.9091 Tf 401.542 0 Td [(17)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Getti)-1(ng)-378(St)67(a)-1(r)67(ted)]TJ/F15 10.9091 Tf 391.3906 0 Td[(17)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G - -401.542 -35.866 Td [(preconditioner)-238(is)-238(c)28(hosen)-238(b)28(y)-238(simply)-238(sp)-27(ecifying)]TJ/F44 10.9091 Tf 212.539 0 Td [('ML')]TJ/F15 10.9091 Tf 25.503 0 Td [(as)-238(second)-238(argumen)28(t)-238(of)]TJ/F44 10.9091 Tf 105.683 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf -343.725 -13.549 Td [(\050a)-359(call)-360(to)]TJ/F44 10.9091 Tf 47.52 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 66.92 0 Td [(is)-359(not)-360(needed\051)-359(and)-360(is)-359(applied)-359(with)-360(the)-359(BiCGST)83(AB)-359(solv)28(er)-360(pro-)]TJ -114.44 -13.549 Td [(vided)-301(b)28(y)-301(PSBLAS.)-301(As)-301(previously)-301(observ)28(ed,)-308(the)-301(mo)-27(dules)]TJ/F44 10.9091 Tf 268.614 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)]TJ/F44 10.9091 Tf 6.385 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf -343.725 -13.549 Td [(and)]TJ/F44 10.9091 Tf 21.212 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 83.818 0 Td [(m)28(ust)-334(b)-27(e)-334(used)-333(b)28(y)-333(the)-334(example)-333(program.)]TJ -88.093 -13.549 Td [(The)-395(part)-395(of)-395(the)-395(co)-28(de)-395(concerning)-395(the)-395(reading)-395(and)-395(assem)27(b)1(ling)-395(of)-396(th)1(e)-396(sparse)-395(matrix)]TJ -16.937 -13.55 Td [(and)-457(the)-456(righ)27(t-hand)-456(side)-457(v)28(ector,)-488(p)-28(erformed)-456(through)-457(the)-457(PSBLAS)-456(routines)-457(for)-457(sparse)]TJ 0 -13.549 Td [(matrix)-385(and)-385(v)28(ector)-386(managemen)28(t,)-398(is)-385(not)-385(rep)-28(orted)-385(here)-385(for)-385(brevit)27(y)1(;)-412(th)1(e)-386(statemen)28(ts)-385(con-)]TJ 0 -13.549 Td [(cerning)-265(the)-264(deallo)-28(cation)-265(of)-264(the)-265(PSBLAS)-265(d)1(ata)-265(structure)-265(are)-264(negle)-1(cted)-264(to)-28(o.)-422(The)-264(complete)]TJ 0 -13.549 Td [(co)-28(de)-306(can)-307(b)-28(e)-306(found)-306(in)-307(the)-306(example)-307(program)-306(\014le)]TJ/F44 10.9091 Tf 223.485 0 Td [(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 108.817 0 Td [(,)-312(in)-306(the)-307(directory)]TJ/F44 10.9091 Tf -332.302 -13.549 Td [(examples/fileread)]TJ/F15 10.9091 Tf 101.625 0 Td [(of)-391(the)-390(MLD2P4)-391(tree)-391(\050see)-391(Section)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F15 10.9091 Tf 93.6002 704.1363 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-237(is)-238(c)27(hosen)-238(b)28(y)-237(s)-1(i)1(m)-1(p)1(ly)-238(sp)-28(ecifyi)1(ng)]TJ/F46 10.9091 Tf 212.5393 0 Td[('ML')]TJ/F15 10.9091 Tf 25.5026 0 Td[(as)-238(s)-1(ec)-1(on)1(d)-238(ar)1(gume)-1(n)29(t)-238(of)]TJ/F46 10.9091 Tf 105.6827 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf -343.7246 -13.5492 Td[(\050a)-359(c)-1(all)-359(to)]TJ/F46 10.9091 Tf 47.52 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 66.9201 0 Td[(is)-360(n)1(ot)-359(nee)-1(d)1(e)-1(d)1(\051)-360(an)1(d)-359(is)-360(ap)1(plied)-359(with)-359(th)1(e)-360(BiCGST)83(AB)-359(s)-1(olv)28(er)-359(pr)1(o-)]TJ -114.4401 -13.5492 Td[(vid)1(e)-1(d)-300(b)28(y)-301(P)1(SBLAS.)-300(As)-302(p)1(re)-1(v)1(iously)-301(ob)1(s)-1(erv)28(ed,)-307(the)-301(mo)-28(du)1(les)]TJ/F46 10.9091 Tf 268.6135 0 Td[(psb_base_mod)]TJ/F15 10.9091 Tf 68.7265 0 Td[(,)]TJ/F46 10.9091 Tf 6.3846 0 Td[(mld_prec_mod)]TJ/F15 10.9091 Tf -343.7246 -13.5492 Td[(and)]TJ/F46 10.9091 Tf 21.2121 0 Td[(psb_krylov_mod)]TJ/F15 10.9091 Tf 83.8173 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(u)1(s)-1(ed)-333(b)28(y)-333(the)-333(e)-1(xamp)1(le)-334(pr)1(ogram.)]TJ -88.0929 -13.5492 Td[(The)-395(part)-394(of)-395(the)-395(c)-1(o)-27(de)-395(c)-1(on)1(c)-1(erni)1(ng)-395(th)1(e)-396(readi)1(ng)-395(and)-394(as)-1(se)-1(m)28(bl)1(ing)-395(of)-394(the)-395(s)-1(p)1(ars)-1(e)-395(matrix)]TJ -16.9365 -13.5492 Td[(and)-456(th)1(e)-458(r)1(igh)28(t-han)1(d)-456(s)-1(id)1(e)-457(v)28(e)-1(ctor,)-487(p)-28(erf)1(orme)-1(d)-456(thr)1(ough)-456(the)-457(P)1(SBLAS)-456(rout)1(ines)-457(for)-456(s)-1(p)1(ars)-1(e)]TJ 0 -13.5492 Td[(matrix)-385(an)1(d)-385(v)28(ec)-1(tor)-384(m)-1(an)1(age)-1(me)-1(n)29(t,)-398(is)-386(n)1(ot)-385(rep)-28(or)1(te)-1(d)-384(here)-386(f)1(or)-385(br)1(e)-1(v)1(it)28(y;)-411(th)1(e)-386(state)-1(men)28(ts)-386(con-)]TJ 0 -13.5492 Td[(ce)-1(rn)1(in)1(g)-265(the)-265(d)1(e)-1(al)1(lo)-28(cation)-264(of)-265(th)1(e)-265(PS)1(B)-1(LAS)-264(d)1(ata)-265(stru)1(c)-1(tu)1(re)-265(are)-265(neglec)-1(ted)-264(to)-28(o.)-421(The)-265(c)-1(omp)1(le)-1(te)]TJ 0 -13.5492 Td[(co)-28(de)-307(can)-306(b)-28(e)-306(foun)1(d)-306(in)-306(th)1(e)-307(e)-1(xamp)1(le)-307(pr)1(ogram)-307(\014)1(le)]TJ/F46 10.9091 Tf 223.4846 0 Td[(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 108.817 0 Td[(,)-312(i)1(n)-306(the)-307(d)1(irec)-1(tor)1(y)]TJ/F46 10.9091 Tf -332.3016 -13.5492 Td[(examples/fileread)]TJ/F15 10.9091 Tf 101.625 0 Td[(of)-390(the)-391(MLD)1(2P4)-391(tr)1(e)-1(e)-391(\050se)-1(e)-391(S)1(e)-1(ction)]TJ +ET +1 0 0 1 359.2243 582.1936 cm 0 0 1 rg 0 0 1 RG - [-390(3.5)]TJ +1 0 0 1 -359.2243 -582.1936 cm +BT +/F15 10.9091 Tf 359.2243 582.1936 Td[(3.5)]TJ +ET +1 0 0 1 373.1637 582.1936 cm 0 g 0 G - [(\051.)-617(F)83(or)-390(details)-391(on)-391(the)-390(use)-391(of)]TJ -101.625 -13.55 Td [(the)-333(PSBLAS)-334(rout)1(ines)-1(,)-333(see)-333(the)-334(PSBLAS)-333(User's)-333(Guide)-334([)]TJ +1 0 0 1 -373.1637 -582.1936 cm +BT +/F15 10.9091 Tf 373.1637 582.1936 Td[(\051.)-616(F)83(or)-390(details)-391(on)-390(th)1(e)-392(u)1(s)-1(e)-391(of)]TJ -279.5635 -13.5492 Td[(th)1(e)-334(PS)1(B)-1(LAS)-333(r)1(outi)1(nes)-1(,)-333(se)-1(e)-334(th)1(e)-334(P)1(SBLAS)-333(Us)-1(er's)-333(Gui)1(de)-334([)]TJ +ET +1 0 0 1 353.3732 568.6444 cm 1 0 0 rg 1 0 0 RG - [(14)]TJ +1 0 0 1 -353.3732 -568.6444 cm +BT +/F15 10.9091 Tf 353.3732 568.6444 Td[(14)]TJ +ET +1 0 0 1 364.2823 568.6444 cm 0 g 0 G - [(].)]TJ 16.937 -13.549 Td [(The)-461(setup)-460(and)-461(application)-460(of)-461(the)-460(default)-461(m)28(ulti-lev)28(el)-461(preconditioners)-460(for)-461(the)-460(real)]TJ -16.937 -13.549 Td [(single)-450(precis)-1(i)1(on)-451(and)-450(the)-451(complex,)-479(single)-451(and)-450(double)-451(precision,)-479(v)27(ersion)1(s)-451(are)-450(obtained)]TJ 0 -13.549 Td [(with)-352(straigh)27(tforw)28(ard)-352(mo)-28(di\014cations)-352(of)-353(the)-352(previous)-353(example)-352(\050see)-353(Section)]TJ +1 0 0 1 -364.2823 -568.6444 cm +BT +/F15 10.9091 Tf 364.2823 568.6444 Td[(].)]TJ -253.7456 -13.5492 Td[(The)-461(se)-1(tu)1(p)-460(and)-460(app)1(lication)-460(of)-460(the)-461(d)1(e)-1(f)1(ault)-460(m)27(u)1(lti-lev)28(e)-1(l)-460(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-461(for)-460(the)-461(r)1(e)-1(al)]TJ -16.9365 -13.5492 Td[(single)-450(prec)-1(i)1(s)-1(ion)-450(an)1(d)-450(the)-450(c)-1(omplex,)-479(s)-1(in)1(gle)-451(an)1(d)-450(dou)1(ble)-451(p)1(rec)-1(ision)1(,)-480(v)28(ersions)-451(ar)1(e)-451(obtai)1(ned)]TJ 0 -13.5492 Td[(with)-352(straigh)28(t)1(forw)28(ard)-352(mo)-28(d)1(i\014cation)1(s)-353(of)-352(the)-353(p)1(revious)-353(exampl)1(e)-353(\050s)-1(ee)-353(Sec)-1(t)1(ion)]TJ +ET +1 0 0 1 441.6029 527.9968 cm 0 0 1 rg 0 0 1 RG - [-352(6)]TJ +1 0 0 1 -441.6029 -527.9968 cm +BT +/F15 10.9091 Tf 441.6029 527.9968 Td[(6)]TJ +ET +1 0 0 1 447.0575 527.9968 cm 0 g 0 G - [-353(for)-352(details\051.)]TJ 0 -13.549 Td [(If)-503(these)-502(v)27(ersions)-502(are)-503(installed,)-545(the)-503(corresp)-28(on)1(ding)-503(F)83(ortran)-502(95)-503(co)-28(des)-503(ar)1(e)-503(a)28(v)55(ailable)-503(i)1(n)]TJ/F44 10.9091 Tf 0 -13.55 Td [(examples/fileread/)]TJ/F15 10.9091 Tf 103.09 0 Td [(.)]TJ -86.153 -13.549 Td [(Di\013eren)28(t)-270(v)28(ersions)-269(of)-270(m)28(ulti-lev)28(el)-270(precondi)1(tioners)-270(can)-269(b)-28(e)-270(obtai)1(ned)-270(b)28(y)-269(c)27(hanging)-269(the)-269(de-)]TJ -16.937 -13.549 Td [(fault)-273(v)56(alues)-273(of)-272(the)-273(preconditioner)-273(parameters.)-424(The)-273(co)-28(de)-272(rep)-28(orted)-273(in)-272(Figure)]TJ +1 0 0 1 -447.0575 -527.9968 cm +BT +/F15 10.9091 Tf 450.9028 527.9968 Td[(for)-352(d)1(e)-1(tai)1(ls)-1(\051.)]TJ -357.3026 -13.5492 Td[(If)-502(thes)-1(e)-503(v)28(ersions)-503(are)-503(i)1(nstalled,)-545(th)1(e)-503(c)-1(or)1(re)-1(sp)-27(ond)1(ing)-502(F)83(ort)1(ran)-502(95)-503(co)-28(des)-503(are)-503(a)28(v)55(ai)1(lable)-503(i)1(n)]TJ/F46 10.9091 Tf 0 -13.5492 Td[(examples/fileread/)]TJ/F15 10.9091 Tf 103.0898 0 Td[(.)]TJ -86.1533 -13.5492 Td[(Di\013ere)-1(n)29(t)-270(v)28(ersions)-269(of)-269(m)27(ul)1(ti-le)-1(v)28(el)-269(pr)1(e)-1(cond)1(ition)1(e)-1(rs)-269(c)-1(an)-269(b)-27(e)-270(obtai)1(ned)-269(b)28(y)-269(c)27(han)1(gin)1(g)-270(th)1(e)-270(de-)]TJ -16.9365 -13.5492 Td[(fau)1(lt)-273(v)56(alu)1(e)-1(s)-273(of)-272(th)1(e)-274(p)1(rec)-1(on)1(dit)1(ioner)-273(p)1(arame)-1(ters.)-424(The)-273(co)-28(de)-273(rep)-27(orted)-273(i)1(n)-273(Fi)1(gure)]TJ +ET +1 0 0 1 447.8587 473.8 cm 0 0 1 rg 0 0 1 RG - [-273(3)]TJ +1 0 0 1 -447.8587 -473.8 cm +BT +/F15 10.9091 Tf 447.8587 473.8 Td[(3)]TJ +ET +1 0 0 1 453.3132 473.8 cm 0 g 0 G - [-273(sho)28(ws)-273(ho)28(w)]TJ 0 -13.549 Td [(to)-282(set)-281(a)-282(three-lev)28(el)-281(h)27(ybri)1(d)-282(Sc)28(h)28(w)27(arz)-281(preconditioner,)-292(whic)28(h)-282(u)1(s)-1(es)-281(blo)-28(c)28(k)-282(Jacobi)-281(with)-282(ILU\0500\051)]TJ 0 -13.549 Td [(on)-265(the)-265(lo)-28(cal)-265(blo)-27(c)27(ks)-265(as)-265(p)-27(ost-smo)-28(other,)-279(has)-265(a)-265(coarsest)-265(matrix)-265(replicated)-265(on)-264(the)-265(pro)-28(cessors,)]TJ 0 -13.55 Td [(and)-250(solv)28(es)-251(the)-250(coarsest-lev)28(el)-251(system)-250(with)-250(the)-250(LU)-250(factorization)-251(fr)1(om)-251(UMFP)84(A)27(CK)-250([)]TJ +1 0 0 1 -453.3132 -473.8 cm +BT +/F15 10.9091 Tf 456.2883 473.8 Td[(sho)28(ws)-274(h)1(o)28(w)]TJ -362.6881 -13.5492 Td[(to)-281(s)-1(et)-282(a)-281(thr)1(e)-1(e-)-1(l)1(e)-1(v)28(el)-282(h)29(ybr)1(id)-281(Sc)28(h)28(w)27(ar)1(z)-282(pr)1(e)-1(cond)1(ition)1(e)-1(r,)-291(whic)28(h)-282(u)1(s)-1(es)-282(b)1(lo)-28(c)27(k)-281(Jacobi)-281(with)-281(ILU\0500\051)]TJ 0 -13.5492 Td[(on)-265(t)1(he)-265(lo)-28(cal)-265(bl)1(o)-28(c)27(ks)-265(as)-265(p)-28(ost-s)-1(mo)-28(oth)1(e)-1(r,)-278(h)1(as)-266(a)-265(coarse)-1(st)-265(matrix)-264(re)-1(p)1(licate)-1(d)-264(on)-265(t)1(he)-265(pro)-27(c)-1(es)-1(sors,)]TJ 0 -13.5492 Td[(and)-249(s)-1(olv)28(es)-251(th)1(e)-251(coarse)-1(st-le)-1(v)28(el)-250(s)-1(y)1(s)-1(tem)-251(with)-249(the)-250(LU)-251(f)1(ac)-1(tor)1(ization)-250(f)1(rom)-251(UM)1(FP)84(A)27(CK)-250([)]TJ +ET +1 0 0 1 471.202 433.1524 cm 1 0 0 rg 1 0 0 RG - [(8)]TJ +1 0 0 1 -471.202 -433.1524 cm +BT +/F15 10.9091 Tf 471.202 433.1524 Td[(8)]TJ +ET +1 0 0 1 476.6566 433.1524 cm 0 g 0 G - [(].)-416(The)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)-362(of)-363(lev)28(els)-362(is)-363(sp)-27(eci\014ed)-363(b)28(y)-362(using)]TJ/F44 10.9091 Tf 182.182 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 68.726 0 Td [(;)-377(the)-362(other)-362(preconditioner)-362(param-)]TJ -250.908 -13.549 Td [(eters)-351(are)-351(set)-350(b)27(y)-350(calling)]TJ/F44 10.9091 Tf 112.04 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 62.999 0 Td [(.)-497(Note)-350(that)-351(the)-351(t)28(yp)-28(e)-350(of)-351(m)28(ultilev)28(e)-1(l)-350(framew)28(ork)-351(\050i.e.)]TJ -175.039 -13.549 Td [(m)28(ultiplicativ)28(e)-280(among)-279(the)-279(lev)28(els)-280(with)-279(p)-28(ost-smo)-27(othing)-280(only\051)-279(is)-279(not)-279(sp)-28(eci\014ed)-279(since)-280(it)-279(is)-279(the)]TJ 0 -13.549 Td [(default)-333(set)-334(b)28(y)]TJ/F44 10.9091 Tf 68.849 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 68.726 0 Td [(.)]TJ -120.638 -13.549 Td [(Figure)]TJ +1 0 0 1 -476.6566 -433.1524 cm +BT +/F15 10.9091 Tf 476.6566 433.1524 Td[(].)-416(T)-1(h)1(e)]TJ -383.0564 -13.5492 Td[(n)28(u)1(m)27(b)-27(e)-1(r)-362(of)-361(le)-1(v)28(els)-363(i)1(s)-363(s)-1(p)-27(ec)-1(i\014)1(e)-1(d)-361(b)28(y)-362(using)]TJ/F46 10.9091 Tf 182.1814 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 68.7266 0 Td[(;)-377(t)1(he)-363(oth)1(e)-1(r)-362(p)1(rec)-1(on)1(dit)1(ioner)-362(par)1(am)-1(-)]TJ -250.908 -13.5492 Td[(ete)-1(r)1(s)-352(ar)1(e)-351(s)-1(et)-351(b)28(y)-350(c)-1(al)1(ling)]TJ/F46 10.9091 Tf 112.0395 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)-496(Note)-351(that)-351(t)1(he)-351(t)28(yp)-27(e)-352(of)-350(m)28(ulti)1(le)-1(v)28(el)-351(f)1(rame)-1(w)28(ork)-350(\050i.e.)]TJ -175.0388 -13.5492 Td[(m)27(u)1(ltip)1(licativ)28(e)-279(am)-1(on)1(g)-280(th)1(e)-280(lev)28(els)-280(with)-279(p)-27(ost-)-1(smo)-28(othi)1(ng)-279(only)1(\051)-279(is)-280(n)1(ot)-280(sp)-27(e)-1(ci\014ed)-279(since)-280(it)-279(i)1(s)-280(the)]TJ 0 -13.5492 Td[(defau)1(lt)-333(s)-1(et)-333(b)28(y)]TJ/F46 10.9091 Tf 68.8486 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 68.7265 0 Td[(.)]TJ -120.6386 -13.5492 Td[(Figu)1(re)]TJ +ET +1 0 0 1 144.6065 365.4064 cm 0 0 1 rg 0 0 1 RG - [-301(4)]TJ +1 0 0 1 -144.6065 -365.4064 cm +BT +/F15 10.9091 Tf 144.6065 365.4064 Td[(4)]TJ +ET +1 0 0 1 150.0611 365.4064 cm 0 g 0 G - [-301(sho)28(ws)-301(ho)28(w)-301(to)-301(set)-300(a)-301(three-lev)27(el)-300(additiv)27(e)-300(Sc)27(h)28(w)28(arz)-301(preconditioner,)-307(whic)28(h)-301(uses)]TJ -16.937 -13.55 Td [(RAS,)-433(with)-433(o)28(v)28(erlap)-433(1)-433(and)-433(ILU\0500\051)-433(on)-433(the)-433(b)1(lo)-28(c)27(k)1(s)-1(,)-457(as)-433(pre-)-433(and)-433(p)-28(ost-smo)-28(other,)-457(and)-433(ap-)]TJ 0 -13.549 Td [(plies)-340(\014v)28(e)-340(blo)-28(c)28(k-Jacobi)-340(sw)28(eeps,)-342(with)-340(the)-340(UMFP)83(A)28(CK)-340(LU)-340(factorization)-340(on)-340(th)1(e)-340(blo)-28(c)28(ks,)-342(as)]TJ 0 -13.549 Td [(distributed)-402(coarsest-lev)27(el)-402(solv)28(er.)-652(Again,)]TJ/F44 10.9091 Tf 196.866 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 67.39 0 Td [(is)-402(use)-1(d)-402(only)-402(to)-403(set)-402(non-default)]TJ -264.256 -13.549 Td [(v)56(alues)-271(of)-271(the)-271(p)1(arame)-1(ters)-270(\050see)-271(T)83(ables)]TJ +1 0 0 1 -150.0611 -365.4064 cm +BT +/F15 10.9091 Tf 153.343 365.4064 Td[(sho)28(ws)-302(h)1(o)27(w)-301(t)1(o)-301(s)-1(et)-301(a)-301(th)1(ree)-1(-lev)28(e)-1(l)-300(addi)1(tiv)28(e)-301(Sc)28(h)28(w)27(ar)1(z)-302(p)1(rec)-1(on)1(diti)1(oner,)-307(whic)28(h)-301(u)1(s)-1(es)]TJ -59.7428 -13.5492 Td[(RAS,)-432(w)-1(i)1(th)-433(o)28(v)28(erlap)-432(1)-433(and)-432(ILU\0500\051)-433(on)-433(th)1(e)-433(blo)-28(c)28(ks,)-458(as)-433(pre-)-433(and)-432(p)-28(ost-s)-1(mo)-28(oth)1(e)-1(r)1(,)-458(and)-432(ap-)]TJ 0 -13.5492 Td[(pl)1(ie)-1(s)-340(\014v)28(e)-340(bl)1(o)-28(c)27(k-Jacobi)-339(s)-1(w)28(e)-1(eps,)-342(with)-339(the)-340(UMF)1(P)83(A)28(CK)-340(LU)-340(f)1(ac)-1(tor)1(iz)-1(at)1(ion)-340(on)-339(the)-340(blo)-27(c)27(ks,)-342(as)]TJ 0 -13.5492 Td[(di)1(s)-1(tr)1(ibu)1(te)-1(d)-402(coarse)-1(st-lev)28(e)-1(l)-402(s)-1(ol)1(v)28(e)-1(r.)-651(Again)1(,)]TJ/F46 10.9091 Tf 196.8657 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 67.3899 0 Td[(is)-403(u)1(s)-1(ed)-402(only)-402(to)-402(s)-1(et)-402(non)1(-)-1(d)1(e)-1(f)1(ault)]TJ -264.2556 -13.5492 Td[(v)56(alues)-271(of)-270(the)-271(par)1(am)-1(eters)-271(\050se)-1(e)-271(T)83(abl)1(e)-1(s)]TJ +ET +1 0 0 1 265.8644 311.2096 cm 0 0 1 rg 0 0 1 RG - [-271(2)]TJ +1 0 0 1 -265.8644 -311.2096 cm +BT +/F15 10.9091 Tf 265.8644 311.2096 Td[(2)]TJ +ET +1 0 0 1 271.319 311.2096 cm 0 g 0 G - [(-)]TJ +1 0 0 1 -271.319 -311.2096 cm +BT +/F15 10.9091 Tf 271.319 311.2096 Td[(-)]TJ +ET +1 0 0 1 274.9553 311.2096 cm 0 0 1 rg 0 0 1 RG - [(5)]TJ +1 0 0 1 -274.9553 -311.2096 cm +BT +/F15 10.9091 Tf 274.9553 311.2096 Td[(5)]TJ +ET +1 0 0 1 280.4099 311.2096 cm 0 g 0 G - [(\051.)-423(In)-271(b)-27(oth)-271(cases,)-284(t)1(he)-271(construction)-271(and)-270(the)-271(appli-)]TJ 0 -13.549 Td [(cation)-269(of)-268(the)-269(preconditioner)-269(are)-268(carried)-269(out)-269(as)-269(f)1(or)-269(the)-269(default)-268(m)27(ulti-lev)28(el)-269(preconditi)1(one)-1(r)1(.)]TJ 0 -13.55 Td [(The)-368(co)-28(de)-368(fragmen)28(ts)-368(sho)28(wn)-368(in)-368(in)-368(Figures)]TJ +1 0 0 1 -280.4099 -311.2096 cm +BT +/F15 10.9091 Tf 280.4099 311.2096 Td[(\051.)-423(In)-271(b)-27(oth)-270(c)-1(ases)-1(,)-283(th)1(e)-271(c)-1(on)1(s)-1(tr)1(uction)-270(and)-270(the)-271(ap)1(pli)1(-)]TJ -186.8097 -13.5492 Td[(cation)-268(of)-269(th)1(e)-269(precondi)1(tioner)-268(are)-269(c)-1(ar)1(ried)-268(out)-269(as)-269(f)1(or)-269(th)1(e)-269(defau)1(lt)-269(m)28(ulti)1(-)-1(lev)28(el)-269(p)1(re)-1(cond)1(ition)1(e)-1(r)1(.)]TJ 0 -13.5492 Td[(The)-368(c)-1(o)-27(de)-369(f)1(ragme)-1(n)29(ts)-369(sho)28(wn)-368(i)1(n)-368(in)-367(Figur)1(e)-1(s)]TJ +ET +1 0 0 1 291.4924 284.1112 cm 0 0 1 rg 0 0 1 RG - [-368(3)]TJ +1 0 0 1 -291.4924 -284.1112 cm +BT +/F15 10.9091 Tf 291.4924 284.1112 Td[(3)]TJ +ET +1 0 0 1 296.947 284.1112 cm 0 g 0 G - [(-)]TJ +1 0 0 1 -296.947 -284.1112 cm +BT +/F15 10.9091 Tf 296.947 284.1112 Td[(-)]TJ +ET +1 0 0 1 300.5833 284.1112 cm 0 0 1 rg 0 0 1 RG - [(4)]TJ +1 0 0 1 -300.5833 -284.1112 cm +BT +/F15 10.9091 Tf 300.5833 284.1112 Td[(4)]TJ +ET +1 0 0 1 306.0379 284.1112 cm 0 g 0 G - [-368(are)-368(included)-368(in)-368(the)-368(example)-368(program)-368(\014le)]TJ/F44 10.9091 Tf 0 -13.549 Td [(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 112.453 0 Td [(to)-28(o.)]TJ -95.516 -13.549 Td [(Finally)84(,)-296(Figure)]TJ +1 0 0 1 -306.0379 -284.1112 cm +BT +/F15 10.9091 Tf 310.0527 284.1112 Td[(are)-368(in)1(c)-1(lu)1(ded)-368(in)-367(the)-368(e)-1(x)1(am)-1(p)1(le)-369(p)1(rogr)1(am)-369(\014)1(le)]TJ/F46 10.9091 Tf -216.4525 -13.5492 Td[(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 112.4534 0 Td[(to)-28(o.)]TJ -95.5169 -13.5492 Td[(Fin)1(ally)84(,)-295(Figu)1(re)]TJ +ET +1 0 0 1 183.2723 257.0128 cm 0 0 1 rg 0 0 1 RG - [-286(5)]TJ +1 0 0 1 -183.2723 -257.0128 cm +BT +/F15 10.9091 Tf 183.2723 257.0128 Td[(5)]TJ +ET +1 0 0 1 188.7268 257.0128 cm 0 g 0 G - [-286(sho)28(ws)-286(the)-286(setup)-286(of)-285(a)-286(one-lev)27(el)-286(addi)1(tiv)27(e)-286(Sc)28(h)28(w)28(arz)-286(preconditioner,)-295(i.e.)]TJ -16.937 -13.549 Td [(RAS)-231(with)-231(o)28(v)27(erlap)-231(2.)-410(The)-231(corresp)-28(onding)-231(example)-231(program)-231(is)-232(a)28(v)56(ailable)-231(in)]TJ/F44 10.9091 Tf 337.997 0 Td [(mld_dexample_)]TJ -337.997 -13.549 Td [(1lev.f90)]TJ/F15 10.9091 Tf 45.818 0 Td [(.)]TJ -28.881 -13.55 Td [(F)83(or)-452(all)-452(the)-452(previou)1(s)-453(pr)1(e)-1(cond)1(itioners,)-482(example)-452(programs)-452(where)-452(the)-452(sparse)-452(matrix)]TJ -16.937 -13.549 Td [(and)-370(the)-371(righ)28(t-hand)-371(side)-370(are)-371(generated)-370(b)27(y)-370(discretizing)-371(a)-370(PDE)-371(with)-370(Diric)28(hlet)-371(b)-28(oundary)]TJ 0 -13.549 Td [(conditions)-333(are)-334(also)-333(a)28(v)55(ailabl)1(e)-334(in)-333(the)-333(directory)]TJ/F44 10.9091 Tf 215.061 0 Td [(examples/pdegen)]TJ/F15 10.9091 Tf 85.908 0 Td [(.)]TJ/F43 10.9091 Tf -300.969 -27.098 Td [(Remark)-319(3.)]TJ/F15 10.9091 Tf 61.378 0 Td [(An)28(y)-277(PSBLAS-based)-277(program)-277(using)-278(th)1(e)-278(basic)-277(preconditioners)-277(implemen)28(ted)]TJ -61.378 -13.55 Td [(in)-269(PSBLAS)-270(2.0,)-282(i.e.)-269(the)-269(diagonal)-270(and)-269(blo)-28(c)28(k-Jacobi)-269(ones,)-283(can)-269(use)-269(the)-270(diagonal)-269(and)-269(blo)-28(c)28(k-)]TJ 0 -13.549 Td [(Jacobi)-337(preconditioners)-337(implemen)28(ted)-337(in)-337(MLD2P4)-337(without)-336(an)27(y)-337(c)28(hange)-337(in)-337(the)-337(co)-27(de.)-456(The)]TJ 0 -13.549 Td [(PSBLAS-based)-333(program)-334(m)28(ust)-333(b)-28(e)-333(only)-333(rec)-1(ompil)1(e)-1(d)-333(and)-333(link)28(ed)-334(to)-333(the)-333(MLD2P4)-333(library)83(.)]TJ +1 0 0 1 -188.7268 -257.0128 cm +BT +/F15 10.9091 Tf 191.8459 257.0128 Td[(sho)28(ws)-287(th)1(e)-287(setup)-285(of)-286(a)-286(on)1(e)-1(-lev)28(e)-1(l)-285(addi)1(tiv)28(e)-286(Sc)27(h)29(w)27(arz)-286(p)1(re)-1(cond)1(ition)1(e)-1(r)1(,)-295(i.e.)]TJ -98.2457 -13.5492 Td[(RAS)-231(with)-230(o)27(v)28(erl)1(ap)-231(2.)-410(T)-1(h)1(e)-232(corresp)-28(on)1(din)1(g)-231(e)-1(xamp)1(le)-232(p)1(rogram)-231(is)-232(a)28(v)56(ailab)1(le)-232(i)1(n)]TJ/F46 10.9091 Tf 337.9974 0 Td[(mld_dexample_)]TJ -337.9974 -13.5492 Td[(1lev.f90)]TJ/F15 10.9091 Tf 45.8177 0 Td[(.)]TJ -28.8812 -13.5492 Td[(F)84(or)-452(all)-452(th)1(e)-453(p)1(reviou)1(s)-453(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-1(,)-481(e)-1(x)1(am)-1(p)1(le)-453(p)1(rogr)1(am)-1(s)-452(where)-453(t)1(he)-452(s)-1(p)1(ars)-1(e)-452(matrix)]TJ -16.9365 -13.5492 Td[(and)-370(th)1(e)-371(righ)29(t-)-1(h)1(and)-370(side)-371(ar)1(e)-371(ge)-1(n)1(e)-1(r)1(ate)-1(d)-370(b)28(y)-370(di)1(s)-1(cretiz)-1(i)1(ng)-370(a)-371(PD)1(E)-371(wit)1(h)-371(D)1(iric)28(hlet)-371(b)-27(ou)1(ndar)1(y)]TJ 0 -13.5492 Td[(condi)1(tions)-333(are)-334(also)-333(a)27(v)56(ail)1(able)-333(in)-333(the)-333(dir)1(e)-1(ctory)]TJ/F46 10.9091 Tf 215.0608 0 Td[(examples/pdegen)]TJ/F15 10.9091 Tf 85.9082 0 Td[(.)]TJ/F45 10.9091 Tf -300.969 -27.0984 Td[(Re)-1(mark)-318(3.)]TJ/F15 10.9091 Tf 61.3782 0 Td[(An)28(y)-277(P)1(SBLAS-based)-277(pr)1(ogram)-278(u)1(s)-1(i)1(ng)-277(th)1(e)-278(basic)-277(prec)-1(on)1(di)1(tioners)-277(implem)-1(en)28(ted)]TJ -61.3782 -13.5492 Td[(in)-269(P)1(SBLAS)-269(2.0,)-282(i.)1(e)-1(.)-269(th)1(e)-270(diagon)1(al)-269(and)-269(b)1(lo)-28(c)27(k)1(-)-1(Jacobi)-269(on)1(e)-1(s,)-282(c)-1(an)-268(use)-270(the)-270(d)1(iagon)1(al)-270(an)1(d)-269(bl)1(o)-28(c)27(k-)]TJ 0 -13.5492 Td[(Jacobi)-337(p)1(rec)-1(on)1(diti)1(oners)-337(implem)-1(en)28(ted)-337(i)1(n)-337(MLD)1(2P4)-337(with)1(out)-337(an)28(y)-336(c)27(han)1(ge)-337(in)-337(th)1(e)-338(co)-28(d)1(e)-1(.)-455(The)]TJ 0 -13.5492 Td[(PS)1(BLAS-base)-1(d)-333(p)1(rogram)-333(m)27(u)1(s)-1(t)-333(b)-27(e)-334(onl)1(y)-334(r)1(e)-1(compiled)-333(an)1(d)-333(lin)1(k)28(e)-1(d)-333(to)-333(th)1(e)-334(MLD2P)1(4)-334(l)1(ibr)1(ary)83(.)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -377 0 obj << +401 0 obj << /Type /Page -/Contents 378 0 R -/Resources 376 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 320 0 R -/Annots [ 375 0 R 364 0 R 365 0 R 366 0 R 367 0 R 368 0 R 369 0 R 370 0 R 371 0 R 372 0 R 373 0 R 374 0 R ] +/Contents 402 0 R +/Resources 400 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 356 0 R +/Annots [ 404 0 R 405 0 R 406 0 R 407 0 R 408 0 R 409 0 R 410 0 R 411 0 R 412 0 R 413 0 R 414 0 R 415 0 R ] >> endobj -375 0 obj << +404 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -364 0 obj << +405 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [358.228 578.47 374.16 591.372] +/Rect [358.2281 578.47 374.16 591.3716] /Subtype /Link /A << /S /GoTo /D (subsection.3.5) >> >> endobj -365 0 obj << +406 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [352.377 567.648 365.279 576.671] +/Rect [352.377 567.6481 365.2786 576.6709] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -366 0 obj << +407 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [440.607 524.273 448.054 537.175] +/Rect [440.6067 524.2732 448.0537 537.1748] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -367 0 obj << +408 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [446.862 470.683 454.309 482.372] +/Rect [446.8624 470.6825 454.3095 482.372] /Subtype /Link /A << /S /GoTo /D (figure.3) >> >> endobj -368 0 obj << +409 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [470.206 432.156 477.653 441.179] +/Rect [470.2058 432.1561 477.6528 441.179] /Subtype /Link /A << /S /GoTo /D (cite.UMFPACK) >> >> endobj -369 0 obj << +410 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [143.61 362.289 151.057 373.978] +/Rect [143.6103 362.2889 151.0573 373.9784] /Subtype /Link /A << /S /GoTo /D (figure.4) >> >> endobj -370 0 obj << +411 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [264.868 307.486 272.315 320.388] +/Rect [264.8682 307.4861 272.3152 320.3877] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -371 0 obj << +412 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [273.959 307.486 281.406 320.388] +/Rect [273.9591 307.4861 281.4062 320.3877] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -372 0 obj << +413 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [290.496 280.994 297.943 292.683] +/Rect [290.4961 280.9938 297.9432 292.6832] /Subtype /Link /A << /S /GoTo /D (figure.3) >> >> endobj -373 0 obj << +414 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [299.587 280.994 307.034 292.683] +/Rect [299.5871 280.9938 307.0341 292.6832] /Subtype /Link /A << /S /GoTo /D (figure.4) >> >> endobj -374 0 obj << +415 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [182.276 253.895 189.723 265.585] +/Rect [182.276 253.8954 189.7231 265.5849] /Subtype /Link /A << /S /GoTo /D (figure.5) >> >> endobj -379 0 obj << -/D [377 0 R /XYZ 93.6 740.002 null] +403 0 obj << +/D [401 0 R /XYZ 93.6002 740.0018 null] >> endobj -376 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F44 200 0 R /F43 158 0 R >> +400 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F46 219 0 R /F45 147 0 R >> /ProcSet [ /PDF /Text ] >> endobj -385 0 obj << -/Length 3387 +421 0 obj << +/Length 3894 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(18)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(18)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G +1 0 0 1 15.1693 -293.8024 cm 0 g 0 G 0 g 0 G +1 0 0 1 0 287.7141 cm 0 g 0 G 0 g 0 G -/F44 9.9626 Tf -172.181 -30.995 Td [(use)-525(psb_base_mod)]TJ 0 -11.955 Td [(use)-525(mld_prec_mod)]TJ 0 -11.955 Td [(use)-525(psb_krylov_mod)]TJ -10.46 -11.956 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(sparse)-525(matrix)]TJ 10.46 -11.955 Td [(type\050psb_dspmat_type\051)-525(::)-525(A)]TJ -10.46 -11.955 Td [(!)-525(sparse)-525(matrix)-525(descriptor)]TJ 10.46 -11.955 Td [(type\050psb_desc_type\051)-1575(::)-525(desc_A)]TJ -10.46 -11.956 Td [(!)-525(preconditioner)]TJ 10.46 -11.955 Td [(type\050mld_dprec_type\051)-1050(::)-525(P)]TJ -10.46 -11.955 Td [(!)-525(right-hand)-525(side)-525(and)-525(solution)-525(vectors)]TJ 10.46 -11.955 Td [(real\050kind\0501.d0\051\051)-3150(::)-525(b\050:\051,)-525(x\050:\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.956 Td [(!)-525(initialize)-525(the)-525(parallel)-525(environment)]TJ 10.46 -11.955 Td [(call)-525(psb_init\050ictxt\051)]TJ 0 -11.955 Td [(call)-525(psb_info\050ictxt,iam,np\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(read)-525(and)-525(assemble)-525(the)-525(matrix)-525(A)-525(and)-525(the)-525(right-hand)-525(side)-525(b)]TJ 0 -11.956 Td [(!)-525(using)-525(PSBLAS)-525(routines)-525(for)-525(sparse)-525(matrix)-525(/)-525(vector)-525(management)]TJ 0 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(initialize)-525(the)-525(default)-525(multi-level)-525(preconditioner,)-525(i.e.)-525(hybrid)]TJ 0 -11.955 Td [(!)-525(Schwarz,)-525(using)-525(RAS)-525(\050with)-525(overlap)-525(1)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)]TJ 0 -11.956 Td [(!)-525(as)-525(post-smoother)-525(and)-525(4)-525(block-Jacobi)-525(sweeps)-525(\050with)-525(UMFPACK)-525(LU)]TJ 0 -11.955 Td [(!)-525(on)-525(the)-525(blocks\051)-525(as)-525(distributed)-525(coarse-level)-525(solver)]TJ 10.46 -11.955 Td [(call)-525(mld_precinit\050P,'ML',info\051)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(build)-525(the)-525(preconditioner)]TJ 10.46 -11.955 Td [(call)-525(mld_precbld\050A,desc_A,P,info\051)]TJ -10.46 -11.956 Td [(!)]TJ 0 -11.955 Td [(!)-525(set)-525(the)-525(solver)-525(parameters)-525(and)-525(the)-525(initial)-525(guess)]TJ 10.46 -11.955 Td [(...)-525(...)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(solve)-525(Ax=b)-525(with)-525(preconditioned)-525(BiCGSTAB)]TJ 10.46 -11.955 Td [(call)-525(psb_krylov\050'BICGSTAB',A,P,b,x,tol,desc_A,info\051)]TJ 0 -11.956 Td [(...)-525(...)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(deallocate)-525(the)-525(preconditioner)]TJ 10.46 -11.955 Td [(call)-525(mld_precfree\050P,info\051)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(deallocate)-525(other)-525(data)-525(structures)]TJ 10.46 -11.956 Td [(...)-525(...)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(exit)-525(the)-525(parallel)-525(environment)]TJ 10.46 -11.955 Td [(call)-525(psb_exit\050ictxt\051)]TJ 0 -11.955 Td [(stop)]TJ +1 0 0 1 -101.5691 -709.0069 cm +BT +/F46 9.9626 Tf 117.4843 709.0069 Td[(use)-525(psb_base_mod)]TJ 0 -11.9552 Td[(use)-525(mld_prec_mod)]TJ 0 -11.9551 Td[(use)-525(psb_krylov_mod)]TJ -10.4607 -11.9552 Td[(...)-525(...)]TJ 0 -11.9552 Td[(!)]TJ 0 -11.9551 Td[(!)-525(sparse)-525(matrix)]TJ 10.4607 -11.9552 Td[(type\050psb_dspmat_type\051)-525(::)-525(A)]TJ -10.4607 -11.9552 Td[(!)-525(sparse)-525(matrix)-525(descriptor)]TJ 10.4607 -11.9551 Td[(type\050psb_desc_type\051)-1575(::)-525(desc_A)]TJ -10.4607 -11.9552 Td[(!)-525(preconditioner)]TJ 10.4607 -11.9552 Td[(type\050mld_dprec_type\051)-1050(::)-525(P)]TJ -10.4607 -11.9551 Td[(!)-525(right-hand)-525(side)-525(and)-525(solution)-525(vectors)]TJ 10.4607 -11.9552 Td[(real\050kind\0501.d0\051\051)-3150(::)-525(b\050:\051,)-525(x\050:\051)]TJ -10.4607 -11.9552 Td[(...)-525(...)]TJ 0 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(initialize)-525(the)-525(parallel)-525(environment)]TJ 10.4607 -11.9552 Td[(call)-525(psb_init\050ictxt\051)]TJ 0 -11.9551 Td[(call)-525(psb_info\050ictxt,iam,np\051)]TJ -10.4607 -11.9552 Td[(...)-525(...)]TJ 0 -11.9552 Td[(!)]TJ 0 -11.9551 Td[(!)-525(read)-525(and)-525(assemble)-525(the)-525(matrix)-525(A)-525(and)-525(the)-525(right-hand)-525(side)-525(b)]TJ 0 -11.9552 Td[(!)-525(using)-525(PSBLAS)-525(routines)-525(for)-525(sparse)-525(matrix)-525(/)-525(vector)-525(management)]TJ 0 -11.9552 Td[(...)-525(...)]TJ 0 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(initialize)-525(the)-525(default)-525(multi-level)-525(preconditioner,)-525(i.e.)-525(hybrid)]TJ 0 -11.9552 Td[(!)-525(Schwarz,)-525(using)-525(RAS)-525(\050with)-525(overlap)-525(1)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)]TJ 0 -11.9551 Td[(!)-525(as)-525(post-smoother)-525(and)-525(4)-525(block-Jacobi)-525(sweeps)-525(\050with)-525(UMFPACK)-525(LU)]TJ 0 -11.9552 Td[(!)-525(on)-525(the)-525(blocks\051)-525(as)-525(distributed)-525(coarse-level)-525(solver)]TJ 10.4607 -11.9552 Td[(call)-525(mld_precinit\050P,'ML',info\051)]TJ -10.4607 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(build)-525(the)-525(preconditioner)]TJ 10.4607 -11.9552 Td[(call)-525(mld_precbld\050A,desc_A,P,info\051)]TJ -10.4607 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(set)-525(the)-525(solver)-525(parameters)-525(and)-525(the)-525(initial)-525(guess)]TJ 10.4607 -11.9552 Td[(...)-525(...)]TJ -10.4607 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(solve)-525(Ax=b)-525(with)-525(preconditioned)-525(BiCGSTAB)]TJ 10.4607 -11.9552 Td[(call)-525(psb_krylov\050'BICGSTAB',A,P,b,x,tol,desc_A,info\051)]TJ 0 -11.9551 Td[(...)-525(...)]TJ -10.4607 -11.9552 Td[(!)]TJ 0 -11.9552 Td[(!)-525(deallocate)-525(the)-525(preconditioner)]TJ 10.4607 -11.9551 Td[(call)-525(mld_precfree\050P,info\051)]TJ -10.4607 -11.9552 Td[(!)]TJ 0 -11.9552 Td[(!)-525(deallocate)-525(other)-525(data)-525(structures)]TJ 10.4607 -11.9551 Td[(...)-525(...)]TJ -10.4607 -11.9552 Td[(!)]TJ 0 -11.9552 Td[(!)-525(exit)-525(the)-525(parallel)-525(environment)]TJ 10.4607 -11.9551 Td[(call)-525(psb_exit\050ictxt\051)]TJ 0 -11.9552 Td[(stop)]TJ +ET +1 0 0 1 94.4585 114.4103 cm 0 g 0 G -/F15 10.9091 Tf -23.026 -20.749 Td [(Figure)-333(2:)-445(Setup)-333(and)-333(application)-333(of)-334(the)-333(default)-333(m)28(ulti-lev)27(el)-333(Sc)28(h)28(w)27(arz)-333(preconditioner.)]TJ +1 0 0 1 -94.4585 -114.4103 cm +BT +/F15 10.9091 Tf 94.4585 114.4103 Td[(Figu)1(re)-334(2:)-444(S)1(e)-1(tu)1(p)-333(and)-333(ap)1(pl)1(ic)-1(ati)1(on)-333(of)-333(the)-333(defau)1(lt)-333(m)27(ul)1(ti-le)-1(v)28(el)-333(Sc)28(h)28(w)27(ar)1(z)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ +ET +1 0 0 1 490.7922 114.4103 cm 0 g 0 G +1 0 0 1 -404.3924 -14.0764 cm 0 g 0 G +1 0 0 1 0 -8.701 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -384 0 obj << +420 0 obj << /Type /Page -/Contents 385 0 R -/Resources 383 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 320 0 R +/Contents 421 0 R +/Resources 419 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 356 0 R >> endobj -386 0 obj << -/D [384 0 R /XYZ 86.4 740.002 null] +422 0 obj << +/D [420 0 R /XYZ 86.3998 740.0018 null] >> endobj -363 0 obj << -/D [384 0 R /XYZ 142.216 127.96 null] +399 0 obj << +/D [420 0 R /XYZ 142.2161 127.9595 null] >> endobj -383 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F44 200 0 R >> +419 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -390 0 obj << -/Length 3024 +425 0 obj << +/Length 4082 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(5)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(5)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(Getting)-378(St)67(ar)67(ted)]TJ/F15 10.9091 Tf 401.542 0 Td [(19)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Getti)-1(ng)-378(St)67(a)-1(r)67(ted)]TJ/F15 10.9091 Tf 391.3906 0 Td[(19)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -47.8206 cm 0 g 0 G +1 0 0 1 15.1693 -57.1482 cm 0 g 0 G 0 g 0 G +1 0 0 1 0 55.9029 cm 0 g 0 G 0 g 0 G -/F44 9.9626 Tf -380.918 -49.066 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(set)-525(a)-525(three-level)-525(hybrid)-525(Schwarz)-525(preconditioner,)-525(which)-525(uses)]TJ 0 -11.955 Td [(!)-525(block)-525(Jacobi)-525(\050with)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(post-smoother,)]TJ 0 -11.956 Td [(!)-525(a)-525(coarsest)-525(matrix)-525(replicated)-525(on)-525(the)-525(processors,)-525(and)-525(the)]TJ 0 -11.955 Td [(!)-525(LU)-525(factorization)-525(from)-525(UMFPACK)-525(as)-525(coarse-level)-525(solver)]TJ 10.461 -11.955 Td [(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.955 Td [(call_mld_precset\050P,mld_smoother_type_,'BJAC',info\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,mld_coarse_mat_,'REPL',info\051)]TJ 0 -11.956 Td [(call)-525(mld_precset\050P,mld_coarse_solve_,'UMF',info\051)]TJ -10.461 -11.955 Td [(...)-525(...)]TJ +1 0 0 1 -108.7695 -690.9359 cm +BT +/F46 9.9626 Tf 114.224 690.9358 Td[(...)-525(...)]TJ 0 -11.9551 Td[(!)-525(set)-525(a)-525(three-level)-525(hybrid)-525(Schwarz)-525(preconditioner,)-525(which)-525(uses)]TJ 0 -11.9552 Td[(!)-525(block)-525(Jacobi)-525(\050with)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(post-smoother,)]TJ 0 -11.9552 Td[(!)-525(a)-525(coarsest)-525(matrix)-525(replicated)-525(on)-525(the)-525(processors,)-525(and)-525(the)]TJ 0 -11.9551 Td[(!)-525(LU)-525(factorization)-525(from)-525(UMFPACK)-525(as)-525(coarse-level)-525(solver)]TJ 10.4607 -11.9552 Td[(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.9552 Td[(call_mld_precset\050P,mld_smoother_type_,'BJAC',info\051)]TJ 0 -11.9551 Td[(call)-525(mld_precset\050P,mld_coarse_mat_,'REPL',info\051)]TJ 0 -11.9552 Td[(call)-525(mld_precset\050P,mld_coarse_solve_,'UMF',info\051)]TJ -10.4607 -11.9552 Td[(...)-525(...)]TJ +ET +1 0 0 1 149.2044 564.8047 cm 0 g 0 G -/F15 10.9091 Tf 34.98 -18.534 Td [(Figure)-333(3:)-445(Setup)-333(of)-333(a)-334(h)28(ybrid)-333(three-lev)28(el)-334(Sc)28(h)28(w)28(arz)-334(p)1(re)-1(cond)1(itioner.)]TJ +1 0 0 1 -149.2044 -564.8047 cm +BT +/F15 10.9091 Tf 149.2044 564.8047 Td[(Figu)1(re)-334(3:)-444(S)1(e)-1(tu)1(p)-333(of)-333(a)-333(h)28(yb)1(rid)-333(th)1(ree)-1(-lev)28(e)-1(l)-333(S)1(c)27(h)28(w)28(arz)-334(p)1(rec)-1(on)1(diti)1(oner.)]TJ +ET +1 0 0 1 450.4471 564.8047 cm 0 g 0 G +1 0 0 1 -356.8469 -14.0764 cm 0 g 0 G +1 0 0 1 0 -23.9103 cm 0 g 0 G +1 0 0 1 15.1693 -57.1482 cm 0 g 0 G 0 g 0 G +1 0 0 1 0 55.9029 cm 0 g 0 G 0 g 0 G -/F44 9.9626 Tf -34.98 -39.232 Td [(...)-525(...)]TJ 0 -11.956 Td [(!)-525(set)-525(a)-525(three-level)-525(additive)-525(Schwarz)-525(preconditioner,)-525(which)-525(uses)]TJ 0 -11.955 Td [(!)-525(RAS)-525(\050with)-525(overlap)-525(1)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(pre-)-525(and)]TJ 0 -11.955 Td [(!)-525(post-smoother,)-525(and)-525(5)-525(block-Jacobi)-525(sweeps)-525(\050with)-525(UMFPACK)-525(LU)]TJ 0 -11.955 Td [(!)-525(on)-525(the)-525(blocks\051)-525(as)-525(distributed)-525(coarsest-level)-525(solver)]TJ 10.461 -11.955 Td [(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,mld_ml_type_,'ADD',info\051)]TJ 0 -11.956 Td [(call_mld_precset\050P,mld_smoother_pos_,'TWOSIDE',info\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,mld_coarse_sweeps_,5,info\051)]TJ -10.461 -11.955 Td [(...)-525(...)]TJ +1 0 0 1 -108.7695 -525.5727 cm +BT +/F46 9.9626 Tf 114.224 525.5727 Td[(...)-525(...)]TJ 0 -11.9552 Td[(!)-525(set)-525(a)-525(three-level)-525(additive)-525(Schwarz)-525(preconditioner,)-525(which)-525(uses)]TJ 0 -11.9552 Td[(!)-525(RAS)-525(\050with)-525(overlap)-525(1)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(pre-)-525(and)]TJ 0 -11.9551 Td[(!)-525(post-smoother,)-525(and)-525(5)-525(block-Jacobi)-525(sweeps)-525(\050with)-525(UMFPACK)-525(LU)]TJ 0 -11.9552 Td[(!)-525(on)-525(the)-525(blocks\051)-525(as)-525(distributed)-525(coarsest-level)-525(solver)]TJ 10.4607 -11.9552 Td[(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.9551 Td[(call)-525(mld_precset\050P,mld_ml_type_,'ADD',info\051)]TJ 0 -11.9552 Td[(call_mld_precset\050P,mld_smoother_pos_,'TWOSIDE',info\051)]TJ 0 -11.9552 Td[(call)-525(mld_precset\050P,mld_coarse_sweeps_,5,info\051)]TJ -10.4607 -11.9551 Td[(...)-525(...)]TJ +ET +1 0 0 1 142.5529 399.4415 cm 0 g 0 G -/F15 10.9091 Tf 28.329 -18.535 Td [(Figure)-333(4:)-445(Setup)-333(of)-333(an)-333(additiv)27(e)-333(three-lev)28(el)-334(Sc)28(h)28(w)28(arz)-334(p)1(re)-1(cond)1(itioner.)]TJ +1 0 0 1 -142.5529 -399.4415 cm +BT +/F15 10.9091 Tf 142.5529 399.4415 Td[(Figu)1(re)-334(4:)-444(S)1(e)-1(tu)1(p)-333(of)-333(an)-333(ad)1(diti)1(v)28(e)-334(thr)1(e)-1(e-)-1(l)1(e)-1(v)28(el)-333(Sc)27(h)29(w)27(ar)1(z)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r.)]TJ +ET +1 0 0 1 457.0986 399.4415 cm 0 g 0 G +1 0 0 1 -363.4984 -14.0764 cm 0 g 0 G +1 0 0 1 0 -23.9103 cm 0 g 0 G +1 0 0 1 15.1693 -27.2603 cm 0 g 0 G 0 g 0 G +1 0 0 1 0 26.0149 cm 0 g 0 G 0 g 0 G -/F44 9.9626 Tf -28.329 -39.232 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(set)-525(RAS)-525(with)-525(overlap)-525(2)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(local)-525(blocks)]TJ 10.461 -11.955 Td [(call)-525(mld_precinit\050P,'AS',info\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,mld_sub_ovr_,2,info\051)]TJ -10.461 -11.955 Td [(...)-525(...)]TJ +1 0 0 1 -108.7695 -360.2094 cm +BT +/F46 9.9626 Tf 114.224 360.2094 Td[(...)-525(...)]TJ 0 -11.9551 Td[(!)-525(set)-525(RAS)-525(with)-525(overlap)-525(2)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(local)-525(blocks)]TJ 10.4607 -11.9552 Td[(call)-525(mld_precinit\050P,'AS',info\051)]TJ 0 -11.9552 Td[(call)-525(mld_precset\050P,mld_sub_ovr_,2,info\051)]TJ -10.4607 -11.9551 Td[(...)-525(...)]TJ +ET +1 0 0 1 170.4469 293.8541 cm 0 g 0 G -/F15 10.9091 Tf 56.223 -18.535 Td [(Figure)-333(5:)-445(Setup)-333(of)-333(a)-334(on)1(e)-1(-lev)28(el)-333(Sc)28(h)27(w)28(arz)-333(preconditioner.)]TJ +1 0 0 1 -170.4469 -293.8541 cm +BT +/F15 10.9091 Tf 170.4469 293.8541 Td[(Figu)1(re)-334(5:)-444(S)1(e)-1(tu)1(p)-333(of)-333(a)-333(one-)-1(l)1(e)-1(v)28(el)-333(Sc)27(h)29(w)27(arz)-333(precondi)1(tioner.)]TJ +ET +1 0 0 1 429.2047 293.8541 cm 0 g 0 G +1 0 0 1 -335.6045 -14.0764 cm 0 g 0 G +1 0 0 1 0 -188.1447 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -389 0 obj << +424 0 obj << /Type /Page -/Contents 390 0 R -/Resources 388 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 392 0 R -/Annots [ 387 0 R ] +/Contents 425 0 R +/Resources 423 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 428 0 R +/Annots [ 427 0 R ] >> endobj -387 0 obj << +427 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -391 0 obj << -/D [389 0 R /XYZ 93.6 740.002 null] +426 0 obj << +/D [424 0 R /XYZ 93.6002 740.0018 null] >> endobj -380 0 obj << -/D [389 0 R /XYZ 196.962 578.354 null] +416 0 obj << +/D [424 0 R /XYZ 196.962 578.3539 null] >> endobj -381 0 obj << -/D [389 0 R /XYZ 190.311 412.991 null] +417 0 obj << +/D [424 0 R /XYZ 190.3105 412.9907 null] >> endobj -382 0 obj << -/D [389 0 R /XYZ 218.204 307.403 null] +418 0 obj << +/D [424 0 R /XYZ 218.2045 307.4033 null] >> endobj -388 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F44 200 0 R >> +423 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -396 0 obj << -/Length 6908 +431 0 obj << +/Length 8713 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(20)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(20)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -203.265 -35.866 Td [(6)-1125(User)-375(In)31(terface)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)-396(basic)-396(user)-396(in)28(terface)-397(of)-396(MLD2P4)-396(consists)-396(of)-396(six)-396(routines.)-633(The)-396(four)-396(routines)]TJ/F44 10.9091 Tf 389.542 0 Td [(mld_)]TJ -389.542 -13.549 Td [(precinit)]TJ/F15 10.9091 Tf 45.817 0 Td [(,)]TJ/F44 10.9091 Tf 6.096 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 62.999 0 Td [(,)]TJ/F44 10.9091 Tf 6.096 0 Td [(mld_precbld)]TJ/F15 10.9091 Tf 65.922 0 Td [(and)]TJ/F44 10.9091 Tf 20.498 0 Td [(mld_precaply)]TJ/F15 10.9091 Tf 71.649 0 Td [(encapsulate)-268(all)-268(the)-268(function-)]TJ -279.077 -13.549 Td [(alities)-323(for)-322(the)-323(setup)-323(an)1(d)-323(the)-323(application)-322(of)-323(an)28(y)-323(one-lev)28(el)-323(and)-322(m)28(ulti-lev)27(el)-322(preconditioner)]TJ 0 -13.549 Td [(implemen)28(ted)-293(in)-292(the)-293(pac)28(k)55(age.)-431(The)-292(routine)]TJ/F44 10.9091 Tf 198.571 0 Td [(mld_precfree)]TJ/F15 10.9091 Tf 71.919 0 Td [(deallo)-28(cates)-293(th)1(e)-293(preconditioner)]TJ -270.49 -13.55 Td [(data)-387(structure,)-401(while)]TJ/F44 10.9091 Tf 105.072 0 Td [(mld_precdescr)]TJ/F15 10.9091 Tf 78.681 0 Td [(prin)28(ts)-388(a)-387(description)-388(of)-387(the)-388(p)1(re)-1(cond)1(itioner)-388(setup)]TJ -183.753 -13.549 Td [(b)28(y)-333(the)-334(user.)]TJ 16.936 -13.549 Td [(F)83(or)-222(eac)28(h)-222(routine,)-245(the)-222(same)-222(user)-222(in)27(terface)-222(is)-222(o)28(v)27(erloaded)-222(with)-222(resp)-28(ect)-222(to)-222(the)-222(real/complex)]TJ -16.936 -13.549 Td [(case)-371(and)-371(t)1(he)-371(single/double)-371(precision;)-389(argumen)28(ts)-371(with)-371(appropriate)-370(data)-371(t)28(yp)-28(es)-371(m)28(ust)-371(b)-28(e)]TJ 0 -13.549 Td [(passed)-333(to)-334(the)-333(routine,)-333(i.e.)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F19 14.3462 Tf 86.3998 704.1363 Td[(6)-1125(User)-376(In)32(t)-1(er)-1(f)1(ace)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(The)-396(basic)-397(u)1(s)-1(er)-396(in)29(te)-1(r)1(face)-397(of)-396(M)1(LD2P4)-396(consists)-397(of)-396(six)-396(r)1(outin)1(e)-1(s.)-632(T)-1(h)1(e)-397(f)1(our)-396(r)1(outin)1(e)-1(s)]TJ/F46 10.9091 Tf 389.5423 0 Td[(mld_)]TJ -389.5423 -13.5492 Td[(precinit)]TJ/F15 10.9091 Tf 45.8177 0 Td[(,)]TJ/F46 10.9091 Tf 6.0956 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(,)]TJ/F46 10.9091 Tf 6.0956 0 Td[(mld_precbld)]TJ/F15 10.9091 Tf 65.9218 0 Td[(and)]TJ/F46 10.9091 Tf 20.4983 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 71.649 0 Td[(encapsulate)-268(all)-267(the)-268(fu)1(nction-)]TJ -279.0773 -13.5492 Td[(alit)1(ie)-1(s)-323(f)1(or)-323(th)1(e)-323(s)-1(etup)-322(an)1(d)-323(t)1(he)-323(app)1(lication)-322(of)-322(an)28(y)-322(one-)-1(lev)28(el)-323(an)1(d)-323(m)28(ult)1(i-)-1(l)1(e)-1(v)28(el)-323(p)1(rec)-1(on)1(diti)1(oner)]TJ 0 -13.5492 Td[(impl)1(e)-1(me)-1(n)29(te)-1(d)-292(in)-292(th)1(e)-293(pac)27(k)56(age.)-431(The)-293(rou)1(tin)1(e)]TJ/F46 10.9091 Tf 198.5716 0 Td[(mld_precfree)]TJ/F15 10.9091 Tf 71.9188 0 Td[(deallo)-27(c)-1(ates)-293(the)-293(p)1(rec)-1(on)1(diti)1(oner)]TJ -270.4904 -13.5492 Td[(dat)1(a)-388(structu)1(re)-1(,)-400(w)-1(h)1(ile)]TJ/F46 10.9091 Tf 105.0723 0 Td[(mld_precdescr)]TJ/F15 10.9091 Tf 78.6811 0 Td[(pr)1(in)28(ts)-388(a)-387(des)-1(cri)1(ption)-387(of)-387(th)1(e)-388(pr)1(e)-1(cond)1(ition)1(e)-1(r)-387(s)-1(etu)1(p)]TJ -183.7534 -13.5492 Td[(b)28(y)-333(th)1(e)-334(use)-1(r)1(.)]TJ 16.9365 -13.5492 Td[(F)84(or)-222(e)-1(ac)28(h)-222(rou)1(tine,)-244(the)-222(s)-1(ame)-223(u)1(s)-1(er)-222(in)28(terf)1(ac)-1(e)-222(is)-223(o)28(v)28(e)-1(r)1(loaded)-222(with)-221(re)-1(sp)-27(e)-1(ct)-222(to)-222(the)-223(r)1(e)-1(al)1(/c)-1(omplex)]TJ -16.9365 -13.5492 Td[(cas)-1(e)-371(and)-370(th)1(e)-372(sin)1(gle)-1(/d)1(oub)1(le)-371(pr)1(e)-1(cis)-1(i)1(on;)-389(argu)1(m)-1(en)28(ts)-371(with)-370(app)1(rop)1(riate)-371(dat)1(a)-371(t)28(yp)-27(e)-1(s)-371(m)27(u)1(s)-1(t)-370(b)-28(e)]TJ 0 -13.5492 Td[(passe)-1(d)-333(to)-333(th)1(e)-334(rou)1(tine,)-333(i.e.)]TJ +ET +1 0 0 1 86.3998 548.875 cm 0 g 0 G -/F25 10.9091 Tf 16.363 -22.516 Td [(\017)]TJ +1 0 0 1 -86.3998 -548.875 cm +BT +/F27 10.9091 Tf 102.7635 548.875 Td[(\017)]TJ +ET +1 0 0 1 108.218 548.875 cm 0 g 0 G -/F15 10.9091 Tf 10.91 0 Td [(the)-463(sparse)-463(matrix)-463(data)-463(structure,)-496(con)28(taining)-463(the)-463(matrix)-463(to)-463(b)-28(e)-463(preconditioned,)]TJ 0 -13.549 Td [(m)28(ust)-424(b)-28(e)-424(of)-423(t)27(yp)-27(e)]TJ/F44 10.9091 Tf 82.797 0 Td [(mld_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(spmat_type)]TJ/F15 10.9091 Tf 61.896 0 Td [(with)]TJ/F18 10.9091 Tf 25.836 0 Td [(x)]TJ/F15 10.9091 Tf 10.998 0 Td [(=)]TJ/F44 10.9091 Tf 13.108 0 Td [(s)]TJ/F15 10.9091 Tf 10.351 0 Td [(for)-424(real)-424(single)-423(precision,)]TJ/F18 10.9091 Tf 121.075 0 Td [(x)]TJ/F15 10.9091 Tf 10.998 0 Td [(=)]TJ/F44 10.9091 Tf 13.109 0 Td [(d)]TJ/F15 10.9091 Tf -379.451 -13.549 Td [(for)-371(real)-371(double)-371(precision,)]TJ/F18 10.9091 Tf 123.413 0 Td [(x)]TJ/F15 10.9091 Tf 10.421 0 Td [(=)]TJ/F44 10.9091 Tf 12.532 0 Td [(c)]TJ/F15 10.9091 Tf 9.775 0 Td [(for)-371(complex)-371(single)-371(precision,)]TJ/F18 10.9091 Tf 140.11 0 Td [(x)]TJ/F15 10.9091 Tf 10.421 0 Td [(=)]TJ/F44 10.9091 Tf 12.533 0 Td [(z)]TJ/F15 10.9091 Tf 9.774 0 Td [(for)-371(complex)]TJ -328.979 -13.55 Td [(double)-333(precision;)]TJ +1 0 0 1 -108.218 -548.875 cm +BT +/F15 10.9091 Tf 113.6726 548.875 Td[(th)1(e)-464(sparse)-464(matri)1(x)-463(data)-463(stru)1(c)-1(tu)1(re,)-496(con)28(tain)1(in)1(g)-464(t)1(he)-464(matr)1(ix)-463(to)-463(b)-27(e)-464(pr)1(e)-1(cond)1(ition)1(e)-1(d)1(,)]TJ 0 -13.5492 Td[(m)27(u)1(s)-1(t)-423(b)-28(e)-424(of)-423(t)28(yp)-28(e)]TJ/F46 10.9091 Tf 82.7978 0 Td[(mld_)]TJ/F20 10.9091 Tf 22.9088 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(spmat_type)]TJ/F15 10.9091 Tf 61.8958 0 Td[(with)]TJ/F20 10.9091 Tf 25.8358 0 Td[(x)]TJ/F15 10.9091 Tf 10.9979 0 Td[(=)]TJ/F46 10.9091 Tf 13.1085 0 Td[(s)]TJ/F15 10.9091 Tf 10.3509 0 Td[(for)-423(real)-424(singl)1(e)-425(p)1(rec)-1(ision)1(,)]TJ/F20 10.9091 Tf 121.0749 0 Td[(x)]TJ/F15 10.9091 Tf 10.9979 0 Td[(=)]TJ/F46 10.9091 Tf 13.1085 0 Td[(d)]TJ/F15 10.9091 Tf -379.4511 -13.5492 Td[(for)-370(real)-371(dou)1(ble)-371(pr)1(e)-1(cision,)]TJ/F20 10.9091 Tf 123.4131 0 Td[(x)]TJ/F15 10.9091 Tf 10.4215 0 Td[(=)]TJ/F46 10.9091 Tf 12.5322 0 Td[(c)]TJ/F15 10.9091 Tf 9.7744 0 Td[(for)-370(c)-1(ompl)1(e)-1(x)-371(sin)1(gle)-372(p)1(rec)-1(i)1(s)-1(ion)1(,)]TJ/F20 10.9091 Tf 140.1102 0 Td[(x)]TJ/F15 10.9091 Tf 10.4214 0 Td[(=)]TJ/F46 10.9091 Tf 12.5322 0 Td[(z)]TJ/F15 10.9091 Tf 9.7745 0 Td[(for)-370(c)-1(ompl)1(e)-1(x)]TJ -328.9795 -13.5492 Td[(dou)1(bl)1(e)-334(pr)1(e)-1(cis)-1(i)1(on;)]TJ +ET +1 0 0 1 86.3998 485.7118 cm 0 g 0 G -/F25 10.9091 Tf -10.91 -22.515 Td [(\017)]TJ +1 0 0 1 -86.3998 -485.7118 cm +BT +/F27 10.9091 Tf 102.7635 485.7118 Td[(\017)]TJ +ET +1 0 0 1 108.218 485.7118 cm 0 g 0 G -/F15 10.9091 Tf 10.91 0 Td [(the)-337(preconditioner)-337(data)-337(structure)-337(m)28(ust)-337(b)-28(e)-337(of)-337(t)28(yp)-28(e)]TJ/F44 10.9091 Tf 241.775 0 Td [(mld_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(prec_type)]TJ/F15 10.9091 Tf 51.545 0 Td [(,)-338(with)]TJ/F18 10.9091 Tf 31.605 0 Td [(x)]TJ/F15 10.9091 Tf 10.051 0 Td [(=)]TJ/F44 10.9091 Tf 12.161 0 Td [(s)]TJ/F15 10.9091 Tf 5.728 0 Td [(,)]TJ/F44 10.9091 Tf -382.148 -13.549 Td [(d)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F44 10.9091 Tf 6.666 0 Td [(c)]TJ/F15 10.9091 Tf 5.728 0 Td [(,)]TJ/F44 10.9091 Tf 6.666 0 Td [(z)]TJ/F15 10.9091 Tf 5.728 0 Td [(,)-333(according)-334(to)-333(the)-333(sparse)-334(matrix)-333(data)-333(structure;)]TJ +1 0 0 1 -108.218 -485.7118 cm +BT +/F15 10.9091 Tf 113.6726 485.7118 Td[(th)1(e)-338(p)1(re)-1(cond)1(ition)1(e)-1(r)-336(data)-337(stru)1(c)-1(tu)1(re)-337(m)27(u)1(s)-1(t)-337(b)-27(e)-338(of)-336(t)28(yp)-27(e)]TJ/F46 10.9091 Tf 241.7755 0 Td[(mld_)]TJ/F20 10.9091 Tf 22.9088 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(prec_type)]TJ/F15 10.9091 Tf 51.5449 0 Td[(,)-338(with)]TJ/F20 10.9091 Tf 31.6054 0 Td[(x)]TJ/F15 10.9091 Tf 10.0506 0 Td[(=)]TJ/F46 10.9091 Tf 12.1613 0 Td[(s)]TJ/F15 10.9091 Tf 5.7273 0 Td[(,)]TJ/F46 10.9091 Tf -382.148 -13.5492 Td[(d)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F46 10.9091 Tf 6.6667 0 Td[(c)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F46 10.9091 Tf 6.6666 0 Td[(z)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)-333(ac)-1(cord)1(ing)-333(to)-333(the)-333(s)-1(p)1(arse)-334(m)-1(at)1(rix)-333(dat)1(a)-334(stru)1(c)-1(tu)1(re;)]TJ +ET +1 0 0 1 86.3998 449.647 cm 0 g 0 G -/F25 10.9091 Tf -41.425 -22.516 Td [(\017)]TJ +1 0 0 1 -86.3998 -449.647 cm +BT +/F27 10.9091 Tf 102.7635 449.647 Td[(\017)]TJ +ET +1 0 0 1 108.218 449.647 cm 0 g 0 G -/F15 10.9091 Tf 10.91 0 Td [(the)-321(arra)28(ys)-321(con)27(t)1(aining)-321(the)-322(v)28(ectors)]TJ/F22 10.9091 Tf 159.846 0 Td [(v)]TJ/F15 10.9091 Tf 9.182 0 Td [(and)]TJ/F22 10.9091 Tf 21.078 0 Td [(w)]TJ/F15 10.9091 Tf 11.607 0 Td [(in)28(v)28(olv)27(ed)-321(in)-321(the)-321(precondition)1(e)-1(r)-321(app)1(lica-)]TJ -201.713 -13.549 Td [(tion)]TJ/F22 10.9091 Tf 21.315 0 Td [(w)]TJ/F15 10.9091 Tf 11.134 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.733 -3.959 Td [(v)]TJ/F15 10.9091 Tf 8.206 0 Td [(m)28(ust)-232(b)-28(e)-231(of)-232(t)28(yp)-28(e)]TJ/F18 10.9091 Tf 74.414 0 Td [(typ)51(e)]TJ/F44 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ +1 0 0 1 -108.218 -449.647 cm +BT +/F15 10.9091 Tf 113.6726 449.647 Td[(th)1(e)-322(arr)1(a)27(y)1(s)-322(con)28(tain)1(ing)-321(th)1(e)-322(v)28(ec)-1(t)1(ors)]TJ/F24 10.9091 Tf 159.8466 0 Td[(v)]TJ/F15 10.9091 Tf 9.1819 0 Td[(and)]TJ/F24 10.9091 Tf 21.0784 0 Td[(w)]TJ/F15 10.9091 Tf 11.6062 0 Td[(in)28(v)28(ol)1(v)28(e)-1(d)-320(in)-321(th)1(e)-322(p)1(rec)-1(on)1(diti)1(oner)-321(app)1(lica-)]TJ -201.7131 -13.5492 Td[(tion)]TJ/F24 10.9091 Tf 21.3155 0 Td[(w)]TJ/F15 10.9091 Tf 11.1338 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(v)]TJ/F15 10.9091 Tf 8.2069 0 Td[(m)27(u)1(s)-1(t)-231(b)-27(e)-233(of)-231(t)28(yp)-27(e)]TJ/F20 10.9091 Tf 74.4135 0 Td[(typ)51(e)]TJ/F46 10.9091 Tf 19.7771 0 Td[(\050)]TJ/F20 10.9091 Tf 5.7272 0 Td[(kind)]TJ ET +1 0 0 1 309.5948 436.0978 cm q -1 0 0 1 309.595 436.297 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -309.5948 -436.0978 cm BT -/F18 10.9091 Tf 312.94 436.098 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-252(with)]TJ/F18 10.9091 Tf 29.52 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 22.304 0 Td [(=)]TJ/F44 10.9091 Tf 11.013 0 Td [(real)]TJ/F15 10.9091 Tf 22.909 0 Td [(,)]TJ/F44 10.9091 Tf 5.779 0 Td [(complex)]TJ/F15 10.9091 Tf -345.087 -13.549 Td [(and)]TJ/F18 10.9091 Tf 21.391 0 Td [(kind)]TJ +/F20 10.9091 Tf 312.9403 436.0978 Td[(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.5678 0 Td[(\051)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)-252(with)]TJ/F20 10.9091 Tf 29.5194 0 Td[(typ)51(e)]TJ/F15 10.9091 Tf 22.3047 0 Td[(=)]TJ/F46 10.9091 Tf 11.0125 0 Td[(real)]TJ/F15 10.9091 Tf 22.9088 0 Td[(,)]TJ/F46 10.9091 Tf 5.7797 0 Td[(complex)]TJ/F15 10.9091 Tf -345.0879 -13.5492 Td[(and)]TJ/F20 10.9091 Tf 21.3918 0 Td[(kind)]TJ ET +1 0 0 1 155.8059 422.5487 cm q -1 0 0 1 155.806 422.748 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -155.8059 -422.5487 cm BT -/F18 10.9091 Tf 159.151 422.549 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 52.384 0 Td [(=)]TJ/F44 10.9091 Tf 12.301 0 Td [(kind\0501.e0\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(,)]TJ/F44 10.9091 Tf 6.891 0 Td [(kind\0501.d0\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(,)-354(according)-350(to)-349(the)-350(sparse)-350(matrix)]TJ -231.598 -13.55 Td [(and)-305(preconditioner)-305(data)-305(structure;)-314(note)-306(t)1(hat)-306(th)1(e)-306(PSBLAS)-305(mo)-27(dule)]TJ/F44 10.9091 Tf 316.451 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf -316.451 -13.549 Td [(pro)28(vides)-333(the)-334(constan)28(ts)]TJ/F44 10.9091 Tf 110.212 0 Td [(psb_spk_)]TJ/F15 10.9091 Tf 49.454 0 Td [(=)]TJ/F44 10.9091 Tf 12.121 0 Td [(kind\0501.e0\051)]TJ/F15 10.9091 Tf 60.908 0 Td [(and)]TJ/F44 10.9091 Tf 21.213 0 Td [(psb_dpk_)]TJ/F15 10.9091 Tf 49.454 0 Td [(=)]TJ/F44 10.9091 Tf 12.121 0 Td [(kind\0501.d0\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(;)]TJ +/F20 10.9091 Tf 159.1514 422.5487 Td[(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 52.3838 0 Td[(=)]TJ/F46 10.9091 Tf 12.3008 0 Td[(kind\0501.e0\051)]TJ/F15 10.9091 Tf 57.2721 0 Td[(,)]TJ/F46 10.9091 Tf 6.8912 0 Td[(kind\0501.d0\051)]TJ/F15 10.9091 Tf 57.2721 0 Td[(,)-354(acc)-1(or)1(din)1(g)-350(to)-350(th)1(e)-350(s)-1(p)1(arse)-351(matri)1(x)]TJ -231.5989 -13.5492 Td[(and)-304(pr)1(e)-1(cond)1(ition)1(e)-1(r)-305(d)1(ata)-305(s)-1(tr)1(uctur)1(e)-1(;)-314(note)-305(th)1(at)-305(the)-305(PSBLAS)-305(mo)-28(d)1(ule)]TJ/F46 10.9091 Tf 316.4518 0 Td[(psb_base_mod)]TJ/F15 10.9091 Tf -316.4518 -13.5492 Td[(pr)1(o)28(vides)-334(th)1(e)-334(constan)28(ts)]TJ/F46 10.9091 Tf 110.2123 0 Td[(psb_spk_)]TJ/F15 10.9091 Tf 49.454 0 Td[(=)]TJ/F46 10.9091 Tf 12.1212 0 Td[(kind\0501.e0\051)]TJ/F15 10.9091 Tf 60.9085 0 Td[(and)]TJ/F46 10.9091 Tf 21.2121 0 Td[(psb_dpk_)]TJ/F15 10.9091 Tf 49.4541 0 Td[(=)]TJ/F46 10.9091 Tf 12.1212 0 Td[(kind\0501.d0\051)]TJ/F15 10.9091 Tf 57.2721 0 Td[(;)]TJ +ET +1 0 0 1 86.3998 372.9347 cm 0 g 0 G -/F25 10.9091 Tf -383.665 -22.515 Td [(\017)]TJ +1 0 0 1 -86.3998 -372.9347 cm +BT +/F27 10.9091 Tf 102.7635 372.9347 Td[(\017)]TJ +ET +1 0 0 1 108.218 372.9347 cm 0 g 0 G -/F15 10.9091 Tf 10.91 0 Td [(real)-450(parameters)-450(de\014ning)-450(the)-450(preconditioner)-450(m)28(ust)-450(b)-27(e)-450(dec)-1(l)1(are)-1(d)-449(acc)-1(or)1(ding)-450(to)-450(the)]TJ 0 -13.549 Td [(precision)-245(of)-246(the)-245(sparse)-246(matrix)-245(and)-245(preconditioner)-246(data)-245(structures)-245(\050see)-246(Section)]TJ +1 0 0 1 -108.218 -372.9347 cm +BT +/F15 10.9091 Tf 113.6726 372.9347 Td[(real)-450(p)1(arame)-1(ters)-450(de\014n)1(ing)-450(th)1(e)-451(p)1(rec)-1(on)1(dit)1(ioner)-450(m)28(ust)-450(b)-28(e)-450(declared)-450(acc)-1(or)1(din)1(g)-450(to)-450(the)]TJ 0 -13.5492 Td[(pr)1(e)-1(cision)-245(of)-245(the)-245(s)-1(p)1(arse)-246(m)-1(atr)1(ix)-245(and)-245(p)1(rec)-1(on)1(diti)1(oner)-246(d)1(ata)-245(s)-1(tr)1(uctures)-246(\050se)-1(e)-245(Sec)-1(tion)]TJ +ET +1 0 0 1 477.6387 359.3855 cm 0 0 1 rg 0 0 1 RG - [-245(6.2)]TJ +1 0 0 1 -477.6387 -359.3855 cm +BT +/F15 10.9091 Tf 477.6387 359.3855 Td[(6.2)]TJ +ET +1 0 0 1 491.5781 359.3855 cm 0 g 0 G - [(\051.)]TJ -27.273 -22.516 Td [(A)-333(description)-334(of)-333(eac)28(h)-333(routine)-334(is)-333(giv)28(en)-334(in)-333(the)-333(remainder)-333(of)-334(this)-333(section.)]TJ +1 0 0 1 -491.5781 -359.3855 cm +BT +/F15 10.9091 Tf 491.5781 359.3855 Td[(\051.)]TJ -405.1783 -22.5156 Td[(A)-333(des)-1(crip)1(tion)-333(of)-333(eac)27(h)-333(r)1(outin)1(e)-334(is)-333(giv)28(e)-1(n)-333(i)1(n)-333(the)-333(re)-1(main)1(der)-333(of)-333(thi)1(s)-334(s)-1(ection.)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -395 0 obj << +430 0 obj << /Type /Page -/Contents 396 0 R -/Resources 394 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 392 0 R -/Annots [ 393 0 R ] +/Contents 431 0 R +/Resources 429 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 428 0 R +/Annots [ 433 0 R ] >> endobj -393 0 obj << +433 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [476.642 355.662 492.574 368.564] +/Rect [476.6425 355.662 492.5744 368.5636] /Subtype /Link /A << /S /GoTo /D (subsection.6.2) >> >> endobj -397 0 obj << -/D [395 0 R /XYZ 86.4 740.002 null] +432 0 obj << +/D [430 0 R /XYZ 86.3998 740.0018 null] >> endobj 66 0 obj << -/D [395 0 R /XYZ 86.4 715.095 null] +/D [430 0 R /XYZ 86.3998 715.0952 null] >> endobj -394 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F17 111 0 R /F44 200 0 R /F25 176 0 R /F18 173 0 R /F22 175 0 R /F26 272 0 R /F20 273 0 R >> +429 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F19 113 0 R /F46 219 0 R /F27 189 0 R /F20 181 0 R /F24 186 0 R /F28 293 0 R /F22 296 0 R >> /ProcSet [ /PDF /Text ] >> endobj -403 0 obj << -/Length 3089 +436 0 obj << +/Length 4242 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(6)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(21)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(21)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.1)-1125(Subroutine)-375(mld)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 11.9552 Tf 93.6002 704.1363 Td[(6.)-1(1)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ ET +1 0 0 1 216.6225 704.1363 cm q -1 0 0 1 216.622 704.336 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -216.6225 -704.1363 cm BT -/F17 11.9552 Tf 220.657 704.136 Td [(precinit)]TJ +/F19 11.9552 Tf 220.6574 704.1363 Td[(pre)-1(cini)-1(t)]TJ +ET +1 0 0 1 219.9175 683.5417 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf 4.715 -20.594 Td [(mld_precinit\050p,ptype,info\051)]TJ -14.318 -13.549 Td [(mld_precinit\050p,ptype,info,nlev\051)]TJ/F15 10.9091 Tf -117.454 -25.505 Td [(This)-268(routine)-268(allo)-28(cates)-268(and)-269(initi)1(alize)-1(s)-268(the)-268(preconditioner)-268(data)-268(structure,)-281(ac)-1(cord)1(ing)-269(to)-268(the)]TJ 0 -13.549 Td [(preconditioner)-333(t)28(yp)-28(e)-333(c)27(hosen)-333(b)28(y)-334(the)-333(user.)]TJ/F17 11.9552 Tf 0 -40.648 Td [(Argumen)31(ts)]TJ/F44 10.9091 Tf 22.914 -12.805 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.18 0 Td [(.)]TJ -201.099 -13.549 Td [(The)-478(preconditioner)-478(data)-478(structure.)-878(Note)-478(that)]TJ/F18 10.9091 Tf 233.108 0 Td [(x)]TJ/F15 10.9091 Tf 11.589 0 Td [(m)28(ust)-478(b)-28(e)-478(c)28(hosen)-478(ac-)]TJ -244.697 -13.549 Td [(cording)-269(to)-269(the)-270(real/complex,)-282(single/double)-269(precision)-269(v)27(ersion)-269(of)-269(MLD2P4)]TJ 0 -13.549 Td [(under)-333(use.)]TJ/F44 10.9091 Tf -45.971 -13.55 Td [(ptype)-1589(character\050len=*\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 206.333 0 Td [(.)]TJ -160.362 -13.549 Td [(The)-333(t)27(yp)-27(e)-334(of)-333(preconditioner.)-444(Its)-334(v)56(alues)-333(are)-334(sp)-28(eci\014ed)-333(in)-333(T)83(able)]TJ +1 0 0 1 -219.9175 -683.5417 cm +BT +/F46 10.9091 Tf 225.372 683.5417 Td[(mld_precinit\050p,ptype,info\051)]TJ -14.318 -13.5492 Td[(mld_precinit\050p,ptype,info,nlev\051)]TJ/F15 10.9091 Tf -117.4538 -25.5044 Td[(This)-268(rou)1(tine)-268(allo)-28(cates)-269(and)-267(init)1(ialize)-1(s)-268(the)-269(p)1(rec)-1(on)1(dit)1(ioner)-268(data)-268(stru)1(c)-1(tu)1(re,)-281(ac)-1(cord)1(ing)-268(to)-268(the)]TJ 0 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-333(t)28(yp)-27(e)-334(c)28(hose)-1(n)-333(b)29(y)-334(t)1(he)-334(u)1(s)-1(er.)]TJ/F19 11.9552 Tf 0 -40.6476 Td[(Arg)-1(umen)31(t)-1(s)]TJ/F46 10.9091 Tf 22.9141 -12.8052 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-478(pr)1(e)-1(cond)1(ition)1(e)-1(r)-478(d)1(ata)-478(stru)1(c)-1(tu)1(re.)-879(Note)-478(th)1(at)]TJ/F20 10.9091 Tf 233.1081 0 Td[(x)]TJ/F15 10.9091 Tf 11.5884 0 Td[(m)27(u)1(s)-1(t)-477(b)-28(e)-478(c)27(h)1(os)-1(en)-478(ac-)]TJ -244.6965 -13.5492 Td[(cordi)1(ng)-269(to)-269(the)-270(r)1(e)-1(al/complex,)-282(singl)1(e)-1(/d)1(oub)1(le)-270(pr)1(e)-1(cision)-269(v)28(ers)-1(i)1(on)-269(of)-269(MLD2P)1(4)]TJ 0 -13.5492 Td[(un)1(der)-333(use)-1(.)]TJ/F46 10.9091 Tf -45.9708 -13.5492 Td[(ptype)-1589(character\050len=*\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 206.3327 0 Td[(.)]TJ -160.3619 -13.5492 Td[(The)-334(t)28(y)1(p)-28(e)-334(of)-332(prec)-1(on)1(di)1(tioner.)-444(Its)-334(v)56(alu)1(e)-1(s)-334(ar)1(e)-334(sp)-28(ec)-1(i)1(\014ed)-333(in)-333(T)83(ab)1(le)]TJ +ET +1 0 0 1 451.849 509.7402 cm 0 0 1 rg 0 0 1 RG - [-333(1)]TJ +1 0 0 1 -451.849 -509.7402 cm +BT +/F15 10.9091 Tf 451.849 509.7402 Td[(1)]TJ +ET +1 0 0 1 457.3035 509.7402 cm 0 g 0 G - [(.)]TJ 0 -13.549 Td [(Note)-333(that)-334(the)-333(strings)-333(are)-334(case)-333(insensitiv)28(e.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ +1 0 0 1 -457.3035 -509.7402 cm +BT +/F15 10.9091 Tf 457.3035 509.7402 Td[(.)]TJ -294.8184 -13.5492 Td[(Note)-334(th)1(at)-333(the)-334(stri)1(ngs)-334(ar)1(e)-334(c)-1(ase)-334(in)1(s)-1(ensiti)1(v)28(e)-1(.)]TJ/F46 10.9091 Tf -45.9708 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-333(co)-28(de.)-444(If)-333(no)-333(e)-1(r)1(ror,)-333(0)-333(is)-334(r)1(e)-1(tu)1(rn)1(e)-1(d)1(.)-445(S)1(e)-1(e)-333(Sec)-1(tion)]TJ +ET +1 0 0 1 403.2429 469.0926 cm 0 0 1 rg 0 0 1 RG - [-333(7)]TJ +1 0 0 1 -403.2429 -469.0926 cm +BT +/F15 10.9091 Tf 403.2429 469.0926 Td[(7)]TJ +ET +1 0 0 1 408.6974 469.0926 cm 0 g 0 G - [-333(for)-334(details.)]TJ/F44 10.9091 Tf -45.971 -13.55 Td [(nlev)-2114(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(The)-436(n)27(um)28(b)-28(er)-436(of)-436(lev)28(els)-437(of)-436(the)-437(m)28(ultilev)28(el)-436(preconditioner.)-754(If)]TJ/F44 10.9091 Tf 284.637 0 Td [(nlev)]TJ/F15 10.9091 Tf 27.669 0 Td [(is)-436(not)]TJ -312.306 -13.549 Td [(presen)28(t)-418(and)]TJ/F44 10.9091 Tf 61.016 0 Td [(ptype)]TJ/F15 10.9091 Tf 28.636 0 Td [(=)]TJ/F44 10.9091 Tf 8.485 0 Td [('ML')]TJ/F15 10.9091 Tf 22.909 0 Td [(,)]TJ/F44 10.9091 Tf 7.584 0 Td [('ml')]TJ/F15 10.9091 Tf 22.909 0 Td [(,)-438(then)]TJ/F44 10.9091 Tf 33.578 0 Td [(nlev)]TJ/F15 10.9091 Tf 22.909 0 Td [(=2)-417(is)-418(assumed.)-697(Oth)1(e)-1(r)1(w)-1(i)1(s)-1(e,)]TJ/F44 10.9091 Tf -208.026 -13.549 Td [(nlev)]TJ/F15 10.9091 Tf 26.545 0 Td [(is)-333(ignored.)]TJ +1 0 0 1 -408.6974 -469.0926 cm +BT +/F15 10.9091 Tf 412.3338 469.0926 Td[(for)-333(d)1(e)-1(t)1(ails.)]TJ/F46 10.9091 Tf -295.8195 -13.5492 Td[(nlev)-2114(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.0599 0 Td[(.)]TJ -166.0891 -13.5492 Td[(The)-437(n)29(um)28(b)-28(er)-436(of)-436(lev)28(e)-1(ls)-436(of)-436(the)-437(m)28(ult)1(ilev)28(e)-1(l)-436(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)-754(If)]TJ/F46 10.9091 Tf 284.637 0 Td[(nlev)]TJ/F15 10.9091 Tf 27.6692 0 Td[(is)-437(n)1(ot)]TJ -312.3062 -13.5492 Td[(pr)1(e)-1(se)-1(n)29(t)-418(an)1(d)]TJ/F46 10.9091 Tf 61.0162 0 Td[(ptype)]TJ/F15 10.9091 Tf 28.636 0 Td[(=)]TJ/F46 10.9091 Tf 8.4849 0 Td[('ML')]TJ/F15 10.9091 Tf 22.9088 0 Td[(,)]TJ/F46 10.9091 Tf 7.5838 0 Td[('ml')]TJ/F15 10.9091 Tf 22.9089 0 Td[(,)-438(then)]TJ/F46 10.9091 Tf 33.5787 0 Td[(nlev)]TJ/F15 10.9091 Tf 22.9089 0 Td[(=2)-417(is)-418(ass)-1(u)1(m)-1(ed.)-696(Oth)1(e)-1(r)1(w)-1(i)1(s)-1(e,)]TJ/F46 10.9091 Tf -208.0262 -13.5492 Td[(nlev)]TJ/F15 10.9091 Tf 26.5452 0 Td[(is)-334(i)1(gnored.)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -402 0 obj << +435 0 obj << /Type /Page -/Contents 403 0 R -/Resources 401 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 392 0 R -/Annots [ 400 0 R 398 0 R 399 0 R ] +/Contents 436 0 R +/Resources 434 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 428 0 R +/Annots [ 438 0 R 439 0 R 440 0 R ] >> endobj -400 0 obj << +438 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -398 0 obj << +439 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [450.853 504.679 458.3 518.312] +/Rect [450.8527 504.6791 458.2998 518.3122] /Subtype /Link /A << /S /GoTo /D (table.1) >> >> endobj -399 0 obj << +440 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [402.247 464.032 409.694 477.665] +/Rect [402.2466 464.0316 409.6937 477.6646] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -404 0 obj << -/D [402 0 R /XYZ 93.6 740.002 null] +437 0 obj << +/D [435 0 R /XYZ 93.6002 740.0018 null] >> endobj 70 0 obj << -/D [402 0 R /XYZ 93.6 715.095 null] +/D [435 0 R /XYZ 93.6002 715.0952 null] >> endobj -401 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F44 200 0 R /F18 173 0 R >> +434 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F46 219 0 R /F20 181 0 R >> /ProcSet [ /PDF /Text ] >> endobj -415 0 obj << -/Length 5118 +443 0 obj << +/Length 8453 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(22)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(22)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.2)-1125(Subroutine)-375(mld)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F19 11.9552 Tf 86.3998 704.1363 Td[(6.)-1(2)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ ET +1 0 0 1 209.422 704.1363 cm q -1 0 0 1 209.422 704.336 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -209.422 -704.1363 cm BT -/F17 11.9552 Tf 213.457 704.136 Td [(precset)]TJ +/F19 11.9552 Tf 213.4569 704.1363 Td[(pre)-1(cset)]TJ +ET +1 0 0 1 206.9898 683.5417 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf -1.013 -20.594 Td [(mld_precset\050p,what,val,info\051)]TJ/F15 10.9091 Tf -126.044 -25.505 Td [(This)-389(routin)1(e)-389(sets)-389(the)-389(parameters)-388(de\014ning)-389(the)-388(preconditioner.)-611(More)-388(precisely)83(,)-402(the)-389(pa-)]TJ 0 -13.549 Td [(rameter)-333(iden)27(ti)1(\014ed)-334(b)28(y)]TJ/F44 10.9091 Tf 103.394 0 Td [(what)]TJ/F15 10.9091 Tf 26.545 0 Td [(is)-333(assigned)-334(the)-333(v)56(alue)-334(con)28(tained)-333(in)]TJ/F44 10.9091 Tf 163.212 0 Td [(val)]TJ/F15 10.9091 Tf 17.182 0 Td [(.)]TJ/F17 11.9552 Tf -310.333 -40.647 Td [(Argumen)31(ts)]TJ/F44 10.9091 Tf 22.914 -12.806 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.18 0 Td [(.)]TJ -201.099 -13.549 Td [(The)-478(preconditioner)-478(data)-478(structure.)-878(Note)-478(that)]TJ/F18 10.9091 Tf 233.108 0 Td [(x)]TJ/F15 10.9091 Tf 11.588 0 Td [(m)28(ust)-478(b)-28(e)-478(c)28(hosen)-478(ac-)]TJ -244.696 -13.549 Td [(cording)-269(to)-269(the)-270(real/complex,)-282(single/double)-269(precision)-269(v)27(ersion)-269(of)-269(MLD2P4)]TJ 0 -13.549 Td [(under)-333(use.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(what)-2114(integer,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.788 0 Td [(.)]TJ -108.817 -13.55 Td [(The)-324(n)28(um)28(b)-28(er)-324(iden)28(tifying)-324(the)-324(parameter)-323(to)-324(b)-28(e)-324(set.)-441(A)-324(mnemonic)-324(constan)28(t)]TJ 0 -13.549 Td [(has)-300(b)-28(een)-300(asso)-28(ciated)-299(to)-300(eac)27(h)-300(of)-300(th)1(e)-1(se)-300(n)28(um)28(b)-28(ers,)-306(as)-300(rep)-28(orted)-300(in)-300(T)83(ables)]TJ +1 0 0 1 -206.9898 -683.5417 cm +BT +/F46 10.9091 Tf 212.4444 683.5417 Td[(mld_precset\050p,what,val,info\051)]TJ/F15 10.9091 Tf -126.0446 -25.5044 Td[(This)-389(r)1(outin)1(e)-389(s)-1(ets)-389(the)-389(p)1(arame)-1(ters)-389(d)1(e)-1(\014)1(nin)1(g)-389(th)1(e)-389(precondi)1(tioner.)-610(Mor)1(e)-389(precis)-1(ely)84(,)-403(t)1(he)-389(pa-)]TJ 0 -13.5492 Td[(ramete)-1(r)-333(id)1(e)-1(n)29(ti\014ed)-333(b)28(y)]TJ/F46 10.9091 Tf 103.394 0 Td[(what)]TJ/F15 10.9091 Tf 26.5452 0 Td[(is)-334(assigned)-333(the)-333(v)55(al)1(ue)-334(con)28(tain)1(e)-1(d)-332(in)]TJ/F46 10.9091 Tf 163.2123 0 Td[(val)]TJ/F15 10.9091 Tf 17.1816 0 Td[(.)]TJ/F19 11.9552 Tf -310.3331 -40.6476 Td[(Arg)-1(umen)31(t)-1(s)]TJ/F46 10.9091 Tf 22.9141 -12.8052 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-478(pr)1(e)-1(cond)1(ition)1(e)-1(r)-478(d)1(ata)-478(stru)1(c)-1(tu)1(re.)-879(Note)-478(th)1(at)]TJ/F20 10.9091 Tf 233.1081 0 Td[(x)]TJ/F15 10.9091 Tf 11.5884 0 Td[(m)27(u)1(s)-1(t)-477(b)-28(e)-478(c)27(h)1(os)-1(en)-478(ac-)]TJ -244.6965 -13.5492 Td[(cordi)1(ng)-269(to)-269(the)-270(r)1(e)-1(al/complex,)-282(singl)1(e)-1(/d)1(oub)1(le)-270(pr)1(e)-1(cision)-269(v)28(ers)-1(i)1(on)-269(of)-269(MLD2P)1(4)]TJ 0 -13.5492 Td[(un)1(der)-333(use)-1(.)]TJ/F46 10.9091 Tf -45.9708 -13.5492 Td[(what)-2114(integer,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.7878 0 Td[(.)]TJ -108.817 -13.5492 Td[(The)-324(n)28(u)1(m)27(b)-27(e)-1(r)-323(iden)28(tif)1(yin)1(g)-324(the)-324(p)1(arame)-1(ter)-324(to)-323(b)-28(e)-324(s)-1(et.)-441(A)-324(mnemonic)-324(c)-1(on)1(s)-1(t)1(an)28(t)]TJ 0 -13.5492 Td[(has)-300(b)-27(e)-1(en)-300(ass)-1(o)-27(c)-1(iat)1(e)-1(d)-299(to)-300(e)-1(ac)28(h)-300(of)-299(thes)-1(e)-300(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-1(,)-306(as)-301(r)1(e)-1(p)-27(orted)-300(i)1(n)-300(T)83(ab)1(le)-1(s)]TJ +ET +1 0 0 1 477.8664 509.7402 cm 0 0 1 rg 0 0 1 RG - [-300(2)]TJ +1 0 0 1 -477.8664 -509.7402 cm +BT +/F15 10.9091 Tf 477.8664 509.7402 Td[(2)]TJ +ET +1 0 0 1 483.3209 509.7402 cm 0 g 0 G - [(-)]TJ +1 0 0 1 -483.3209 -509.7402 cm +BT +/F15 10.9091 Tf 483.3209 509.7402 Td[(-)]TJ +ET +1 0 0 1 486.9573 509.7402 cm 0 0 1 rg 0 0 1 RG - [(5)]TJ +1 0 0 1 -486.9573 -509.7402 cm +BT +/F15 10.9091 Tf 486.9573 509.7402 Td[(5)]TJ +ET +1 0 0 1 492.4118 509.7402 cm 0 g 0 G - [(.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(val)-2639(integer)]TJ/F18 10.9091 Tf 105.136 0 Td [(or)]TJ/F44 10.9091 Tf 30.425 0 Td [(character\050len=*\051)]TJ/F18 10.9091 Tf 110.711 0 Td [(or)]TJ/F44 10.9091 Tf 30.424 0 Td [(real\050psb_spk_\051)]TJ/F18 10.9091 Tf 99.256 0 Td [(or)]TJ/F44 10.9091 Tf -329.981 -13.549 Td [(real\050psb_dpk_\051)]TJ/F15 10.9091 Tf 80.181 0 Td [(,)]TJ/F44 10.9091 Tf 6.666 0 Td [(intent\050in\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(.)]TJ -144.119 -13.549 Td [(The)-306(v)56(alue)-306(of)-305(the)-306(parameter)-306(to)-305(b)-28(e)-306(set.)-435(The)-306(list)-305(of)-306(allo)28(w)28(ed)-306(v)55(al)1(ues)-306(and)-306(the)]TJ 0 -13.55 Td [(corresp)-28(onding)-391(data)-392(t)28(yp)-28(es)-391(is)-392(giv)28(en)-391(in)-392(T)84(ables)]TJ +1 0 0 1 -492.4118 -509.7402 cm +BT +/F15 10.9091 Tf 492.4118 509.7402 Td[(.)]TJ/F46 10.9091 Tf -383.098 -13.5492 Td[(val)-2639(integer)]TJ/F20 10.9091 Tf 105.1364 0 Td[(or)]TJ/F46 10.9091 Tf 30.4249 0 Td[(character\050len=*\051)]TJ/F20 10.9091 Tf 110.7104 0 Td[(or)]TJ/F46 10.9091 Tf 30.425 0 Td[(real\050psb_spk_\051)]TJ/F20 10.9091 Tf 99.2559 0 Td[(or)]TJ/F46 10.9091 Tf -329.9817 -13.5492 Td[(real\050psb_dpk_\051)]TJ/F15 10.9091 Tf 80.1809 0 Td[(,)]TJ/F46 10.9091 Tf 6.6667 0 Td[(intent\050in\051)]TJ/F15 10.9091 Tf 57.2721 0 Td[(.)]TJ -144.1197 -13.5492 Td[(The)-306(v)56(alu)1(e)-307(of)-305(th)1(e)-306(paramete)-1(r)-305(to)-306(b)-27(e)-306(se)-1(t.)-435(The)-306(l)1(is)-1(t)-305(of)-305(allo)28(w)27(ed)-305(v)55(al)1(ues)-306(and)-305(the)]TJ 0 -13.5492 Td[(corres)-1(p)-27(ond)1(in)1(g)-392(dat)1(a)-392(t)28(yp)-27(e)-1(s)-392(i)1(s)-392(giv)28(en)-392(i)1(n)-391(T)83(ables)]TJ +ET +1 0 0 1 370.0301 455.5434 cm 0 0 1 rg 0 0 1 RG - [-392(2)]TJ +1 0 0 1 -370.0301 -455.5434 cm +BT +/F15 10.9091 Tf 370.0301 455.5434 Td[(2)]TJ +ET +1 0 0 1 375.4847 455.5434 cm 0 g 0 G - [(-)]TJ +1 0 0 1 -375.4847 -455.5434 cm +BT +/F15 10.9091 Tf 375.4847 455.5434 Td[(-)]TJ +ET +1 0 0 1 379.121 455.5434 cm 0 0 1 rg 0 0 1 RG - [(5)]TJ +1 0 0 1 -379.121 -455.5434 cm +BT +/F15 10.9091 Tf 379.121 455.5434 Td[(5)]TJ +ET +1 0 0 1 384.5756 455.5434 cm 0 g 0 G - [(.)-619(When)-391(the)-392(v)56(alue)-392(is)-391(of)]TJ 0 -13.549 Td [(t)28(yp)-28(e)]TJ/F44 10.9091 Tf 24.545 0 Td [(character\050len=*\051)]TJ/F15 10.9091 Tf 91.636 0 Td [(,)-333(it)-334(is)-333(also)-333(treated)-334(as)-333(case)-333(insensitiv)27(e.)]TJ/F44 10.9091 Tf -162.152 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ +1 0 0 1 -384.5756 -455.5434 cm +BT +/F15 10.9091 Tf 384.5756 455.5434 Td[(.)-619(Wh)1(e)-1(n)-391(t)1(he)-392(v)56(alue)-391(is)-392(of)]TJ -229.2909 -13.5492 Td[(t)28(yp)-27(e)]TJ/F46 10.9091 Tf 24.5455 0 Td[(character\050len=*\051)]TJ/F15 10.9091 Tf 91.6353 0 Td[(,)-333(it)-333(is)-334(al)1(s)-1(o)-333(treate)-1(d)-332(as)-334(c)-1(ase)-334(in)1(s)-1(ensitiv)28(e.)]TJ/F46 10.9091 Tf -162.1517 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.5151 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-333(co)-28(de.)-444(If)-333(no)-333(e)-1(r)1(ror,)-333(0)-333(is)-334(r)1(e)-1(tu)1(rn)1(e)-1(d)1(.)-445(S)1(e)-1(e)-333(Sec)-1(tion)]TJ +ET +1 0 0 1 396.0424 414.8958 cm 0 0 1 rg 0 0 1 RG - [-333(7)]TJ +1 0 0 1 -396.0424 -414.8958 cm +BT +/F15 10.9091 Tf 396.0424 414.8958 Td[(7)]TJ +ET +1 0 0 1 401.497 414.8958 cm 0 g 0 G - [-333(for)-334(d)1(e)-1(tail)1(s)-1(.)]TJ -68.885 -18.61 Td [(A)-383(v)56(ariet)28(y)-383(of)-383(\050one-lev)28(el)-383(and)-383(m)28(ulti-lev)28(el\051)-383(preconditioners)-383(can)-383(b)-27(e)-383(obtained)-383(b)28(y)-383(a)-383(suitable)]TJ 0 -13.55 Td [(setting)-425(of)-425(the)-426(p)1(re)-1(cond)1(itioner)-426(parameters.)-720(These)-425(parameters)-425(can)-425(b)-28(e)-425(logically)-426(di)1(vided)]TJ 0 -13.549 Td [(in)28(to)-333(four)-334(groups,)-333(i.e.)-333(parameters)-334(de\014nin)1(g)]TJ +1 0 0 1 -401.497 -414.8958 cm +BT +/F15 10.9091 Tf 405.1333 414.8958 Td[(for)-333(d)1(e)-1(t)1(ails.)]TJ -318.7335 -18.6102 Td[(A)-383(v)56(ari)1(e)-1(t)28(y)-383(of)-382(\050on)1(e)-1(-lev)28(e)-1(l)-383(an)1(d)-383(m)28(ul)1(ti-le)-1(v)28(el\051)-383(p)1(rec)-1(on)1(dit)1(ioners)-383(c)-1(an)-382(b)-27(e)-384(ob)1(tain)1(e)-1(d)-382(b)28(y)-383(a)-383(sui)1(table)]TJ 0 -13.5492 Td[(se)-1(tti)1(ng)-425(of)-425(th)1(e)-426(pr)1(e)-1(cond)1(ition)1(e)-1(r)-425(p)1(arame)-1(t)1(e)-1(rs.)-720(Thes)-1(e)-425(par)1(am)-1(ete)-1(r)1(s)-426(can)-425(b)-27(e)-426(logically)-425(d)1(ivi)1(ded)]TJ 0 -13.5492 Td[(in)28(t)1(o)-334(f)1(our)-333(grou)1(ps,)-333(i.e.)-333(paramete)-1(r)1(s)-334(de\014n)1(ing)]TJ +ET +1 0 0 1 86.3998 346.6716 cm 0 g 0 G - 13.333 -22.515 Td [(1.)]TJ +1 0 0 1 -86.3998 -346.6716 cm +BT +/F15 10.9091 Tf 99.7331 346.6716 Td[(1.)]TJ +ET +1 0 0 1 108.218 346.6716 cm 0 g 0 G - [-500(the)-333(t)27(yp)-27(e)-334(of)-333(m)28(ulti-lev)28(el)-334(preconditioner;)]TJ +1 0 0 1 -108.218 -346.6716 cm +BT +/F15 10.9091 Tf 113.6726 346.6716 Td[(th)1(e)-334(t)28(yp)-27(e)-334(of)-333(m)27(u)1(lti-lev)28(e)-1(l)-333(p)1(rec)-1(on)1(diti)1(oner;)]TJ +ET +1 0 0 1 86.3998 324.1561 cm 0 g 0 G - 0 -22.516 Td [(2.)]TJ +1 0 0 1 -86.3998 -324.1561 cm +BT +/F15 10.9091 Tf 99.7331 324.1561 Td[(2.)]TJ +ET +1 0 0 1 108.218 324.1561 cm 0 g 0 G - [-500(the)-333(one-lev)27(el)-333(preconditioner)-333(used)-333(as)-334(smo)-28(other;)]TJ +1 0 0 1 -108.218 -324.1561 cm +BT +/F15 10.9091 Tf 113.6726 324.1561 Td[(th)1(e)-334(one-)-1(l)1(e)-1(v)28(el)-333(precondi)1(tioner)-333(used)-333(as)-334(s)-1(mo)-28(oth)1(e)-1(r)1(;)]TJ +ET +1 0 0 1 86.3998 301.6405 cm 0 g 0 G - 0 -22.515 Td [(3.)]TJ +1 0 0 1 -86.3998 -301.6405 cm +BT +/F15 10.9091 Tf 99.7331 301.6405 Td[(3.)]TJ +ET +1 0 0 1 108.218 301.6405 cm 0 g 0 G - [-500(the)-333(aggregation)-334(algorith)1(m;)]TJ +1 0 0 1 -108.218 -301.6405 cm +BT +/F15 10.9091 Tf 113.6726 301.6405 Td[(th)1(e)-334(aggregation)-333(algor)1(ithm;)]TJ +ET +1 0 0 1 86.3998 279.1249 cm 0 g 0 G - 0 -22.516 Td [(4.)]TJ +1 0 0 1 -86.3998 -279.1249 cm +BT +/F15 10.9091 Tf 99.7331 279.1249 Td[(4.)]TJ +ET +1 0 0 1 108.218 279.1249 cm 0 g 0 G - [-500(the)-333(coarse-space)-334(correction)-333(at)-334(th)1(e)-334(coarsest)-333(lev)27(el.)]TJ -13.333 -22.516 Td [(A)-313(list)-314(of)-313(the)-313(parameters)-314(that)-313(can)-313(b)-28(e)-314(set,)-317(along)-313(with)-314(their)-313(allo)28(w)28(ed)-314(and)-313(default)-313(v)55(alues,)-317(is)]TJ 0 -13.549 Td [(giv)28(en)-296(in)-296(T)83(ables)]TJ +1 0 0 1 -108.218 -279.1249 cm +BT +/F15 10.9091 Tf 113.6726 279.1249 Td[(th)1(e)-334(c)-1(oar)1(s)-1(e-)-1(space)-334(correction)-333(at)-333(the)-333(c)-1(oarses)-1(t)-333(lev)28(e)-1(l.)]TJ -27.2728 -22.5156 Td[(A)-313(list)-314(of)-313(t)1(he)-314(p)1(arame)-1(ters)-314(th)1(at)-313(c)-1(an)-313(b)-27(e)-314(se)-1(t,)-317(alon)1(g)-313(w)-1(i)1(th)-313(their)-313(allo)28(w)28(e)-1(d)-313(an)1(d)-313(defau)1(lt)-313(v)56(alues)-1(,)-317(is)]TJ 0 -13.5492 Td[(giv)28(en)-296(in)-295(T)83(ables)]TJ +ET +1 0 0 1 160.6958 243.0601 cm 0 0 1 rg 0 0 1 RG - [-296(2)]TJ +1 0 0 1 -160.6958 -243.0601 cm +BT +/F15 10.9091 Tf 160.6958 243.0601 Td[(2)]TJ +ET +1 0 0 1 166.1504 243.0601 cm 0 g 0 G - [(-)]TJ +1 0 0 1 -166.1504 -243.0601 cm +BT +/F15 10.9091 Tf 166.1504 243.0601 Td[(-)]TJ +ET +1 0 0 1 169.7867 243.0601 cm 0 0 1 rg 0 0 1 RG - [(5)]TJ +1 0 0 1 -169.7867 -243.0601 cm +BT +/F15 10.9091 Tf 169.7867 243.0601 Td[(5)]TJ +ET +1 0 0 1 175.2413 243.0601 cm 0 g 0 G - [(.)-432(F)83(or)-296(a)-296(detailed)-296(description)-296(of)-296(the)-296(meaning)-296(of)-296(the)-296(parameters,)-304(please)]TJ 0 -13.549 Td [(refer)-333(to)-334(Section)]TJ +1 0 0 1 -175.2413 -243.0601 cm +BT +/F15 10.9091 Tf 175.2413 243.0601 Td[(.)-432(F)84(or)-296(a)-296(detailed)-296(d)1(e)-1(sc)-1(r)1(ipt)1(ion)-296(of)-295(the)-296(m)-1(eanin)1(g)-296(of)-296(th)1(e)-297(p)1(arame)-1(ters,)-304(p)1(leas)-1(e)]TJ -88.8415 -13.5492 Td[(refer)-333(to)-333(Sec)-1(ti)1(on)]TJ +ET +1 0 0 1 163.1271 229.5109 cm 0 0 1 rg 0 0 1 RG - [-333(4)]TJ +1 0 0 1 -163.1271 -229.5109 cm +BT +/F15 10.9091 Tf 163.1271 229.5109 Td[(4)]TJ +ET +1 0 0 1 168.5817 229.5109 cm 0 g 0 G - [(.)]TJ +1 0 0 1 -168.5817 -229.5109 cm +BT +/F15 10.9091 Tf 168.5817 229.5109 Td[(.)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -414 0 obj << +442 0 obj << /Type /Page -/Contents 415 0 R -/Resources 413 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 392 0 R -/Annots [ 405 0 R 406 0 R 407 0 R 408 0 R 409 0 R 410 0 R 411 0 R 412 0 R ] +/Contents 443 0 R +/Resources 441 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 428 0 R +/Annots [ 445 0 R 446 0 R 447 0 R 448 0 R 449 0 R 454 0 R 455 0 R 456 0 R ] >> endobj -405 0 obj << +445 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [476.87 504.679 484.317 518.312] +/Rect [476.8701 504.6791 484.3172 518.3122] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -406 0 obj << +446 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [485.961 504.679 493.408 518.312] +/Rect [485.961 504.6791 493.4081 518.3122] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -407 0 obj << +447 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [369.034 452.426 376.481 464.115] +/Rect [369.0338 452.4259 376.4809 464.1154] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -408 0 obj << +448 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [378.125 452.426 385.572 464.115] +/Rect [378.1248 452.4259 385.5718 464.1154] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -409 0 obj << +449 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 409.835 402.493 423.468] +/Rect [395.0462 409.8348 402.4932 423.4679] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -410 0 obj << +454 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [159.7 239.943 167.147 251.632] +/Rect [159.6996 239.9427 167.1466 251.6322] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -411 0 obj << +455 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [168.79 239.943 176.238 251.632] +/Rect [168.7905 239.9427 176.2375 251.6322] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -412 0 obj << +456 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [162.131 228.515 169.578 238.083] +/Rect [162.1309 228.5147 169.5779 238.083] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -416 0 obj << -/D [414 0 R /XYZ 86.4 740.002 null] +444 0 obj << +/D [442 0 R /XYZ 86.3998 740.0018 null] >> endobj 74 0 obj << -/D [414 0 R /XYZ 86.4 715.095 null] +/D [442 0 R /XYZ 86.3998 715.0952 null] >> endobj -417 0 obj << -/D [414 0 R /XYZ 86.4 362.583 null] +450 0 obj << +/D [442 0 R /XYZ 86.3998 362.5828 null] >> endobj -418 0 obj << -/D [414 0 R /XYZ 86.4 340.067 null] +451 0 obj << +/D [442 0 R /XYZ 86.3998 340.0672 null] >> endobj -419 0 obj << -/D [414 0 R /XYZ 86.4 317.552 null] +452 0 obj << +/D [442 0 R /XYZ 86.3998 317.5517 null] >> endobj -420 0 obj << -/D [414 0 R /XYZ 86.4 295.036 null] +453 0 obj << +/D [442 0 R /XYZ 86.3998 295.0361 null] >> endobj -413 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F17 111 0 R /F44 200 0 R /F18 173 0 R >> +441 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F19 113 0 R /F46 219 0 R /F20 181 0 R >> /ProcSet [ /PDF /Text ] >> endobj -424 0 obj << -/Length 4357 +459 0 obj << +/Length 6002 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(6)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(23)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(23)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -q -0 1 -1 0 0 0 cm +1 0 0 1 206.2256 0 cm + q 0 -1 1 0 0 0 cm 0 g 0 G +1 0 0 1 15.408 16.3055 cm 0 g 0 G 0 g 0 G +1 0 0 1 5.4545 71.071 cm q -1 0 0 1 20.862 87.576 cm -[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +551.8492 0.1992 l +S Q +1 0 0 1 -0.1992 -13.5492 cm q -1 0 0 1 20.862 73.827 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q -1 0 0 1 -299.826 -121.521 cm +1 0 0 1 -320.4891 -788.9225 cm BT -/F44 10.9091 Tf 326.666 199.413 Td [(what)]TJ +/F46 10.9091 Tf 326.6659 792.9873 Td[(what)]TJ ET +1 0 0 1 435.5341 788.9225 cm q -1 0 0 1 435.733 195.348 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -435.5341 -788.9225 cm BT -/F41 10.9091 Tf 441.711 199.413 Td [(d)22(a)67(t)66(a)-377(type)]TJ +/F43 10.9091 Tf 441.7109 792.9873 Td[(d)22(a)66(t)67(a)-378(t)-1(ype)]TJ ET +1 0 0 1 539.1246 788.9225 cm q -1 0 0 1 539.324 195.348 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -539.1246 -788.9225 cm BT -/F44 10.9091 Tf 545.301 199.413 Td [(val)]TJ +/F46 10.9091 Tf 545.3014 792.9873 Td[(val)]TJ ET +1 0 0 1 607.7727 788.9225 cm q -1 0 0 1 607.972 195.348 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -607.7727 -788.9225 cm BT -/F41 10.9091 Tf 613.95 199.413 Td [(def)89(a)22(ul)67(t)]TJ +/F43 10.9091 Tf 613.9495 792.9873 Td[(def)89(a)22(ul)66(t)]TJ ET +1 0 0 1 661.958 788.9225 cm q -1 0 0 1 662.157 195.348 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -661.958 -788.9225 cm BT -/F41 10.9091 Tf 668.135 199.413 Td [(comments)]TJ +/F43 10.9091 Tf 668.1348 792.9873 Td[(com)1(ments)]TJ ET +1 0 0 1 872.3383 788.9225 cm q -1 0 0 1 872.538 195.348 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -551.65 -0.3985 cm q -1 0 0 1 320.688 195.149 cm -[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +551.8492 0.1992 l +S Q +1 0 0 1 -0.1992 -40.6476 cm q -1 0 0 1 320.688 154.302 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -320.4891 -747.8764 cm BT -/F44 10.9091 Tf 326.666 185.465 Td [(mld_ml_type_)]TJ +/F46 10.9091 Tf 326.6659 779.0396 Td[(mld_ml_type_)]TJ ET +1 0 0 1 435.5341 747.8764 cm q -1 0 0 1 435.733 154.302 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -435.5341 -747.8764 cm BT -/F44 10.9091 Tf 441.711 185.465 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 441.7109 779.0396 Td[(character\050len=*\051)]TJ ET +1 0 0 1 539.1246 747.8764 cm q -1 0 0 1 539.324 154.302 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -539.1246 -747.8764 cm BT -/F44 10.9091 Tf 545.301 185.465 Td [('ADD')]TJ 0 -13.549 Td [('MULT')]TJ +/F46 10.9091 Tf 545.3014 779.0396 Td[('ADD')]TJ 0 -13.5492 Td[('MULT')]TJ ET +1 0 0 1 607.7727 747.8764 cm q -1 0 0 1 607.972 154.302 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -607.7727 -747.8764 cm BT -/F44 10.9091 Tf 613.95 185.465 Td [('MULT')]TJ +/F46 10.9091 Tf 613.9495 779.0396 Td[('MULT')]TJ ET +1 0 0 1 661.958 747.8764 cm q -1 0 0 1 662.157 154.302 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -661.958 -747.8764 cm BT -/F15 10.9091 Tf 668.135 185.465 Td [(Basic)-449(m)28(ulti-lev)28(el)-449(framew)27(ork:)-675(additiv)28(e)-449(or)]TJ 0 -13.549 Td [(m)28(ultiplicativ)28(e)-586(among)-587(the)-586(lev)28(els)-586(\050alw)28(a)27(ys)]TJ 0 -13.549 Td [(additiv)28(e)-333(inside)-334(a)-333(lev)28(el\051.)]TJ +/F15 10.9091 Tf 668.1348 779.0396 Td[(Bas)-1(ic)-449(m)28(ulti)1(-)-1(lev)28(el)-449(fr)1(am)-1(ew)27(or)1(k:)-675(addi)1(tiv)28(e)-449(or)]TJ 0 -13.5492 Td[(m)27(u)1(ltip)1(licativ)28(e)-586(am)-1(on)1(g)-586(the)-586(le)-1(v)28(els)-586(\050alw)27(a)28(ys)]TJ 0 -13.5492 Td[(add)1(itiv)28(e)-333(insid)1(e)-334(a)-334(l)1(e)-1(v)28(el\051.)]TJ ET +1 0 0 1 872.3383 747.8764 cm q -1 0 0 1 872.538 154.302 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -551.65 -0.3985 cm q -1 0 0 1 320.688 154.103 cm -[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +551.8492 0.1992 l +S Q +1 0 0 1 -0.1992 -40.6475 cm q -1 0 0 1 320.688 113.256 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -320.4891 -706.8304 cm BT -/F44 10.9091 Tf 326.666 144.419 Td [(mld_smoother_type_)]TJ +/F46 10.9091 Tf 326.6659 737.9936 Td[(mld_smoother_type_)]TJ ET +1 0 0 1 435.5341 706.8304 cm q -1 0 0 1 435.733 113.256 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -435.5341 -706.8304 cm BT -/F44 10.9091 Tf 441.711 144.419 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 441.7109 737.9936 Td[(character\050len=*\051)]TJ ET +1 0 0 1 539.1246 706.8304 cm q -1 0 0 1 539.324 113.256 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -539.1246 -706.8304 cm BT -/F44 10.9091 Tf 545.301 144.419 Td [('DIAG')]TJ 0 -13.549 Td [('BJAC')]TJ 0 -13.549 Td [('AS')]TJ +/F46 10.9091 Tf 545.3014 737.9936 Td[('DIAG')]TJ 0 -13.5492 Td[('BJAC')]TJ 0 -13.5492 Td[('AS')]TJ ET +1 0 0 1 607.7727 706.8304 cm q -1 0 0 1 607.972 113.256 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -607.7727 -706.8304 cm BT -/F44 10.9091 Tf 613.95 144.419 Td [('AS')]TJ +/F46 10.9091 Tf 613.9495 737.9936 Td[('AS')]TJ ET +1 0 0 1 661.958 706.8304 cm q -1 0 0 1 662.157 113.256 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -661.958 -706.8304 cm BT -/F15 10.9091 Tf 668.135 144.419 Td [(Basic)-1379(one-lev)28(el)-1379(preconditioner)-1378(\050i.e.)]TJ 0 -13.549 Td [(smo)-28(other\051:)-444(diagonal,)-333(blo)-28(c)28(k)-334(Jacobi,)-333(AS.)]TJ +/F15 10.9091 Tf 668.1348 737.9936 Td[(Bas)-1(ic)-1379(on)1(e)-1(-lev)28(e)-1(l)-1378(pr)1(e)-1(cond)1(ition)1(e)-1(r)-1378(\050i.e.)]TJ 0 -13.5492 Td[(sm)-1(o)-28(ot)1(her\051:)-444(diagon)1(al,)-333(bl)1(o)-28(c)27(k)-333(Jacobi,)-333(AS)1(.)]TJ ET +1 0 0 1 872.3383 706.8304 cm q -1 0 0 1 872.538 113.256 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -551.65 -0.3985 cm q -1 0 0 1 320.688 113.057 cm -[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +551.8492 0.1992 l +S Q +1 0 0 1 -0.1992 -40.6476 cm q -1 0 0 1 320.688 72.21 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -320.4891 -665.7843 cm BT -/F44 10.9091 Tf 326.666 103.373 Td [(mld_smoother_pos_)]TJ +/F46 10.9091 Tf 326.6659 696.9475 Td[(mld_smoother_pos_)]TJ ET +1 0 0 1 435.5341 665.7843 cm q -1 0 0 1 435.733 72.21 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -435.5341 -665.7843 cm BT -/F44 10.9091 Tf 441.711 103.373 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 441.7109 696.9475 Td[(character\050len=*\051)]TJ ET +1 0 0 1 539.1246 665.7843 cm q -1 0 0 1 539.324 72.21 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -539.1246 -665.7843 cm BT -/F44 10.9091 Tf 545.301 103.373 Td [('PRE')]TJ 0 -13.549 Td [('POST')]TJ 0 -13.549 Td [('TWOSIDE')]TJ +/F46 10.9091 Tf 545.3014 696.9475 Td[('PRE')]TJ 0 -13.5492 Td[('POST')]TJ 0 -13.5492 Td[('TWOSIDE')]TJ ET +1 0 0 1 607.7727 665.7843 cm q -1 0 0 1 607.972 72.21 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -607.7727 -665.7843 cm BT -/F44 10.9091 Tf 613.95 103.373 Td [('POST')]TJ +/F46 10.9091 Tf 613.9495 696.9475 Td[('POST')]TJ ET +1 0 0 1 661.958 665.7843 cm q -1 0 0 1 662.157 72.21 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -661.958 -665.7843 cm BT -/F15 10.9091 Tf 668.135 103.373 Td [(\134P)28(osition")-233(of)-234(the)-233(smo)-28(other:)-394(pre-smo)-28(other,)]TJ 0 -13.549 Td [(p)-28(ost-smo)-28(other,)-333(pre-)-333(and)-333(p)-28(ost-smo)-28(other.)]TJ +/F15 10.9091 Tf 668.1348 696.9475 Td[(\134P)28(osition)1(")-234(of)-232(the)-234(sm)-1(o)-27(other:)-394(pr)1(e)-1(-s)-1(mo)-28(oth)1(e)-1(r)1(,)]TJ 0 -13.5492 Td[(p)-27(os)-1(t-sm)-1(o)-28(ot)1(her,)-333(pr)1(e)-1(-)-334(an)1(d)-333(p)-27(os)-1(t-sm)-1(o)-28(ot)1(her.)]TJ ET +1 0 0 1 872.3383 665.7843 cm q -1 0 0 1 872.538 72.21 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -551.65 -0.3985 cm q -1 0 0 1 320.688 72.011 cm -[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +551.8492 0.1992 l +S Q +1 0 0 1 111.97 -30.4898 cm 0 g 0 G +1 0 0 1 -432.6583 -634.896 cm BT -/F15 10.9091 Tf 432.658 41.322 Td [(T)83(able)-333(2:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(t)28(yp)-27(e)-334(of)-333(m)28(ulti-lev)27(el)-333(preconditioner.)]TJ +/F15 10.9091 Tf 432.6583 634.896 Td[(T)83(ab)1(le)-334(2:)-444(P)28(aramete)-1(r)1(s)-334(de\014n)1(ing)-333(th)1(e)-334(t)28(yp)-27(e)-334(of)-333(m)27(u)1(lti-lev)28(e)-1(l)-333(p)1(rec)-1(on)1(diti)1(oner.)]TJ +ET +1 0 0 1 760.5676 634.896 cm 0 g 0 G +1 0 0 1 132.8325 80.1992 cm 0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -Q +1 0 0 1 -593.5743 0 cm + Q +1 0 0 1 -206.2256 -593.5743 cm 0 g 0 G +1 0 0 1 0 -29.8879 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -423 0 obj << +458 0 obj << /Type /Page -/Contents 424 0 R -/Resources 422 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 392 0 R -/Annots [ 421 0 R ] +/Contents 459 0 R +/Resources 457 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 428 0 R +/Annots [ 461 0 R ] >> endobj -421 0 obj << +461 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -425 0 obj << -/D [423 0 R /XYZ 93.6 740.002 null] +460 0 obj << +/D [458 0 R /XYZ 93.6002 740.0018 null] >> endobj -355 0 obj << -/D [423 0 R /XYZ 366.433 4378.384 null] +388 0 obj << +/D [458 0 R /XYZ 475.9916 648.4452 null] >> endobj -422 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F44 200 0 R >> +457 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -428 0 obj << -/Length 9704 +464 0 obj << +/Length 12566 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(24)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(24)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -q -0 -1 1 0 0 0 cm +1 0 0 1 206.2255 0 cm + q 0 -1 1 0 0 0 cm 0 g 0 G +1 0 0 1 291.3327 163.5907 cm 0 g 0 G 0 g 0 G +1 0 0 1 -291.3327 -1.3948 cm q -1 0 0 1 0 162.395 cm -[]0 d 0 J 0.398 w 0 0 m 614.686 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +614.6861 0.1992 l +S Q +1 0 0 1 -0.1992 -13.5492 cm q -1 0 0 1 0 148.647 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q -1 0 0 1 -292.625 -715.095 cm +1 0 0 1 -292.4261 -863.7419 cm BT -/F44 10.9091 Tf 298.603 867.807 Td [(what)]TJ +/F46 10.9091 Tf 298.6029 867.8067 Td[(what)]TJ ET +1 0 0 1 396.0166 863.7419 cm q -1 0 0 1 396.216 863.742 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -396.0166 -863.7419 cm BT -/F41 10.9091 Tf 402.193 867.807 Td [(d)22(a)67(t)66(a)-377(type)]TJ +/F43 10.9091 Tf 402.1935 867.8067 Td[(d)22(a)66(t)67(a)-378(t)-1(ype)]TJ ET +1 0 0 1 514.99 863.7419 cm q -1 0 0 1 515.189 863.742 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -514.99 -863.7419 cm BT -/F44 10.9091 Tf 521.167 867.807 Td [(val)]TJ +/F46 10.9091 Tf 521.1668 867.8067 Td[(val)]TJ ET +1 0 0 1 617.6537 863.7419 cm q -1 0 0 1 617.853 863.742 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -617.6537 -863.7419 cm BT -/F41 10.9091 Tf 623.831 867.807 Td [(def)89(a)22(ul)67(t)]TJ +/F43 10.9091 Tf 623.8306 867.8067 Td[(def)89(a)22(ul)66(t)]TJ ET +1 0 0 1 696.7318 863.7419 cm q -1 0 0 1 696.931 863.742 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -696.7318 -863.7419 cm BT -/F41 10.9091 Tf 702.909 867.807 Td [(comments)]TJ +/F43 10.9091 Tf 702.9086 867.8067 Td[(com)1(ments)]TJ ET +1 0 0 1 907.1122 863.7419 cm q -1 0 0 1 907.311 863.742 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -614.4869 -0.3985 cm q -1 0 0 1 292.625 863.543 cm -[]0 d 0 J 0.398 w 0 0 m 614.686 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +614.6861 0.1992 l +S Q +1 0 0 1 -0.1992 -13.5492 cm q -1 0 0 1 292.625 849.794 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -292.4261 -849.7942 cm BT -/F44 10.9091 Tf 298.603 853.859 Td [(mld_sub_ovr_)]TJ +/F46 10.9091 Tf 298.6029 853.859 Td[(mld_sub_ovr_)]TJ ET +1 0 0 1 396.0166 849.7943 cm q -1 0 0 1 396.216 849.794 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -396.0166 -849.7943 cm BT -/F44 10.9091 Tf 402.193 853.859 Td [(integer)]TJ +/F46 10.9091 Tf 402.1935 853.8591 Td[(integer)]TJ ET +1 0 0 1 514.99 849.7943 cm q -1 0 0 1 515.189 849.794 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -514.99 -849.7943 cm BT -/F15 10.9091 Tf 521.167 853.859 Td [(an)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 67.879 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ +/F15 10.9091 Tf 521.1668 853.8591 Td[(an)28(y)-333(in)29(t.)-333(n)28(um.)]TJ/F27 10.9091 Tf 67.8788 0 Td[(\025)]TJ/F15 10.9091 Tf 11.5152 0 Td[(0)]TJ ET +1 0 0 1 617.6537 849.7943 cm q -1 0 0 1 617.853 849.794 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -617.6537 -849.7943 cm BT -/F15 10.9091 Tf 623.831 853.859 Td [(1)]TJ +/F15 10.9091 Tf 623.8306 853.8591 Td[(1)]TJ ET +1 0 0 1 696.7318 849.7943 cm q -1 0 0 1 696.931 849.794 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -696.7318 -849.7943 cm BT -/F15 10.9091 Tf 702.909 853.859 Td [(Num)28(b)-28(er)-333(of)-334(o)28(v)28(erlap)-333(la)28(y)27(ers.)]TJ +/F15 10.9091 Tf 702.9086 853.8591 Td[(Num)28(b)-27(e)-1(r)-333(of)-333(o)28(v)28(erlap)-333(la)28(y)28(ers.)]TJ ET +1 0 0 1 907.1122 849.7943 cm q -1 0 0 1 907.311 849.794 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -614.4869 -0.3985 cm q -1 0 0 1 292.625 849.595 cm -[]0 d 0 J 0.398 w 0 0 m 614.686 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +614.6861 0.1992 l +S Q +1 0 0 1 -0.1992 -40.6476 cm q -1 0 0 1 292.625 808.748 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -292.4261 -808.7482 cm BT -/F44 10.9091 Tf 298.603 839.911 Td [(mld_sub_restr_)]TJ +/F46 10.9091 Tf 298.6029 839.9114 Td[(mld_sub_restr_)]TJ ET +1 0 0 1 396.0166 808.7482 cm q -1 0 0 1 396.216 808.748 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -396.0166 -808.7482 cm BT -/F44 10.9091 Tf 402.193 839.911 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 402.1935 839.9114 Td[(character\050len=*\051)]TJ ET +1 0 0 1 514.99 808.7482 cm q -1 0 0 1 515.189 808.748 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -514.99 -808.7482 cm BT -/F44 10.9091 Tf 521.167 839.911 Td [('HALO')]TJ 0 -13.549 Td [('NONE')]TJ +/F46 10.9091 Tf 521.1668 839.9114 Td[('HALO')]TJ 0 -13.5492 Td[('NONE')]TJ ET +1 0 0 1 617.6537 808.7482 cm q -1 0 0 1 617.853 808.748 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -617.6537 -808.7482 cm BT -/F44 10.9091 Tf 623.831 839.911 Td [('HALO')]TJ +/F46 10.9091 Tf 623.8306 839.9114 Td[('HALO')]TJ ET +1 0 0 1 696.7318 808.7482 cm q -1 0 0 1 696.931 808.748 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -696.7318 -808.7482 cm BT -/F15 10.9091 Tf 702.909 839.911 Td [(T)28(yp)-28(e)-429(of)-429(restriction)-429(op)-28(erator:)]TJ/F44 10.9091 Tf 146.32 0 Td [('HALO')]TJ/F15 10.9091 Tf 39.044 0 Td [(for)]TJ -185.364 -13.549 Td [(taking)-478(in)28(to)-478(accoun)28(t)-478(the)-477(o)27(v)28(erlap,)]TJ/F44 10.9091 Tf 164.062 0 Td [('NONE')]TJ/F15 10.9091 Tf -164.062 -13.549 Td [(for)-333(neglecting)-334(it.)]TJ +/F15 10.9091 Tf 702.9086 839.9114 Td[(T)28(yp)-28(e)-429(of)-429(res)-1(t)1(riction)-429(op)-27(e)-1(r)1(ator:)]TJ/F46 10.9091 Tf 146.3202 0 Td[('HALO')]TJ/F15 10.9091 Tf 39.0444 0 Td[(for)]TJ -185.3646 -13.5492 Td[(taki)1(ng)-478(in)29(to)-478(acc)-1(ou)1(n)28(t)-478(th)1(e)-479(o)28(v)28(erlap)1(,)]TJ/F46 10.9091 Tf 164.062 0 Td[('NONE')]TJ/F15 10.9091 Tf -164.062 -13.5492 Td[(for)-333(n)1(e)-1(gl)1(e)-1(ctin)1(g)-334(it)1(.)]TJ ET +1 0 0 1 907.1122 808.7482 cm q -1 0 0 1 907.311 808.748 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -614.4869 -0.3985 cm q -1 0 0 1 292.625 808.549 cm -[]0 d 0 J 0.398 w 0 0 m 614.686 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +614.6861 0.1992 l +S Q +1 0 0 1 -0.1992 -40.6476 cm q -1 0 0 1 292.625 767.702 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -292.4261 -767.7021 cm BT -/F44 10.9091 Tf 298.603 798.865 Td [(mld_sub_prol_)]TJ +/F46 10.9091 Tf 298.6029 798.8653 Td[(mld_sub_prol_)]TJ ET +1 0 0 1 396.0166 767.7021 cm q -1 0 0 1 396.216 767.702 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -396.0166 -767.7021 cm BT -/F44 10.9091 Tf 402.193 798.865 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 402.1935 798.8653 Td[(character\050len=*\051)]TJ ET +1 0 0 1 514.99 767.7021 cm q -1 0 0 1 515.189 767.702 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -514.99 -767.7021 cm BT -/F44 10.9091 Tf 521.167 798.865 Td [('SUM')]TJ 0 -13.549 Td [('NONE')]TJ +/F46 10.9091 Tf 521.1668 798.8653 Td[('SUM')]TJ 0 -13.5492 Td[('NONE')]TJ ET +1 0 0 1 617.6537 767.7021 cm q -1 0 0 1 617.853 767.702 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -617.6537 -767.7021 cm BT -/F44 10.9091 Tf 623.831 798.865 Td [('NONE')]TJ +/F46 10.9091 Tf 623.8306 798.8653 Td[('NONE')]TJ ET +1 0 0 1 696.7318 767.7021 cm q -1 0 0 1 696.931 767.702 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -696.7318 -767.7021 cm BT -/F15 10.9091 Tf 702.909 798.865 Td [(T)28(yp)-28(e)-342(of)-342(prolongation)-342(op)-28(erator:)]TJ/F44 10.9091 Tf 152.996 0 Td [('SUM')]TJ/F15 10.9091 Tf 32.368 0 Td [(for)]TJ -185.364 -13.549 Td [(adding)-251(the)-252(con)28(tributions)-252(from)-252(th)1(e)-252(o)28(v)27(erlap,)]TJ/F44 10.9091 Tf 0 -13.549 Td [('NONE')]TJ/F15 10.9091 Tf 37.999 0 Td [(for)-333(neglecting)-334(them.)]TJ +/F15 10.9091 Tf 702.9086 798.8653 Td[(T)28(yp)-28(e)-342(of)-342(p)1(rolon)1(gation)-342(op)-27(e)-1(r)1(ator:)]TJ/F46 10.9091 Tf 152.9961 0 Td[('SUM')]TJ/F15 10.9091 Tf 32.3685 0 Td[(for)]TJ -185.3646 -13.5492 Td[(add)1(in)1(g)-252(the)-252(con)28(tr)1(ibu)1(tions)-252(f)1(rom)-252(th)1(e)-253(o)28(v)28(erlap)1(,)]TJ/F46 10.9091 Tf 0 -13.5492 Td[('NONE')]TJ/F15 10.9091 Tf 37.9997 0 Td[(for)-333(n)1(e)-1(gl)1(e)-1(ctin)1(g)-334(th)1(e)-1(m.)]TJ ET +1 0 0 1 907.1122 767.7021 cm q -1 0 0 1 907.311 767.702 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -614.4869 -0.3985 cm q -1 0 0 1 292.625 767.503 cm -[]0 d 0 J 0.398 w 0 0 m 614.686 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +614.6861 0.1992 l +S Q +1 0 0 1 -0.1992 -67.746 cm q -1 0 0 1 292.625 699.558 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -292.4261 -699.5576 cm BT -/F44 10.9091 Tf 298.603 757.819 Td [(mld_sub_solve_)]TJ +/F46 10.9091 Tf 298.6029 757.8192 Td[(mld_sub_solve_)]TJ ET +1 0 0 1 396.0166 699.5577 cm q -1 0 0 1 396.216 699.558 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -396.0166 -699.5577 cm BT -/F44 10.9091 Tf 402.193 757.819 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 402.1935 757.8192 Td[(character\050len=*\051)]TJ ET +1 0 0 1 514.99 699.5577 cm q -1 0 0 1 515.189 699.558 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -514.99 -699.5577 cm BT -/F44 10.9091 Tf 521.167 757.819 Td [('ILU')]TJ 0 -13.549 Td [('MILU')]TJ 0 -13.549 Td [('ILUT')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.55 Td [('SLU')]TJ +/F46 10.9091 Tf 521.1668 757.8192 Td[('ILU')]TJ 0 -13.5492 Td[('MILU')]TJ 0 -13.5492 Td[('ILUT')]TJ 0 -13.5492 Td[('UMF')]TJ 0 -13.5492 Td[('SLU')]TJ ET +1 0 0 1 617.6537 699.5577 cm q -1 0 0 1 617.853 699.558 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -617.6537 -699.5577 cm BT -/F44 10.9091 Tf 623.831 757.819 Td [('UMF')]TJ +/F46 10.9091 Tf 623.8306 757.8192 Td[('UMF')]TJ ET +1 0 0 1 696.7318 699.5577 cm q -1 0 0 1 696.931 699.558 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -696.7318 -699.5577 cm BT -/F15 10.9091 Tf 702.909 757.819 Td [(Lo)-28(cal)-326(solv)28(er:)-441(ILU\050)]TJ/F22 10.9091 Tf 87.847 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-327(MILU\050)]TJ/F22 10.9091 Tf 44.025 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-327(ILU\050)]TJ/F22 10.9091 Tf 34.026 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051,)]TJ -191.152 -13.549 Td [(LU)-411(from)-411(UMFP)83(A)28(CK,)-411(LU)-411(from)-411(Sup)-28(erLU)]TJ 0 -13.549 Td [(\050plus)-333(triangular)-333(solv)27(e\051.)]TJ +/F15 10.9091 Tf 702.9086 757.8192 Td[(Lo)-28(cal)-326(solv)28(e)-1(r)1(:)-441(ILU\050)]TJ/F24 10.9091 Tf 87.8474 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)-327(MILU\050)]TJ/F24 10.9091 Tf 44.0257 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)-327(ILU\050)]TJ/F24 10.9091 Tf 34.0257 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051,)]TJ -191.1524 -13.5492 Td[(LU)-411(fr)1(om)-412(UM)1(FP)84(A)27(CK,)-411(LU)-411(f)1(rom)-411(Sup)-27(erLU)]TJ 0 -13.5492 Td[(\050p)1(lus)-334(t)1(rian)1(gular)-333(solv)28(e\051.)]TJ ET +1 0 0 1 907.1122 699.5577 cm q -1 0 0 1 907.311 699.558 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -614.4869 -0.3985 cm q -1 0 0 1 292.625 699.358 cm -[]0 d 0 J 0.398 w 0 0 m 614.686 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +614.6861 0.1992 l +S Q +1 0 0 1 -0.1992 -27.0984 cm q -1 0 0 1 292.625 672.061 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -292.4261 -672.0608 cm BT -/F44 10.9091 Tf 298.603 689.675 Td [(mld_sub_fillin_)]TJ +/F46 10.9091 Tf 298.6029 689.6748 Td[(mld_sub_fillin_)]TJ ET +1 0 0 1 396.0166 672.0608 cm q -1 0 0 1 396.216 672.061 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -396.0166 -672.0608 cm BT -/F44 10.9091 Tf 402.193 689.675 Td [(integer)]TJ +/F46 10.9091 Tf 402.1935 689.6748 Td[(integer)]TJ ET +1 0 0 1 514.99 672.0608 cm q -1 0 0 1 515.189 672.061 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -514.99 -672.0608 cm BT -/F15 10.9091 Tf 521.167 689.675 Td [(An)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 70.606 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ +/F15 10.9091 Tf 521.1668 689.6748 Td[(An)28(y)-333(in)29(t.)-333(n)28(um.)]TJ/F27 10.9091 Tf 70.6061 0 Td[(\025)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ ET +1 0 0 1 617.6537 672.0608 cm q -1 0 0 1 617.853 672.061 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -617.6537 -672.0608 cm BT -/F15 10.9091 Tf 623.831 689.675 Td [(0)]TJ +/F15 10.9091 Tf 623.8306 689.6748 Td[(0)]TJ ET +1 0 0 1 696.7318 672.0608 cm q -1 0 0 1 696.931 672.061 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -696.7318 -672.0608 cm BT -/F15 10.9091 Tf 702.909 689.675 Td [(Fill-in)-276(lev)28(el)]TJ/F22 10.9091 Tf 56.176 0 Td [(p)]TJ/F15 10.9091 Tf 8.502 0 Td [(of)-276(the)-276(incomplete)-276(LU)-277(f)1(ac)-1(tor)1(-)]TJ -64.678 -13.549 Td [(izations.)]TJ +/F15 10.9091 Tf 702.9086 689.6748 Td[(Fil)1(l-in)-276(lev)28(e)-1(l)]TJ/F24 10.9091 Tf 56.1769 0 Td[(p)]TJ/F15 10.9091 Tf 8.5013 0 Td[(of)-276(th)1(e)-277(in)1(c)-1(omp)1(le)-1(te)-276(LU)-276(factor-)]TJ -64.6781 -13.5492 Td[(ization)1(s)-1(.)]TJ ET +1 0 0 1 907.1122 672.0608 cm q -1 0 0 1 907.311 672.061 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -614.4869 -0.3985 cm q -1 0 0 1 292.625 671.862 cm -[]0 d 0 J 0.398 w 0 0 m 614.686 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +614.6861 0.1992 l +S Q +1 0 0 1 -0.1992 -27.0984 cm q -1 0 0 1 292.625 644.564 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -292.4261 -644.5639 cm BT -/F44 10.9091 Tf 298.603 662.178 Td [(mld_sub_iluthrs_)]TJ +/F46 10.9091 Tf 298.6029 662.1779 Td[(mld_sub_iluthrs_)]TJ ET +1 0 0 1 396.0166 644.5639 cm q -1 0 0 1 396.216 644.564 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -396.0166 -644.5639 cm BT -/F44 10.9091 Tf 402.193 662.178 Td [(real\050)]TJ/F18 10.9091 Tf 28.637 0 Td [(kind)]TJ +/F46 10.9091 Tf 402.1935 662.1779 Td[(real\050)]TJ/F20 10.9091 Tf 28.636 0 Td[(kind)]TJ ET +1 0 0 1 451.5712 662.1779 cm q -1 0 0 1 451.571 662.377 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -451.5712 -662.1779 cm BT -/F18 10.9091 Tf 454.917 662.178 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.567 0 Td [(\051)]TJ +/F20 10.9091 Tf 454.9166 662.1779 Td[(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.5678 0 Td[(\051)]TJ ET +1 0 0 1 514.99 644.5639 cm q -1 0 0 1 515.189 644.564 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -514.99 -644.5639 cm BT -/F15 10.9091 Tf 521.167 662.178 Td [(An)28(y)-333(real)-334(n)28(um.)]TJ/F25 10.9091 Tf 72.151 0 Td [(\025)]TJ/F15 10.9091 Tf 11.516 0 Td [(0)]TJ +/F15 10.9091 Tf 521.1668 662.1779 Td[(An)28(y)-333(real)-333(n)28(u)1(m)-1(.)]TJ/F27 10.9091 Tf 72.1516 0 Td[(\025)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ ET +1 0 0 1 617.6537 644.5639 cm q -1 0 0 1 617.853 644.564 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -617.6537 -644.5639 cm BT -/F15 10.9091 Tf 623.831 662.178 Td [(0)]TJ +/F15 10.9091 Tf 623.8306 662.1779 Td[(0)]TJ ET +1 0 0 1 696.7318 644.5639 cm q -1 0 0 1 696.931 644.564 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -696.7318 -644.5639 cm BT -/F15 10.9091 Tf 702.909 662.178 Td [(Drop)-256(tolerance)]TJ/F22 10.9091 Tf 72.776 0 Td [(t)]TJ/F15 10.9091 Tf 6.737 0 Td [(in)-256(the)-257(ILU\050)]TJ/F22 10.9091 Tf 53.02 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-256(factoriza-)]TJ -146.809 -13.549 Td [(tion.)]TJ +/F15 10.9091 Tf 702.9086 662.1779 Td[(Drop)-256(t)1(ole)-1(r)1(ance)]TJ/F24 10.9091 Tf 72.7769 0 Td[(t)]TJ/F15 10.9091 Tf 6.7369 0 Td[(in)-256(th)1(e)-257(ILU\050)]TJ/F24 10.9091 Tf 53.0192 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051)-256(factoriza-)]TJ -146.8095 -13.5492 Td[(tion)1(.)]TJ ET +1 0 0 1 907.1122 644.5639 cm q -1 0 0 1 907.311 644.564 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -614.4869 -0.3985 cm q -1 0 0 1 292.625 644.365 cm -[]0 d 0 J 0.398 w 0 0 m 614.686 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +614.6861 0.1992 l +S Q +1 0 0 1 -0.1992 -54.1968 cm q -1 0 0 1 292.625 589.969 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 54.1968 l +S Q +1 0 0 1 -292.4261 -589.9686 cm BT -/F44 10.9091 Tf 298.603 634.681 Td [(mld_sub_ren_)]TJ +/F46 10.9091 Tf 298.6029 634.681 Td[(mld_sub_ren_)]TJ ET +1 0 0 1 396.0166 589.9686 cm q -1 0 0 1 396.216 589.969 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 54.1968 l +S Q +1 0 0 1 -396.0166 -589.9686 cm BT -/F44 10.9091 Tf 402.193 634.681 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 402.1935 634.681 Td[(character\050len=*\051)]TJ ET +1 0 0 1 514.99 589.9686 cm q -1 0 0 1 515.189 589.969 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 54.1968 l +S Q +1 0 0 1 -514.99 -589.9686 cm BT -/F44 10.9091 Tf 521.167 634.681 Td [('RENUM)]TJ +/F46 10.9091 Tf 521.1668 634.681 Td[('RENUM)]TJ ET +1 0 0 1 556.2173 634.681 cm q -1 0 0 1 556.217 634.88 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4364 0.1992 l +S Q +1 0 0 1 -556.2173 -634.681 cm BT -/F44 10.9091 Tf 559.654 634.681 Td [(NONE')]TJ -38.487 -13.549 Td [('RENUM)]TJ +/F46 10.9091 Tf 559.6537 634.681 Td[(NONE')]TJ -38.4869 -13.5492 Td[('RENUM)]TJ ET +1 0 0 1 556.2173 621.1318 cm q -1 0 0 1 556.217 621.331 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4364 0.1992 l +S Q +1 0 0 1 -556.2173 -621.1318 cm BT -/F44 10.9091 Tf 559.654 621.132 Td [(GLOBAL')]TJ +/F46 10.9091 Tf 559.6537 621.1318 Td[(GLOBAL')]TJ ET +1 0 0 1 617.6537 589.9686 cm q -1 0 0 1 617.853 589.969 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 54.1968 l +S Q +1 0 0 1 -617.6537 -589.9686 cm BT -/F44 10.9091 Tf 623.831 634.681 Td [('RENUM)]TJ +/F46 10.9091 Tf 623.8306 634.681 Td[('RENUM)]TJ ET +1 0 0 1 658.8811 634.681 cm q -1 0 0 1 658.881 634.88 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4364 0.1992 l +S Q +1 0 0 1 -658.8811 -634.681 cm BT -/F44 10.9091 Tf 662.317 634.681 Td [(NONE')]TJ +/F46 10.9091 Tf 662.3174 634.681 Td[(NONE')]TJ ET +1 0 0 1 696.7318 589.9686 cm q -1 0 0 1 696.931 589.969 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 54.1968 l +S Q +1 0 0 1 -696.7318 -589.9686 cm BT -/F15 10.9091 Tf 702.909 634.681 Td [(Ro)28(w)-468(and)-467(column)-468(reordering)-467(of)-468(the)-468(lo)-27(cal)]TJ 0 -13.549 Td [(submatrices:)-410(n)1(o)-264(reordering,)-277(reordering)-264(ac-)]TJ 0 -13.549 Td [(cording)-540(to)-540(th)1(e)-540(global)-540(n)28(um)28(b)-28(ering)-540(of)-540(the)]TJ 0 -13.55 Td [(ro)28(ws)-334(and)-333(columns)-333(of)-333(the)-334(whole)-333(matrix.)]TJ +/F15 10.9091 Tf 702.9086 634.681 Td[(Ro)28(w)-468(and)-467(column)-467(reord)1(e)-1(ri)1(ng)-468(of)-467(th)1(e)-468(lo)-28(cal)]TJ 0 -13.5492 Td[(submatr)1(ic)-1(es)-1(:)-409(n)1(o)-264(reord)1(e)-1(r)1(ing,)-277(reord)1(e)-1(r)1(ing)-263(ac)-1(-)]TJ 0 -13.5492 Td[(cordi)1(ng)-540(to)-540(t)1(he)-540(global)-539(n)28(um)28(b)-27(e)-1(ri)1(ng)-540(of)-539(the)]TJ 0 -13.5492 Td[(ro)28(ws)-334(an)1(d)-333(c)-1(olu)1(mns)-334(of)-333(th)1(e)-334(whol)1(e)-334(m)-1(at)1(rix.)]TJ ET +1 0 0 1 907.1122 589.9686 cm q -1 0 0 1 907.311 589.969 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 54.1968 l +S Q +1 0 0 1 -614.4869 -0.3985 cm q -1 0 0 1 292.625 589.769 cm -[]0 d 0 J 0.398 w 0 0 m 614.686 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +614.6861 0.1992 l +S Q +1 0 0 1 112.7264 -30.4898 cm 0 g 0 G +1 0 0 1 -405.3517 -559.0803 cm BT -/F15 10.9091 Tf 405.352 559.08 Td [(T)83(able)-333(3:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(on)1(e)-1(-lev)28(el)-333(preconditioner)-333(used)-334(as)-333(smo)-28(other.)]TJ +/F15 10.9091 Tf 405.3518 559.0803 Td[(T)83(ab)1(le)-334(3:)-444(P)28(aramete)-1(r)1(s)-334(de\014n)1(ing)-333(th)1(e)-334(one-)-1(l)1(e)-1(v)28(el)-333(precondi)1(tioner)-333(used)-333(as)-334(s)-1(mo)-28(oth)1(e)-1(r)1(.)]TJ +ET +1 0 0 1 773.4733 559.0803 cm 0 g 0 G +1 0 0 1 112.7264 156.0149 cm 0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -Q +1 0 0 1 -593.5744 0 cm + Q +1 0 0 1 -206.2255 -593.5743 cm 0 g 0 G +1 0 0 1 0 -29.888 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -427 0 obj << +463 0 obj << /Type /Page -/Contents 428 0 R -/Resources 426 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 392 0 R +/Contents 464 0 R +/Resources 462 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 428 0 R >> endobj -429 0 obj << -/D [427 0 R /XYZ 86.4 740.002 null] +465 0 obj << +/D [463 0 R /XYZ 86.3998 740.0018 null] >> endobj -430 0 obj << -/D [427 0 R /XYZ -3930.538 559.035 null] +466 0 obj << +/D [463 0 R /XYZ 448.6851 572.6295 null] >> endobj -426 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F44 200 0 R /F25 176 0 R /F22 175 0 R /F18 173 0 R >> +462 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F46 219 0 R /F27 189 0 R /F24 186 0 R /F20 181 0 R >> /ProcSet [ /PDF /Text ] >> endobj -434 0 obj << -/Length 10169 +469 0 obj << +/Length 13114 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(6)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(25)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(25)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -q -0 1 -1 0 0 0 cm +1 0 0 1 206.2256 0 cm + q 0 -1 1 0 0 0 cm 0 g 0 G +1 0 0 1 291.3326 170.166 cm 0 g 0 G 0 g 0 G +1 0 0 1 -291.3326 -1.3947 cm q -1 0 0 1 0 168.97 cm -[]0 d 0 J 0.398 w 0 0 m 610.099 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +610.0989 0.1992 l +S Q +1 0 0 1 -0.1993 -13.5492 cm q -1 0 0 1 0 155.222 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q -1 0 0 1 -299.826 -121.521 cm +1 0 0 1 -299.6265 -870.3173 cm BT -/F44 10.9091 Tf 305.803 280.808 Td [(what)]TJ +/F46 10.9091 Tf 305.8034 874.3821 Td[(what)]TJ ET +1 0 0 1 420.3987 870.3173 cm q -1 0 0 1 420.598 276.743 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -420.3987 -870.3173 cm BT -/F41 10.9091 Tf 426.576 280.808 Td [(d)22(a)67(t)67(a)-378(type)]TJ +/F43 10.9091 Tf 426.5756 874.3821 Td[(d)22(a)66(t)67(a)-378(t)-1(ype)]TJ ET +1 0 0 1 539.3721 870.3173 cm q -1 0 0 1 539.571 276.743 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -539.3721 -870.3173 cm BT -/F44 10.9091 Tf 545.549 280.808 Td [(val)]TJ +/F46 10.9091 Tf 545.5489 874.3821 Td[(val)]TJ ET +1 0 0 1 619.3586 870.3173 cm q -1 0 0 1 619.558 276.743 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -619.3586 -870.3173 cm BT -/F41 10.9091 Tf 625.535 280.808 Td [(def)89(a)22(ul)67(t)]TJ +/F43 10.9091 Tf 625.5354 874.3821 Td[(def)89(a)22(ul)66(t)]TJ ET +1 0 0 1 699.345 870.3173 cm q -1 0 0 1 699.544 276.743 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -699.345 -870.3173 cm BT -/F41 10.9091 Tf 705.522 280.808 Td [(comments)]TJ +/F43 10.9091 Tf 705.5219 874.3821 Td[(com)1(ments)]TJ ET +1 0 0 1 909.7254 870.3173 cm q -1 0 0 1 909.925 276.743 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -609.8996 -0.3985 cm q -1 0 0 1 299.826 276.544 cm -[]0 d 0 J 0.398 w 0 0 m 610.099 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +610.0989 0.1992 l +S Q +1 0 0 1 -0.1993 -27.0984 cm q -1 0 0 1 299.826 249.246 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -299.6265 -842.8204 cm BT -/F44 10.9091 Tf 305.803 266.86 Td [(mld_aggr_alg_)]TJ +/F46 10.9091 Tf 305.8034 860.4344 Td[(mld_aggr_alg_)]TJ ET +1 0 0 1 420.3987 842.8204 cm q -1 0 0 1 420.598 249.246 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -420.3987 -842.8204 cm BT -/F44 10.9091 Tf 426.576 266.86 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 426.5756 860.4344 Td[(character\050len=*\051)]TJ ET +1 0 0 1 539.3721 842.8204 cm q -1 0 0 1 539.571 249.246 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -539.3721 -842.8204 cm BT -/F44 10.9091 Tf 545.549 266.86 Td [('DEC')]TJ +/F46 10.9091 Tf 545.5489 860.4344 Td[('DEC')]TJ ET +1 0 0 1 619.3586 842.8204 cm q -1 0 0 1 619.558 249.246 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -619.3586 -842.8204 cm BT -/F44 10.9091 Tf 625.535 266.86 Td [('DEC')]TJ +/F46 10.9091 Tf 625.5354 860.4344 Td[('DEC')]TJ ET +1 0 0 1 699.345 842.8204 cm q -1 0 0 1 699.544 249.246 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -699.345 -842.8204 cm BT -/F15 10.9091 Tf 705.522 266.86 Td [(Aggregation)-521(algorit)1(hm.)-1007(Curren)28(tly)83(,)-567(only)]TJ 0 -13.549 Td [(the)-333(decoupled)-334(aggregation)-333(is)-333(a)28(v)55(ailable.)]TJ +/F15 10.9091 Tf 705.5219 860.4344 Td[(Aggregation)-520(algor)1(ithm.)-1006(Curr)1(e)-1(n)29(tly)83(,)-567(on)1(ly)]TJ 0 -13.5492 Td[(th)1(e)-334(dec)-1(ou)1(pled)-333(aggregation)-333(i)1(s)-334(a)28(v)55(ai)1(labl)1(e)-1(.)]TJ ET +1 0 0 1 909.7254 842.8204 cm q -1 0 0 1 909.925 249.246 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -609.8996 -0.3985 cm q -1 0 0 1 299.826 249.047 cm -[]0 d 0 J 0.398 w 0 0 m 610.099 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +610.0989 0.1992 l +S Q +1 0 0 1 -0.1993 -27.0984 cm q -1 0 0 1 299.826 221.749 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -299.6265 -815.3235 cm BT -/F44 10.9091 Tf 305.803 239.363 Td [(mld_aggr_kind_)]TJ +/F46 10.9091 Tf 305.8034 832.9375 Td[(mld_aggr_kind_)]TJ ET +1 0 0 1 420.3987 815.3235 cm q -1 0 0 1 420.598 221.749 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -420.3987 -815.3235 cm BT -/F44 10.9091 Tf 426.576 239.363 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 426.5756 832.9375 Td[(character\050len=*\051)]TJ ET +1 0 0 1 539.3721 815.3235 cm q -1 0 0 1 539.571 221.749 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -539.3721 -815.3235 cm BT -/F44 10.9091 Tf 545.549 239.363 Td [('SMOOTH')]TJ 0 -13.549 Td [('RAW')]TJ +/F46 10.9091 Tf 545.5489 832.9375 Td[('SMOOTH')]TJ 0 -13.5492 Td[('RAW')]TJ ET +1 0 0 1 619.3586 815.3235 cm q -1 0 0 1 619.558 221.749 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -619.3586 -815.3235 cm BT -/F44 10.9091 Tf 625.535 239.363 Td [('SMOOTH')]TJ +/F46 10.9091 Tf 625.5354 832.9375 Td[('SMOOTH')]TJ ET +1 0 0 1 699.345 815.3235 cm q -1 0 0 1 699.544 221.749 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -699.345 -815.3235 cm BT -/F15 10.9091 Tf 705.522 239.363 Td [(T)28(yp)-28(e)-380(of)-379(aggregation:)-537(smo)-28(othed,)-391(ra)28(w)-380(\050i.e.)]TJ 0 -13.549 Td [(using)-333(the)-334(ten)28(tativ)28(e)-333(prolongator\051.)]TJ +/F15 10.9091 Tf 705.5219 832.9375 Td[(T)28(yp)-28(e)-380(of)-379(aggr)1(e)-1(gati)1(on:)-537(sm)-1(o)-27(othed,)-391(r)1(a)27(w)-379(\050i.e.)]TJ 0 -13.5492 Td[(usin)1(g)-334(th)1(e)-334(ten)28(tativ)28(e)-333(prol)1(ongator)1(\051.)]TJ ET +1 0 0 1 909.7254 815.3235 cm q -1 0 0 1 909.925 221.749 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -609.8996 -0.3985 cm q -1 0 0 1 299.826 221.55 cm -[]0 d 0 J 0.398 w 0 0 m 610.099 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +610.0989 0.1992 l +S Q +1 0 0 1 -0.1993 -27.0983 cm q -1 0 0 1 299.826 194.252 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -299.6265 -787.8267 cm BT -/F44 10.9091 Tf 305.803 211.866 Td [(mld_aggr_thresh_)]TJ +/F46 10.9091 Tf 305.8034 805.4406 Td[(mld_aggr_thresh_)]TJ ET +1 0 0 1 420.3987 787.8267 cm q -1 0 0 1 420.598 194.252 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -420.3987 -787.8267 cm BT -/F44 10.9091 Tf 426.576 211.866 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ +/F46 10.9091 Tf 426.5756 805.4407 Td[(real\050)]TJ/F20 10.9091 Tf 28.636 0 Td[(kind)]TJ ET +1 0 0 1 475.9532 805.4407 cm q -1 0 0 1 475.953 212.066 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -475.9532 -805.4407 cm BT -/F18 10.9091 Tf 479.299 211.866 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ +/F20 10.9091 Tf 479.2987 805.4407 Td[(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.5678 0 Td[(\051)]TJ ET +1 0 0 1 539.3721 787.8267 cm q -1 0 0 1 539.571 194.252 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -539.3721 -787.8267 cm BT -/F15 10.9091 Tf 545.549 211.866 Td [(An)28(y)-311(real)-311(n)27(um.)]TJ/F25 10.9091 Tf 0 -13.549 Td [(2)]TJ/F15 10.9091 Tf 10.303 0 Td [([0)]TJ/F22 10.9091 Tf 8.485 0 Td [(;)]TJ/F15 10.9091 Tf 4.848 0 Td [(1])]TJ +/F15 10.9091 Tf 545.5489 805.4407 Td[(An)28(y)-311(r)1(e)-1(al)-311(n)28(u)1(m.)]TJ/F27 10.9091 Tf 0 -13.5492 Td[(2)]TJ/F15 10.9091 Tf 10.303 0 Td[([0)]TJ/F24 10.9091 Tf 8.4849 0 Td[(;)]TJ/F15 10.9091 Tf 4.8484 0 Td[(1])]TJ ET +1 0 0 1 619.3586 787.8267 cm q -1 0 0 1 619.558 194.252 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -619.3586 -787.8267 cm BT -/F15 10.9091 Tf 625.535 211.866 Td [(0)]TJ +/F15 10.9091 Tf 625.5354 805.4407 Td[(0)]TJ ET +1 0 0 1 699.345 787.8267 cm q -1 0 0 1 699.544 194.252 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -699.345 -787.8267 cm BT -/F15 10.9091 Tf 705.522 211.866 Td [(Threshold)]TJ/F22 10.9091 Tf 51.267 0 Td [(\022)]TJ/F15 10.9091 Tf 8.721 0 Td [(in)-302(the)-302(aggregation)-303(algorit)1(hm.)]TJ +/F15 10.9091 Tf 705.5219 805.4407 Td[(Thr)1(e)-1(shold)]TJ/F24 10.9091 Tf 51.2669 0 Td[(\022)]TJ/F15 10.9091 Tf 8.7213 0 Td[(in)-302(t)1(he)-303(aggr)1(e)-1(gati)1(on)-302(algori)1(thm.)]TJ ET +1 0 0 1 909.7254 787.8267 cm q -1 0 0 1 909.925 194.252 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -609.8996 -0.3985 cm q -1 0 0 1 299.826 194.053 cm -[]0 d 0 J 0.398 w 0 0 m 610.099 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +610.0989 0.1992 l +S Q +1 0 0 1 -0.1993 -67.746 cm q -1 0 0 1 299.826 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -299.6265 -719.6822 cm BT -/F44 10.9091 Tf 305.803 184.369 Td [(mld_aggr_omega_alg_)]TJ +/F46 10.9091 Tf 305.8034 777.9438 Td[(mld_aggr_omega_alg_)]TJ ET +1 0 0 1 420.3987 719.6822 cm q -1 0 0 1 420.598 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -420.3987 -719.6822 cm BT -/F44 10.9091 Tf 426.576 184.369 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 426.5756 777.9438 Td[(character\050len=*\051)]TJ ET +1 0 0 1 539.3721 719.6822 cm q -1 0 0 1 539.571 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -539.3721 -719.6822 cm BT -/F44 10.9091 Tf 545.549 184.369 Td [('EIG)]TJ +/F46 10.9091 Tf 545.5489 777.9438 Td[('EIG)]TJ ET +1 0 0 1 569.145 777.9438 cm q -1 0 0 1 569.145 184.569 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4364 0.1992 l +S Q +1 0 0 1 -569.145 -777.9438 cm BT -/F44 10.9091 Tf 572.581 184.369 Td [(EST')]TJ -27.032 -13.549 Td [('USER)]TJ +/F46 10.9091 Tf 572.5813 777.9438 Td[(EST')]TJ -27.0324 -13.5492 Td[('USER)]TJ ET +1 0 0 1 574.8722 764.3946 cm q -1 0 0 1 574.872 171.02 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4364 0.1992 l +S Q +1 0 0 1 -574.8722 -764.3946 cm BT -/F44 10.9091 Tf 578.309 170.82 Td [(CHOICE')]TJ +/F46 10.9091 Tf 578.3085 764.3946 Td[(CHOICE')]TJ ET +1 0 0 1 619.3586 719.6822 cm q -1 0 0 1 619.558 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -619.3586 -719.6822 cm BT -/F44 10.9091 Tf 625.535 184.369 Td [('EIG)]TJ +/F46 10.9091 Tf 625.5354 777.9438 Td[('EIG)]TJ ET +1 0 0 1 649.1315 777.9438 cm q -1 0 0 1 649.131 184.569 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4364 0.1992 l +S Q +1 0 0 1 -649.1315 -777.9438 cm BT -/F44 10.9091 Tf 652.568 184.369 Td [(EST')]TJ +/F46 10.9091 Tf 652.5678 777.9438 Td[(EST')]TJ ET +1 0 0 1 699.345 719.6822 cm q -1 0 0 1 699.544 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -699.345 -719.6822 cm BT -/F15 10.9091 Tf 705.522 184.369 Td [(Ho)28(w)-625(the)-624(damping)-625(parameter)]TJ/F22 10.9091 Tf 153.374 0 Td [(!)]TJ/F15 10.9091 Tf 13.995 0 Td [(in)-625(th)1(e)]TJ -167.369 -13.549 Td [(smo)-28(othed)-738(aggregation)-738(should)-738(b)-28(e)-738(com-)]TJ 0 -13.549 Td [(puted:)-453(either)-338(via)-338(an)-338(estimate)-338(of)-338(the)-337(s)-1(p)-27(ec-)]TJ 0 -13.549 Td [(tral)-337(radius)-338(of)]TJ/F22 10.9091 Tf 66.016 0 Td [(D)]TJ/F26 7.9701 Tf 9.335 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)-339(or)-337(explicily)-338(sp)-27(eci\014ed)]TJ -94.852 -13.549 Td [(b)28(y)-333(the)-334(user.)]TJ +/F15 10.9091 Tf 705.5219 777.9438 Td[(Ho)28(w)-625(th)1(e)-625(dampin)1(g)-625(p)1(arame)-1(ter)]TJ/F24 10.9091 Tf 153.3744 0 Td[(!)]TJ/F15 10.9091 Tf 13.9951 0 Td[(in)-624(th)1(e)]TJ -167.3695 -13.5492 Td[(sm)-1(o)-28(ot)1(hed)-738(aggregation)-738(shou)1(ld)-738(b)-27(e)-739(com)-1(-)]TJ 0 -13.5492 Td[(pu)1(ted:)-453(e)-1(i)1(ther)-338(vi)1(a)-338(an)-338(es)-1(ti)1(m)-1(ate)-338(of)-337(the)-338(sp)-28(ec)-1(-)]TJ 0 -13.5492 Td[(tral)-337(rad)1(iu)1(s)-338(of)]TJ/F24 10.9091 Tf 66.0164 0 Td[(D)]TJ/F28 7.9701 Tf 9.3348 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(,)-338(or)-338(exp)1(licily)-337(s)-1(p)-27(ec)-1(i\014)1(e)-1(d)]TJ -94.8518 -13.5492 Td[(b)28(y)-333(th)1(e)-334(use)-1(r)1(.)]TJ ET +1 0 0 1 909.7254 719.6822 cm q -1 0 0 1 909.925 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -609.8996 -0.3985 cm q -1 0 0 1 299.826 125.909 cm -[]0 d 0 J 0.398 w 0 0 m 610.099 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +610.0989 0.1992 l +S Q +1 0 0 1 -0.1993 -40.6476 cm q -1 0 0 1 299.826 85.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -299.6265 -678.6361 cm BT -/F44 10.9091 Tf 305.803 116.225 Td [(mld_aggr_eig_)]TJ +/F46 10.9091 Tf 305.8034 709.7993 Td[(mld_aggr_eig_)]TJ ET +1 0 0 1 420.3987 678.6361 cm q -1 0 0 1 420.598 85.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -420.3987 -678.6361 cm BT -/F44 10.9091 Tf 426.576 116.225 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 426.5756 709.7993 Td[(character\050len=*\051)]TJ ET +1 0 0 1 539.3721 678.6361 cm q -1 0 0 1 539.571 85.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -539.3721 -678.6361 cm BT -/F44 10.9091 Tf 545.549 116.225 Td [('A)]TJ +/F46 10.9091 Tf 545.5489 709.7993 Td[('A)]TJ ET +1 0 0 1 557.6906 709.7993 cm q -1 0 0 1 557.691 116.424 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4364 0.1992 l +S Q +1 0 0 1 -557.6906 -709.7993 cm BT -/F44 10.9091 Tf 561.127 116.225 Td [(NORMI')]TJ +/F46 10.9091 Tf 561.1269 709.7993 Td[(NORMI')]TJ ET +1 0 0 1 619.3586 678.6361 cm q -1 0 0 1 619.558 85.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -619.3586 -678.6361 cm BT -/F44 10.9091 Tf 625.535 116.225 Td [('A)]TJ +/F46 10.9091 Tf 625.5354 709.7993 Td[('A)]TJ ET +1 0 0 1 637.677 709.7993 cm q -1 0 0 1 637.677 116.424 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4364 0.1992 l +S Q +1 0 0 1 -637.677 -709.7993 cm BT -/F44 10.9091 Tf 641.113 116.225 Td [(NORMI')]TJ +/F46 10.9091 Tf 641.1134 709.7993 Td[(NORMI')]TJ ET +1 0 0 1 699.345 678.6361 cm q -1 0 0 1 699.544 85.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -699.345 -678.6361 cm BT -/F15 10.9091 Tf 705.522 116.225 Td [(Ho)28(w)-565(to)-565(estimate)-565(the)-565(sp)-27(ec)-1(tr)1(al)-565(radius)-565(of)]TJ/F22 10.9091 Tf 0 -13.549 Td [(D)]TJ/F26 7.9701 Tf 9.335 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.733 -3.959 Td [(A)]TJ/F15 10.9091 Tf 8.181 0 Td [(.)-710(Curren)27(tly)-422(onl)1(y)-422(the)-422(in\014nit)27(y)-422(n)1(orm)]TJ -28.835 -13.549 Td [(estimate)-333(is)-334(a)28(v)56(ailable.)]TJ +/F15 10.9091 Tf 705.5219 709.7993 Td[(Ho)28(w)-565(to)-565(es)-1(timate)-565(th)1(e)-566(sp)-28(ectral)-565(r)1(adiu)1(s)-565(of)]TJ/F24 10.9091 Tf 0 -13.5492 Td[(D)]TJ/F28 7.9701 Tf 9.3348 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(A)]TJ/F15 10.9091 Tf 8.1819 0 Td[(.)-710(Curr)1(e)-1(n)28(t)1(ly)-422(onl)1(y)-422(the)-422(in)1(\014n)1(it)28(y)-422(nor)1(m)]TJ -28.8355 -13.5492 Td[(es)-1(timate)-334(i)1(s)-334(a)28(v)55(ai)1(labl)1(e)-1(.)]TJ ET +1 0 0 1 909.7254 678.6361 cm q -1 0 0 1 909.925 85.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 40.6476 l +S Q +1 0 0 1 -609.8996 -0.3985 cm q -1 0 0 1 299.826 84.863 cm -[]0 d 0 J 0.398 w 0 0 m 610.099 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +610.0989 0.1992 l +S Q +1 0 0 1 -0.1993 -94.8443 cm q -1 0 0 1 299.826 -10.181 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -299.6265 -583.3933 cm BT -/F44 10.9091 Tf 305.803 75.179 Td [(mld_aggr_omega_val_)]TJ +/F46 10.9091 Tf 305.8034 668.7532 Td[(mld_aggr_omega_val_)]TJ ET +1 0 0 1 420.3987 583.3933 cm q -1 0 0 1 420.598 -10.181 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -420.3987 -583.3933 cm BT -/F44 10.9091 Tf 426.576 75.179 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ +/F46 10.9091 Tf 426.5756 668.7532 Td[(real\050)]TJ/F20 10.9091 Tf 28.636 0 Td[(kind)]TJ ET +1 0 0 1 475.9532 668.7532 cm q -1 0 0 1 475.953 75.378 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -475.9532 -668.7532 cm BT -/F18 10.9091 Tf 479.299 75.179 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ +/F20 10.9091 Tf 479.2987 668.7532 Td[(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.5678 0 Td[(\051)]TJ ET +1 0 0 1 539.3721 583.3933 cm q -1 0 0 1 539.571 -10.181 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -539.3721 -583.3933 cm BT -/F15 10.9091 Tf 545.549 75.179 Td [(An)28(y)-486(nonnega-)]TJ 0 -13.549 Td [(tiv)28(e)-334(real)-333(n)28(um.)]TJ +/F15 10.9091 Tf 545.5489 668.7532 Td[(An)28(y)-486(n)1(onn)1(e)-1(ga-)]TJ 0 -13.5492 Td[(tiv)28(e)-333(re)-1(al)-333(n)29(um.)]TJ ET +1 0 0 1 619.3586 583.3933 cm q -1 0 0 1 619.558 -10.181 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -619.3586 -583.3933 cm BT -/F15 10.9091 Tf 625.535 75.179 Td [(4)]TJ/F22 10.9091 Tf 5.455 0 Td [(=)]TJ/F15 10.9091 Tf 5.454 0 Td [(\0503)]TJ/F22 10.9091 Tf 9.697 0 Td [(\032)]TJ/F15 10.9091 Tf 5.641 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(D)]TJ/F26 7.9701 Tf 9.335 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.733 -3.959 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(\051\051)]TJ +/F15 10.9091 Tf 625.5354 668.7532 Td[(4)]TJ/F24 10.9091 Tf 5.4546 0 Td[(=)]TJ/F15 10.9091 Tf 5.4545 0 Td[(\0503)]TJ/F24 10.9091 Tf 9.697 0 Td[(\032)]TJ/F15 10.9091 Tf 5.6402 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(D)]TJ/F28 7.9701 Tf 9.3349 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(\051\051)]TJ ET +1 0 0 1 699.345 583.3933 cm q -1 0 0 1 699.544 -10.181 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -699.345 -583.3933 cm BT -/F15 10.9091 Tf 705.522 75.179 Td [(Damping)-534(parameter)]TJ/F22 10.9091 Tf 103.691 0 Td [(!)]TJ/F15 10.9091 Tf 13.012 0 Td [(in)-534(the)-535(smo)-28(othed)]TJ -116.703 -13.549 Td [(aggregation)-576(algorithm.)-1173(It)-576(m)27(u)1(s)-1(t)-576(b)-27(e)-577(set)]TJ 0 -13.549 Td [(b)28(y)-589(the)-589(user)-589(if)]TJ/F44 10.9091 Tf 78.215 0 Td [(USER_CHOICE)]TJ/F15 10.9091 Tf 69.421 0 Td [(w)28(as)-589(sp)-28(eci-)]TJ -147.636 -13.55 Td [(\014ed)-353(for)]TJ/F44 10.9091 Tf 37.733 0 Td [(mld_aggr_omega_alg_)]TJ/F15 10.9091 Tf 108.817 0 Td [(,)-358(otherwise)]TJ -146.55 -13.549 Td [(it)-472(is)-472(computed)-472(b)28(y)-472(the)-472(library)83(,)-506(using)-472(the)]TJ 0 -13.549 Td [(selected)-566(estimate)-565(of)-566(the)-565(s)-1(p)-27(ectral)-566(radius)]TJ/F22 10.9091 Tf 0 -13.549 Td [(\032)]TJ/F15 10.9091 Tf 5.64 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(D)]TJ/F26 7.9701 Tf 9.335 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(\051)-333(of)]TJ/F22 10.9091 Tf 20.303 0 Td [(D)]TJ/F26 7.9701 Tf 9.335 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.733 -3.959 Td [(A)]TJ/F15 10.9091 Tf 8.181 0 Td [(.)]TJ +/F15 10.9091 Tf 705.5219 668.7532 Td[(Dampin)1(g)-535(p)1(arame)-1(t)1(e)-1(r)]TJ/F24 10.9091 Tf 103.6913 0 Td[(!)]TJ/F15 10.9091 Tf 13.0123 0 Td[(in)-534(th)1(e)-535(s)-1(mo)-28(oth)1(e)-1(d)]TJ -116.7036 -13.5492 Td[(aggregation)-576(al)1(gorith)1(m)-1(.)-1172(It)-577(m)28(ust)-576(b)-28(e)-576(s)-1(et)]TJ 0 -13.5492 Td[(b)28(y)-589(t)1(he)-589(use)-1(r)-588(if)]TJ/F46 10.9091 Tf 78.2151 0 Td[(USER_CHOICE)]TJ/F15 10.9091 Tf 69.4215 0 Td[(w)28(as)-590(sp)-28(ec)-1(i)1(-)]TJ -147.6366 -13.5492 Td[(\014ed)-353(f)1(or)]TJ/F46 10.9091 Tf 37.7332 0 Td[(mld_aggr_omega_alg_)]TJ/F15 10.9091 Tf 108.817 0 Td[(,)-358(oth)1(e)-1(r)1(w)-1(i)1(s)-1(e)]TJ -146.5502 -13.5492 Td[(it)-472(i)1(s)-473(com)-1(p)1(uted)-472(b)28(y)-471(the)-472(lib)1(rary)84(,)-507(u)1(s)-1(i)1(ng)-472(the)]TJ 0 -13.5492 Td[(se)-1(lec)-1(t)1(e)-1(d)-565(es)-1(timate)-566(of)-565(th)1(e)-566(s)-1(p)-27(e)-1(ctral)-565(rad)1(ius)]TJ/F24 10.9091 Tf 0 -13.5492 Td[(\032)]TJ/F15 10.9091 Tf 5.6402 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(D)]TJ/F28 7.9701 Tf 9.3349 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(\051)-333(of)]TJ/F24 10.9091 Tf 20.303 0 Td[(D)]TJ/F28 7.9701 Tf 9.3349 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(.)]TJ ET +1 0 0 1 909.7254 583.3933 cm q -1 0 0 1 909.925 -10.181 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -609.8996 -0.3985 cm q -1 0 0 1 299.826 -10.38 cm -[]0 d 0 J 0.398 w 0 0 m 610.099 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +610.0989 0.1992 l +S Q +1 0 0 1 159.9537 -30.4898 cm 0 g 0 G +1 0 0 1 -459.7795 -552.505 cm BT -/F15 10.9091 Tf 459.779 -41.069 Td [(T)83(able)-333(4:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(aggregation)-333(algorithm.)]TJ +/F15 10.9091 Tf 459.7795 552.505 Td[(T)83(ab)1(le)-334(4:)-444(P)28(aramete)-1(r)1(s)-334(de\014n)1(ing)-333(th)1(e)-334(aggregation)-333(algor)1(ithm.)]TJ +ET +1 0 0 1 733.4464 552.505 cm 0 g 0 G +1 0 0 1 159.9537 162.5903 cm 0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -Q +1 0 0 1 -593.5743 0 cm + Q +1 0 0 1 -206.2256 -593.5744 cm 0 g 0 G +1 0 0 1 0 -29.8879 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -433 0 obj << +468 0 obj << /Type /Page -/Contents 434 0 R -/Resources 432 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R -/Annots [ 431 0 R ] +/Contents 469 0 R +/Resources 467 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 473 0 R +/Annots [ 471 0 R ] >> endobj -431 0 obj << +471 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -435 0 obj << -/D [433 0 R /XYZ 93.6 740.002 null] +470 0 obj << +/D [468 0 R /XYZ 93.6002 740.0018 null] >> endobj -436 0 obj << -/D [433 0 R /XYZ 448.665 4405.505 null] +472 0 obj << +/D [468 0 R /XYZ 503.1128 566.0541 null] >> endobj -432 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F44 200 0 R /F18 173 0 R /F25 176 0 R /F22 175 0 R /F26 272 0 R /F20 273 0 R >> +467 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F46 219 0 R /F20 181 0 R /F27 189 0 R /F24 186 0 R /F28 293 0 R /F22 296 0 R >> /ProcSet [ /PDF /Text ] >> endobj -440 0 obj << -/Length 9038 +476 0 obj << +/Length 11673 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(26)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(26)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -q -0 -1 1 0 0 0 cm +1 0 0 1 206.2255 0 cm + q 0 -1 1 0 0 0 cm 0 g 0 G +1 0 0 1 291.3327 163.3914 cm 0 g 0 G 0 g 0 G +1 0 0 1 -291.3327 -1.3947 cm q -1 0 0 1 0 162.196 cm -[]0 d 0 J 0.398 w 0 0 m 612.702 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +612.7021 0.1992 l +S Q +1 0 0 1 -0.1992 -13.5492 cm q -1 0 0 1 0 148.448 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q -1 0 0 1 -292.625 -715.095 cm +1 0 0 1 -292.4261 -863.5427 cm BT -/F44 10.9091 Tf 298.603 867.608 Td [(what)]TJ +/F46 10.9091 Tf 298.6029 867.6075 Td[(what)]TJ ET +1 0 0 1 418.9255 863.5427 cm q -1 0 0 1 419.125 863.543 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -418.9255 -863.5427 cm BT -/F41 10.9091 Tf 425.102 867.608 Td [(d)22(a)67(t)66(a)-377(type)]TJ +/F43 10.9091 Tf 425.1023 867.6075 Td[(d)22(a)66(t)67(a)-378(t)-1(ype)]TJ ET +1 0 0 1 537.8988 863.5427 cm q -1 0 0 1 538.098 863.543 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -537.8988 -863.5427 cm BT -/F44 10.9091 Tf 544.076 867.608 Td [(val)]TJ +/F46 10.9091 Tf 544.0757 867.6075 Td[(val)]TJ ET +1 0 0 1 640.5626 863.5427 cm q -1 0 0 1 640.762 863.543 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -640.5626 -863.5427 cm BT -/F41 10.9091 Tf 646.739 867.608 Td [(def)89(a)22(ul)67(t)]TJ +/F43 10.9091 Tf 646.7394 867.6075 Td[(def)89(a)22(ul)66(t)]TJ ET +1 0 0 1 694.7478 863.5427 cm q -1 0 0 1 694.947 863.543 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -694.7478 -863.5427 cm BT -/F41 10.9091 Tf 700.925 867.608 Td [(comments)]TJ +/F43 10.9091 Tf 700.9247 867.6075 Td[(com)1(ments)]TJ ET +1 0 0 1 905.1282 863.5427 cm q -1 0 0 1 905.327 863.543 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 13.5492 l +S Q +1 0 0 1 -612.5029 -0.3985 cm q -1 0 0 1 292.625 863.343 cm -[]0 d 0 J 0.398 w 0 0 m 612.702 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +612.7021 0.1992 l +S Q +1 0 0 1 -0.1992 -27.0984 cm q -1 0 0 1 292.625 836.046 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -292.4261 -836.0458 cm BT -/F44 10.9091 Tf 298.603 853.66 Td [(mld_coarse_mat_)]TJ +/F46 10.9091 Tf 298.6029 853.6598 Td[(mld_coarse_mat_)]TJ ET +1 0 0 1 418.9255 836.0458 cm q -1 0 0 1 419.125 836.046 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -418.9255 -836.0458 cm BT -/F44 10.9091 Tf 425.102 853.66 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 425.1023 853.6598 Td[(character\050len=*\051)]TJ ET +1 0 0 1 537.8988 836.0458 cm q -1 0 0 1 538.098 836.046 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -537.8988 -836.0458 cm BT -/F44 10.9091 Tf 544.076 853.66 Td [('DISTR')]TJ 0 -13.549 Td [('REPL')]TJ +/F46 10.9091 Tf 544.0757 853.6598 Td[('DISTR')]TJ 0 -13.5492 Td[('REPL')]TJ ET +1 0 0 1 640.5626 836.0458 cm q -1 0 0 1 640.762 836.046 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -640.5626 -836.0458 cm BT -/F44 10.9091 Tf 646.739 853.66 Td [('DISTR')]TJ +/F46 10.9091 Tf 646.7394 853.6598 Td[('DISTR')]TJ ET +1 0 0 1 694.7478 836.0458 cm q -1 0 0 1 694.947 836.046 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -694.7478 -836.0458 cm BT -/F15 10.9091 Tf 700.925 853.66 Td [(Coarsest)-483(matrix:)-743(distributed)-483(among)-483(the)]TJ 0 -13.549 Td [(pro)-28(cessors)-333(or)-333(re)-1(p)1(licate)-1(d)-333(on)-333(eac)28(h)-334(of)-333(them.)]TJ +/F15 10.9091 Tf 700.9247 853.6598 Td[(Coarse)-1(st)-483(matrix)1(:)-743(distrib)1(uted)-482(am)-1(on)1(g)-483(the)]TJ 0 -13.5492 Td[(pr)1(o)-28(ce)-1(ss)-1(or)1(s)-334(or)-333(repli)1(c)-1(ated)-333(on)-333(eac)27(h)-333(of)-333(th)1(e)-1(m.)]TJ ET +1 0 0 1 905.1282 836.0458 cm q -1 0 0 1 905.327 836.046 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -612.5029 -0.3985 cm q -1 0 0 1 292.625 835.847 cm -[]0 d 0 J 0.398 w 0 0 m 612.702 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +612.7021 0.1992 l +S Q +1 0 0 1 -0.1992 -94.8443 cm q -1 0 0 1 292.625 740.803 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -292.4261 -740.803 cm BT -/F44 10.9091 Tf 298.603 826.163 Td [(mld_coarse_solve_)]TJ +/F46 10.9091 Tf 298.6029 826.1629 Td[(mld_coarse_solve_)]TJ ET +1 0 0 1 418.9255 740.803 cm q -1 0 0 1 419.125 740.803 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -418.9255 -740.803 cm BT -/F44 10.9091 Tf 425.102 826.163 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 425.1023 826.1629 Td[(character\050len=*\051)]TJ ET +1 0 0 1 537.8988 740.803 cm q -1 0 0 1 538.098 740.803 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -537.8988 -740.803 cm BT -/F44 10.9091 Tf 544.076 826.163 Td [('BJAC')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ 0 -13.55 Td [('SLUDIST')]TJ +/F46 10.9091 Tf 544.0757 826.1629 Td[('BJAC')]TJ 0 -13.5492 Td[('UMF')]TJ 0 -13.5492 Td[('SLU')]TJ 0 -13.5492 Td[('SLUDIST')]TJ ET +1 0 0 1 640.5626 740.803 cm q -1 0 0 1 640.762 740.803 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -640.5626 -740.803 cm BT -/F44 10.9091 Tf 646.739 826.163 Td [('BJAC')]TJ +/F46 10.9091 Tf 646.7394 826.1629 Td[('BJAC')]TJ ET +1 0 0 1 694.7478 740.803 cm q -1 0 0 1 694.947 740.803 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -694.7478 -740.803 cm BT -/F15 10.9091 Tf 700.925 826.163 Td [(Solv)28(er)-504(used)-504(at)-504(the)-504(coarsest)-504(lev)28(el:)-786(blo)-28(c)28(k)]TJ 0 -13.549 Td [(Jacobi,)-517(sequen)28(tial)-481(LU)-480(from)-480(UMFP)83(A)28(CK,)]TJ 0 -13.549 Td [(sequen)28(tial)-369(LU)-369(from)-368(Sup)-28(erLU,)-369(distributed)]TJ 0 -13.55 Td [(LU)-701(from)-702(Sup)-28(erLU)]TJ +/F15 10.9091 Tf 700.9247 826.1629 Td[(Sol)1(v)28(e)-1(r)-503(use)-1(d)-503(at)-504(the)-504(c)-1(oar)1(s)-1(es)-1(t)-503(le)-1(v)28(el:)-785(blo)-28(c)28(k)]TJ 0 -13.5492 Td[(Jacobi,)-517(se)-1(q)1(uen)28(tial)-480(LU)-480(from)-480(UMFP)84(A)28(CK,)]TJ 0 -13.5492 Td[(se)-1(qu)1(e)-1(n)29(tial)-369(LU)-368(from)-369(S)1(up)-27(e)-1(r)1(LU,)-369(d)1(is)-1(tr)1(ibu)1(ted)]TJ 0 -13.5492 Td[(LU)-701(from)-702(S)1(up)-27(e)-1(r)1(LU)]TJ ET +1 0 0 1 796.643 785.5153 cm q -1 0 0 1 796.643 785.715 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.2728 0.1992 l +S Q +1 0 0 1 -796.643 -785.5153 cm BT -/F15 10.9091 Tf 799.916 785.515 Td [(Dist.)]TJ/F44 10.9091 Tf 39.844 0 Td [('BJAC')]TJ/F15 10.9091 Tf 42.014 0 Td [(and)]TJ/F44 10.9091 Tf -180.849 -13.549 Td [('SLUDIST')]TJ/F15 10.9091 Tf 55.417 0 Td [(require)-355(the)-355(coarsest)-355(matrix)-355(to)]TJ -55.417 -13.549 Td [(b)-28(e)-297(distributed,)-304(while)]TJ/F44 10.9091 Tf 101.101 0 Td [('UMF')]TJ/F15 10.9091 Tf 31.876 0 Td [(and)]TJ/F44 10.9091 Tf 20.815 0 Td [('SLU')]TJ/F15 10.9091 Tf 31.875 0 Td [(re-)]TJ -185.667 -13.549 Td [(quire)-333(it)-334(to)-333(b)-28(e)-333(replicated.)]TJ +/F15 10.9091 Tf 799.9158 785.5153 Td[(Dist.)]TJ/F46 10.9091 Tf 39.844 0 Td[('BJAC')]TJ/F15 10.9091 Tf 42.0143 0 Td[(and)]TJ/F46 10.9091 Tf -180.8494 -13.5492 Td[('SLUDIST')]TJ/F15 10.9091 Tf 55.4177 0 Td[(requ)1(ire)-355(the)-355(c)-1(oar)1(s)-1(es)-1(t)-355(matri)1(x)-355(to)]TJ -55.4177 -13.5492 Td[(b)-27(e)-298(d)1(is)-1(t)1(rib)1(uted,)-304(whi)1(le)]TJ/F46 10.9091 Tf 101.1015 0 Td[('UMF')]TJ/F15 10.9091 Tf 31.8753 0 Td[(and)]TJ/F46 10.9091 Tf 20.8155 0 Td[('SLU')]TJ/F15 10.9091 Tf 31.8753 0 Td[(re-)]TJ -185.6676 -13.5492 Td[(qu)1(ire)-334(i)1(t)-334(t)1(o)-334(b)-27(e)-334(repl)1(ic)-1(at)1(e)-1(d)1(.)]TJ ET +1 0 0 1 905.1282 740.803 cm q -1 0 0 1 905.327 740.803 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 94.8444 l +S Q +1 0 0 1 -612.5029 -0.3985 cm q -1 0 0 1 292.625 740.604 cm -[]0 d 0 J 0.398 w 0 0 m 612.702 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +612.7021 0.1992 l +S Q +1 0 0 1 -0.1992 -67.746 cm q -1 0 0 1 292.625 672.659 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -292.4261 -672.6585 cm BT -/F44 10.9091 Tf 298.603 730.92 Td [(mld_coarse_subsolve_)]TJ +/F46 10.9091 Tf 298.6029 730.9201 Td[(mld_coarse_subsolve_)]TJ ET +1 0 0 1 418.9255 672.6585 cm q -1 0 0 1 419.125 672.659 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -418.9255 -672.6585 cm BT -/F44 10.9091 Tf 425.102 730.92 Td [(character\050len=*\051)]TJ +/F46 10.9091 Tf 425.1023 730.9201 Td[(character\050len=*\051)]TJ ET +1 0 0 1 537.8988 672.6585 cm q -1 0 0 1 538.098 672.659 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -537.8988 -672.6585 cm BT -/F44 10.9091 Tf 544.076 730.92 Td [('ILU')]TJ 0 -13.549 Td [('MILU')]TJ 0 -13.549 Td [('ILUT')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.55 Td [('SLU')]TJ +/F46 10.9091 Tf 544.0757 730.9201 Td[('ILU')]TJ 0 -13.5492 Td[('MILU')]TJ 0 -13.5492 Td[('ILUT')]TJ 0 -13.5492 Td[('UMF')]TJ 0 -13.5492 Td[('SLU')]TJ ET +1 0 0 1 640.5626 672.6585 cm q -1 0 0 1 640.762 672.659 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -640.5626 -672.6585 cm BT -/F44 10.9091 Tf 646.739 730.92 Td [('UMF')]TJ +/F46 10.9091 Tf 646.7394 730.9201 Td[('UMF')]TJ ET +1 0 0 1 694.7478 672.6585 cm q -1 0 0 1 694.947 672.659 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -694.7478 -672.6585 cm BT -/F15 10.9091 Tf 700.925 730.92 Td [(Solv)28(er)-243(for)-242(the)-242(diagonal)-243(blo)-28(c)28(ks)-242(of)-243(the)-242(coarse)]TJ 0 -13.549 Td [(matrix,)-609(in)-555(case)-554(the)-554(blo)-28(c)28(k)-554(Jacobi)-555(solv)28(er)]TJ 0 -13.549 Td [(is)-360(c)28(hosen)-361(as)-360(coarsest-lev)28(el)-360(solv)27(er:)-498(ILU\050)]TJ/F22 10.9091 Tf 185.663 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)]TJ -191.152 -13.549 Td [(MILU\050)]TJ/F22 10.9091 Tf 33.182 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-271(ILU\050)]TJ/F22 10.9091 Tf 33.416 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.277 0 Td [(\051,)-271(LU)-256(from)-256(UMFP)83(A)28(CK,)]TJ -86.363 -13.55 Td [(LU)-333(from)-334(Sup)-27(erLU,)-334(plu)1(s)-334(triangular)-333(solv)28(e.)]TJ +/F15 10.9091 Tf 700.9247 730.9201 Td[(Sol)1(v)28(e)-1(r)-242(f)1(or)-243(th)1(e)-243(di)1(agonal)-242(bl)1(o)-28(c)27(ks)-243(of)-242(th)1(e)-243(coars)-1(e)]TJ 0 -13.5492 Td[(matrix)1(,)-610(i)1(n)-554(c)-1(ase)-555(th)1(e)-555(bl)1(o)-28(c)27(k)-554(Jacobi)-554(solv)28(er)]TJ 0 -13.5492 Td[(is)-360(c)27(hosen)-360(as)-361(coarse)-1(st-le)-1(v)28(el)-360(solv)28(e)-1(r)1(:)-498(ILU\050)]TJ/F24 10.9091 Tf 185.6638 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)]TJ -191.1524 -13.5492 Td[(MILU\050)]TJ/F24 10.9091 Tf 33.1819 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)-271(ILU\050)]TJ/F24 10.9091 Tf 33.4162 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051,)-271(LU)-256(fr)1(om)-257(UM)1(FP)84(A)27(CK,)]TJ -86.3632 -13.5492 Td[(LU)-333(from)-333(Su)1(p)-28(erLU,)-333(p)1(lus)-334(t)1(rian)1(gular)-333(solv)28(e.)]TJ ET +1 0 0 1 905.1282 672.6585 cm q -1 0 0 1 905.327 672.659 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 67.746 l +S Q +1 0 0 1 -612.5029 -0.3985 cm q -1 0 0 1 292.625 672.459 cm -[]0 d 0 J 0.398 w 0 0 m 612.702 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +612.7021 0.1992 l +S Q +1 0 0 1 -0.1992 -27.0984 cm q -1 0 0 1 292.625 645.162 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -292.4261 -645.1616 cm BT -/F44 10.9091 Tf 298.603 662.776 Td [(mld_coarse_sweeps_)]TJ +/F46 10.9091 Tf 298.6029 662.7756 Td[(mld_coarse_sweeps_)]TJ ET +1 0 0 1 418.9255 645.1616 cm q -1 0 0 1 419.125 645.162 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -418.9255 -645.1616 cm BT -/F44 10.9091 Tf 425.102 662.776 Td [(integer)]TJ +/F46 10.9091 Tf 425.1023 662.7756 Td[(integer)]TJ ET +1 0 0 1 537.8988 645.1616 cm q -1 0 0 1 538.098 645.162 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -537.8988 -645.1616 cm BT -/F15 10.9091 Tf 544.076 662.776 Td [(An)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F22 10.9091 Tf 70.606 0 Td [(>)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ +/F15 10.9091 Tf 544.0757 662.7756 Td[(An)28(y)-333(in)29(t.)-333(n)28(um.)]TJ/F24 10.9091 Tf 70.6061 0 Td[(>)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ ET +1 0 0 1 640.5626 645.1616 cm q -1 0 0 1 640.762 645.162 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -640.5626 -645.1616 cm BT -/F15 10.9091 Tf 646.739 662.776 Td [(4)]TJ +/F15 10.9091 Tf 646.7394 662.7756 Td[(4)]TJ ET +1 0 0 1 694.7478 645.1616 cm q -1 0 0 1 694.947 645.162 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -694.7478 -645.1616 cm BT -/F15 10.9091 Tf 700.925 662.776 Td [(Num)28(b)-28(er)-766(of)-766(Blo)-28(c)28(k-Jacobi)-766(sw)28(eeps)-766(when)]TJ 0 -13.55 Td [('BJA)28(C')-334(is)-333(used)-333(as)-334(coarsest-lev)28(el)-333(solv)27(er.)]TJ +/F15 10.9091 Tf 700.9247 662.7756 Td[(Num)28(b)-27(e)-1(r)-766(of)-765(Blo)-28(c)27(k)1(-)-1(Jacobi)-765(s)-1(w)28(e)-1(eps)-766(when)]TJ 0 -13.5492 Td[('BJA)28(C')-334(i)1(s)-334(use)-1(d)-332(as)-334(c)-1(oar)1(s)-1(es)-1(t-lev)28(e)-1(l)-333(solv)28(er.)]TJ ET +1 0 0 1 905.1282 645.1616 cm q -1 0 0 1 905.327 645.162 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -612.5029 -0.3985 cm q -1 0 0 1 292.625 644.962 cm -[]0 d 0 J 0.398 w 0 0 m 612.702 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +612.7021 0.1992 l +S Q +1 0 0 1 -0.1992 -27.0984 cm q -1 0 0 1 292.625 617.665 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -292.4261 -617.6647 cm BT -/F44 10.9091 Tf 298.603 635.279 Td [(mld_coarse_fillin_)]TJ +/F46 10.9091 Tf 298.6029 635.2787 Td[(mld_coarse_fillin_)]TJ ET +1 0 0 1 418.9255 617.6647 cm q -1 0 0 1 419.125 617.665 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -418.9255 -617.6647 cm BT -/F44 10.9091 Tf 425.102 635.279 Td [(integer)]TJ +/F46 10.9091 Tf 425.1023 635.2787 Td[(integer)]TJ ET +1 0 0 1 537.8988 617.6647 cm q -1 0 0 1 538.098 617.665 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -537.8988 -617.6647 cm BT -/F15 10.9091 Tf 544.076 635.279 Td [(An)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 70.606 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ +/F15 10.9091 Tf 544.0757 635.2787 Td[(An)28(y)-333(in)29(t.)-333(n)28(um.)]TJ/F27 10.9091 Tf 70.6061 0 Td[(\025)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ ET +1 0 0 1 640.5626 617.6647 cm q -1 0 0 1 640.762 617.665 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -640.5626 -617.6647 cm BT -/F15 10.9091 Tf 646.739 635.279 Td [(0)]TJ +/F15 10.9091 Tf 646.7394 635.2787 Td[(0)]TJ ET +1 0 0 1 694.7478 617.6647 cm q -1 0 0 1 694.947 617.665 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -694.7478 -617.6647 cm BT -/F15 10.9091 Tf 700.925 635.279 Td [(Fill-in)-276(lev)28(el)]TJ/F22 10.9091 Tf 56.177 0 Td [(p)]TJ/F15 10.9091 Tf 8.501 0 Td [(of)-276(the)-276(incomplete)-276(LU)-277(f)1(ac)-1(tor)1(-)]TJ -64.678 -13.549 Td [(izations.)]TJ +/F15 10.9091 Tf 700.9247 635.2787 Td[(Fil)1(l-in)-276(lev)28(e)-1(l)]TJ/F24 10.9091 Tf 56.1768 0 Td[(p)]TJ/F15 10.9091 Tf 8.5013 0 Td[(of)-276(th)1(e)-277(in)1(c)-1(omp)1(le)-1(te)-276(LU)-276(factor-)]TJ -64.6781 -13.5492 Td[(ization)1(s)-1(.)]TJ ET +1 0 0 1 905.1282 617.6647 cm q -1 0 0 1 905.327 617.665 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -612.5029 -0.3985 cm q -1 0 0 1 292.625 617.466 cm -[]0 d 0 J 0.398 w 0 0 m 612.702 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +612.7021 0.1992 l +S Q +1 0 0 1 -0.1992 -27.0983 cm q -1 0 0 1 292.625 590.168 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -292.4261 -590.1679 cm BT -/F44 10.9091 Tf 298.603 607.782 Td [(mld_coarse_iluthrs_)]TJ +/F46 10.9091 Tf 298.6029 607.7819 Td[(mld_coarse_iluthrs_)]TJ ET +1 0 0 1 418.9255 590.1679 cm q -1 0 0 1 419.125 590.168 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -418.9255 -590.1679 cm BT -/F44 10.9091 Tf 425.102 607.782 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ +/F46 10.9091 Tf 425.1023 607.7819 Td[(real\050)]TJ/F20 10.9091 Tf 28.6361 0 Td[(kind)]TJ ET +1 0 0 1 474.48 607.7819 cm q -1 0 0 1 474.48 607.981 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -474.48 -607.7819 cm BT -/F18 10.9091 Tf 477.825 607.782 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ +/F20 10.9091 Tf 477.8255 607.7819 Td[(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.5678 0 Td[(\051)]TJ ET +1 0 0 1 537.8988 590.1679 cm q -1 0 0 1 538.098 590.168 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -537.8988 -590.1679 cm BT -/F15 10.9091 Tf 544.076 607.782 Td [(An)28(y)-289(real.)-290(n)28(um.)]TJ/F25 10.9091 Tf 73.739 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ +/F15 10.9091 Tf 544.0757 607.7819 Td[(An)28(y)-289(r)1(e)-1(al.)-289(n)29(um.)]TJ/F27 10.9091 Tf 73.7389 0 Td[(\025)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ ET +1 0 0 1 640.5626 590.1679 cm q -1 0 0 1 640.762 590.168 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -640.5626 -590.1679 cm BT -/F15 10.9091 Tf 646.739 607.782 Td [(0)]TJ +/F15 10.9091 Tf 646.7394 607.7819 Td[(0)]TJ ET +1 0 0 1 694.7478 590.1679 cm q -1 0 0 1 694.947 590.168 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -694.7478 -590.1679 cm BT -/F15 10.9091 Tf 700.925 607.782 Td [(Drop)-256(tolerance)]TJ/F22 10.9091 Tf 72.777 0 Td [(t)]TJ/F15 10.9091 Tf 6.736 0 Td [(in)-256(the)-257(ILU\050)]TJ/F22 10.9091 Tf 53.02 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-256(factoriza-)]TJ -146.809 -13.549 Td [(tion.)]TJ +/F15 10.9091 Tf 700.9247 607.7819 Td[(Drop)-256(t)1(ole)-1(r)1(ance)]TJ/F24 10.9091 Tf 72.7768 0 Td[(t)]TJ/F15 10.9091 Tf 6.7369 0 Td[(in)-256(th)1(e)-257(ILU\050)]TJ/F24 10.9091 Tf 53.0193 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051)-256(factoriza-)]TJ -146.8095 -13.5492 Td[(tion)1(.)]TJ ET +1 0 0 1 905.1282 590.1679 cm q -1 0 0 1 905.327 590.168 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +[]0 d +0 J +0.3985 w +0.1992 0 m +0.1992 27.0984 l +S Q +1 0 0 1 -612.5029 -0.3985 cm q -1 0 0 1 292.625 589.969 cm -[]0 d 0 J 0.398 w 0 0 m 612.702 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +612.7021 0.1992 l +S Q +1 0 0 1 111.0143 -30.4898 cm 0 g 0 G +1 0 0 1 -403.6396 -559.2796 cm BT -/F15 10.9091 Tf 403.64 559.28 Td [(T)83(able)-333(5:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(coarse-space)-333(correction)-333(at)-334(the)-333(coarsest)-334(l)1(e)-1(v)28(el.)]TJ +/F15 10.9091 Tf 403.6396 559.2796 Td[(T)83(ab)1(le)-334(5:)-444(P)28(aramete)-1(r)1(s)-334(de\014n)1(ing)-333(th)1(e)-334(c)-1(oar)1(s)-1(e-)-1(space)-334(correction)-333(at)-333(the)-333(c)-1(oarses)-1(t)-333(lev)28(e)-1(l.)]TJ +ET +1 0 0 1 775.1854 559.2796 cm 0 g 0 G +1 0 0 1 111.0143 155.8157 cm 0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -Q +1 0 0 1 -593.5744 0 cm + Q +1 0 0 1 -206.2255 -593.5744 cm 0 g 0 G +1 0 0 1 0 -29.8879 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -439 0 obj << +475 0 obj << /Type /Page -/Contents 440 0 R -/Resources 438 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R +/Contents 476 0 R +/Resources 474 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 473 0 R >> endobj -441 0 obj << -/D [439 0 R /XYZ 86.4 740.002 null] +477 0 obj << +/D [475 0 R /XYZ 86.3998 740.0018 null] >> endobj -356 0 obj << -/D [439 0 R /XYZ -3930.339 560.748 null] +389 0 obj << +/D [475 0 R /XYZ 446.973 572.8287 null] >> endobj -438 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F44 200 0 R /F22 175 0 R /F25 176 0 R /F18 173 0 R >> +474 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F46 219 0 R /F24 186 0 R /F27 189 0 R /F20 181 0 R >> /ProcSet [ /PDF /Text ] >> endobj -448 0 obj << -/Length 3122 +480 0 obj << +/Length 4533 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(6)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(27)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(27)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.3)-1125(Subroutine)-375(mld)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 11.9552 Tf 93.6002 704.1363 Td[(6.)-1(3)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ ET +1 0 0 1 216.6225 704.1363 cm q -1 0 0 1 216.622 704.336 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -216.6225 -704.1363 cm BT -/F17 11.9552 Tf 220.657 704.136 Td [(precbld)]TJ +/F19 11.9552 Tf 220.6574 704.1363 Td[(pre)-1(cbld)]TJ +ET +1 0 0 1 214.1903 683.5417 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf -1.012 -20.594 Td [(mld_precbld\050a,desc_a,p,info\051)]TJ/F15 10.9091 Tf -126.045 -25.505 Td [(This)-319(r)1(outine)-319(builds)-318(the)-319(preconditioner)-318(according)-319(t)1(o)-319(the)-318(requiremen)27(ts)-318(made)-319(b)28(y)-318(the)-319(user)]TJ 0 -13.549 Td [(through)-333(the)-334(r)1(outines)]TJ/F44 10.9091 Tf 101.94 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 72.363 0 Td [(and)]TJ/F44 10.9091 Tf 21.212 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 62.999 0 Td [(.)]TJ/F17 11.9552 Tf -258.514 -40.647 Td [(Argumen)31(ts)]TJ/F44 10.9091 Tf 22.914 -12.806 Td [(a)-3689(type\050psb_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(spmat_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 131.726 0 Td [(.)]TJ -189.645 -13.549 Td [(The)-501(sparse)-501(matrix)-501(structure)-501(con)28(taining)-501(th)1(e)-501(lo)-28(cal)-501(part)-501(of)-501(the)-501(matrix)]TJ 0 -13.549 Td [(to)-470(b)-28(e)-469(preconditioned.)-854(Note)-470(that)]TJ/F18 10.9091 Tf 166.818 0 Td [(x)]TJ/F15 10.9091 Tf 11.5 0 Td [(m)28(ust)-470(b)-28(e)-470(c)28(hosen)-470(according)-470(to)-469(the)]TJ -178.318 -13.549 Td [(real/complex,)-534(single/doubl)1(e)-494(precision)-494(v)28(ersion)-493(of)-494(MLD2P4)-493(under)-494(use.)]TJ 0 -13.549 Td [(See)-333(the)-334(PSBLAS)-333(User's)-333(Guide)-334(for)-333(details)-333([)]TJ +1 0 0 1 -214.1903 -683.5417 cm +BT +/F46 10.9091 Tf 219.6448 683.5417 Td[(mld_precbld\050a,desc_a,p,info\051)]TJ/F15 10.9091 Tf -126.0446 -25.5044 Td[(This)-318(routi)1(ne)-319(b)1(uild)1(s)-319(th)1(e)-319(prec)-1(on)1(di)1(tioner)-318(ac)-1(cord)1(ing)-318(to)-319(t)1(he)-319(requ)1(irem)-1(en)28(ts)-319(made)-318(b)28(y)-319(t)1(he)-319(u)1(s)-1(er)]TJ 0 -13.5492 Td[(th)1(rough)-333(t)1(he)-334(r)1(outin)1(e)-1(s)]TJ/F46 10.9091 Tf 101.9395 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 72.3629 0 Td[(and)]TJ/F46 10.9091 Tf 21.2121 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)]TJ/F19 11.9552 Tf -258.5138 -40.6476 Td[(Arg)-1(umen)31(t)-1(s)]TJ/F46 10.9091 Tf 22.9141 -12.8052 Td[(a)-3689(type\050psb_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(spmat_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 131.7258 0 Td[(.)]TJ -189.6449 -13.5492 Td[(The)-501(s)-1(p)1(arse)-502(matr)1(ix)-501(stru)1(c)-1(tu)1(re)-501(c)-1(on)28(t)1(ainin)1(g)-501(th)1(e)-502(lo)-27(c)-1(al)-500(part)-500(of)-501(th)1(e)-502(matri)1(x)]TJ 0 -13.5492 Td[(to)-470(b)-27(e)-470(precondi)1(tioned.)-853(Note)-470(that)]TJ/F20 10.9091 Tf 166.818 0 Td[(x)]TJ/F15 10.9091 Tf 11.4997 0 Td[(m)27(u)1(s)-1(t)-469(b)-28(e)-470(c)27(h)1(os)-1(en)-469(ac)-1(cordi)1(ng)-470(to)-469(the)]TJ -178.3177 -13.5492 Td[(real/com)-1(p)1(lex,)-534(sin)1(gle)-1(/d)1(oub)1(le)-494(pr)1(e)-1(cision)-493(v)28(e)-1(r)1(s)-1(ion)-493(of)-493(MLD)1(2P4)-494(u)1(nd)1(e)-1(r)-493(u)1(s)-1(e.)]TJ 0 -13.5492 Td[(See)-334(th)1(e)-334(PS)1(BLAS)-333(Us)-1(er's)-333(Guid)1(e)-334(f)1(or)-333(details)-334([)]TJ +ET +1 0 0 1 365.6823 536.8385 cm 1 0 0 rg 1 0 0 RG - [(14)]TJ +1 0 0 1 -365.6823 -536.8385 cm +BT +/F15 10.9091 Tf 365.6823 536.8385 Td[(14)]TJ +ET +1 0 0 1 376.5914 536.8385 cm 0 g 0 G - [(].)]TJ/F44 10.9091 Tf -45.971 -13.55 Td [(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.515 0 Td [(.)]TJ -177.544 -13.549 Td [(The)-354(comm)28(unication)-354(descriptor)-354(of)]TJ/F44 10.9091 Tf 162.836 0 Td [(a)]TJ/F15 10.9091 Tf 5.727 0 Td [(.)-506(See)-354(the)-354(PSBLAS)-354(User's)-353(Guide)-354(for)]TJ -168.563 -13.549 Td [(details)-333([)]TJ +1 0 0 1 -376.5914 -536.8385 cm +BT +/F15 10.9091 Tf 376.5914 536.8385 Td[(].)]TJ/F46 10.9091 Tf -260.0771 -13.5492 Td[(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.5144 0 Td[(.)]TJ -177.5436 -13.5492 Td[(The)-354(c)-1(omm)28(uni)1(c)-1(ati)1(on)-354(d)1(e)-1(sc)-1(r)1(iptor)-353(of)]TJ/F46 10.9091 Tf 162.8355 0 Td[(a)]TJ/F15 10.9091 Tf 5.7272 0 Td[(.)-506(S)1(e)-1(e)-354(the)-354(P)1(SBLAS)-354(Use)-1(r)1('s)-354(Gui)1(de)-354(for)]TJ -168.5627 -13.5492 Td[(detail)1(s)-334([)]TJ +ET +1 0 0 1 200.1215 496.191 cm 1 0 0 rg 1 0 0 RG - [(14)]TJ +1 0 0 1 -200.1215 -496.191 cm +BT +/F15 10.9091 Tf 200.1215 496.191 Td[(14)]TJ +ET +1 0 0 1 211.0306 496.191 cm 0 g 0 G - [(].)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.18 0 Td [(.)]TJ -201.099 -13.549 Td [(The)-478(preconditioner)-478(data)-478(structure.)-878(Note)-478(that)]TJ/F18 10.9091 Tf 233.108 0 Td [(x)]TJ/F15 10.9091 Tf 11.589 0 Td [(m)28(ust)-478(b)-28(e)-478(c)28(hosen)-478(ac-)]TJ -244.697 -13.55 Td [(cording)-269(to)-269(the)-270(real/complex,)-282(single/double)-269(precision)-269(v)27(ersion)-269(of)-269(MLD2P4)]TJ 0 -13.549 Td [(under)-333(use.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ +1 0 0 1 -211.0306 -496.191 cm +BT +/F15 10.9091 Tf 211.0306 496.191 Td[(].)]TJ/F46 10.9091 Tf -94.5163 -13.5492 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-478(pr)1(e)-1(cond)1(ition)1(e)-1(r)-478(d)1(ata)-478(stru)1(c)-1(tu)1(re.)-879(Note)-478(th)1(at)]TJ/F20 10.9091 Tf 233.1081 0 Td[(x)]TJ/F15 10.9091 Tf 11.5884 0 Td[(m)27(u)1(s)-1(t)-477(b)-28(e)-478(c)27(h)1(os)-1(en)-478(ac-)]TJ -244.6965 -13.5492 Td[(cordi)1(ng)-269(to)-269(the)-270(r)1(e)-1(al/complex,)-282(singl)1(e)-1(/d)1(oub)1(le)-270(pr)1(e)-1(cision)-269(v)28(ers)-1(i)1(on)-269(of)-269(MLD2P)1(4)]TJ 0 -13.5492 Td[(un)1(der)-333(use)-1(.)]TJ/F46 10.9091 Tf -45.9708 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-333(co)-28(de.)-444(If)-333(no)-333(e)-1(r)1(ror,)-333(0)-333(is)-334(r)1(e)-1(tu)1(rn)1(e)-1(d)1(.)-445(S)1(e)-1(e)-333(Sec)-1(tion)]TJ +ET +1 0 0 1 403.2429 414.8958 cm 0 0 1 rg 0 0 1 RG - [-333(7)]TJ +1 0 0 1 -403.2429 -414.8958 cm +BT +/F15 10.9091 Tf 403.2429 414.8958 Td[(7)]TJ +ET +1 0 0 1 408.6974 414.8958 cm 0 g 0 G - [-333(for)-334(details.)]TJ +1 0 0 1 -408.6974 -414.8958 cm +BT +/F15 10.9091 Tf 412.3338 414.8958 Td[(for)-333(d)1(e)-1(t)1(ails.)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -447 0 obj << +479 0 obj << /Type /Page -/Contents 448 0 R -/Resources 446 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R -/Annots [ 445 0 R 442 0 R 443 0 R 444 0 R ] +/Contents 480 0 R +/Resources 478 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 473 0 R +/Annots [ 482 0 R 483 0 R 484 0 R 485 0 R ] >> endobj -445 0 obj << +482 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -442 0 obj << +483 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [364.686 535.842 377.588 544.865] +/Rect [364.686 535.8423 377.5877 544.8651] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -443 0 obj << +484 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [199.125 495.195 212.027 504.218] +/Rect [199.1253 495.1947 212.0269 504.2175] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -444 0 obj << +485 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [402.247 409.835 409.694 423.468] +/Rect [402.2466 409.8348 409.6937 423.4679] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -449 0 obj << -/D [447 0 R /XYZ 93.6 740.002 null] +481 0 obj << +/D [479 0 R /XYZ 93.6002 740.0018 null] >> endobj 78 0 obj << -/D [447 0 R /XYZ 93.6 715.095 null] +/D [479 0 R /XYZ 93.6002 715.0952 null] >> endobj -446 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F44 200 0 R /F18 173 0 R >> +478 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F46 219 0 R /F20 181 0 R >> /ProcSet [ /PDF /Text ] >> endobj -453 0 obj << -/Length 9096 +488 0 obj << +/Length 10566 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(28)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(28)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.4)-1125(Subroutine)-375(mld)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F19 11.9552 Tf 86.3998 704.1363 Td[(6.)-1(4)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ ET +1 0 0 1 209.422 704.1363 cm q -1 0 0 1 209.422 704.336 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -209.422 -704.1363 cm BT -/F17 11.9552 Tf 213.457 704.136 Td [(precaply)]TJ +/F19 11.9552 Tf 213.4569 704.1363 Td[(pre)-1(caply)]TJ +ET +1 0 0 1 198.399 683.5417 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf -9.603 -20.594 Td [(mld_precaply\050p,x,y,desc_a,info\051)]TJ -31.5 -13.549 Td [(mld_precaply\050p,x,y,desc_a,info,trans,work\051)]TJ/F15 10.9091 Tf -85.954 -25.505 Td [(This)-382(routine)-381(computes)]TJ/F22 10.9091 Tf 112.644 0 Td [(y)]TJ/F15 10.9091 Tf 9.65 0 Td [(=)]TJ/F22 10.9091 Tf 12.394 0 Td [(op)]TJ/F15 10.9091 Tf 10.777 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 4.733 -3.959 Td [(\051)]TJ/F22 10.9091 Tf 6.06 0 Td [(x)]TJ/F15 10.9091 Tf 6.235 0 Td [(,)-394(where)]TJ/F22 10.9091 Tf 39.4 0 Td [(M)]TJ/F15 10.9091 Tf 15.937 0 Td [(is)-382(a)-381(previously)-382(built)-382(precondi)1(tioner,)]TJ -240.431 -13.549 Td [(stored)-423(in)27(to)]TJ/F44 10.9091 Tf 56.907 0 Td [(p)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-446(and)]TJ/F22 10.9091 Tf 30.092 0 Td [(op)]TJ/F15 10.9091 Tf 15.397 0 Td [(denotes)-424(th)1(e)-424(preconditioner)-423(itself)-424(or)-423(its)-424(transp)-28(ose,)-446(according)-423(to)]TJ -108.123 -13.549 Td [(the)-496(v)56(alue)-496(of)]TJ/F44 10.9091 Tf 64.719 0 Td [(trans)]TJ/F15 10.9091 Tf 28.636 0 Td [(.)-933(Note)-496(that,)-536(when)-496(MLD2P4)-496(is)-496(used)-496(with)-496(a)-496(Krylo)27(v)-496(solv)28(er)-496(from)]TJ -93.355 -13.549 Td [(PSBLAS,)]TJ/F44 10.9091 Tf 49.363 0 Td [(mld_precaply)]TJ/F15 10.9091 Tf 72.787 0 Td [(is)-372(called)-372(within)-373(th)1(e)-373(PSBLAS)-372(routine)]TJ/F44 10.9091 Tf 180.666 0 Td [(mld_krylov)]TJ/F15 10.9091 Tf 61.332 0 Td [(and)-372(hence)]TJ -364.148 -13.55 Td [(it)-333(is)-334(completely)-333(transparen)28(t)-333(to)-334(the)-333(user.)]TJ/F17 11.9552 Tf 0 -40.647 Td [(Argumen)31(ts)]TJ/F44 10.9091 Tf 22.914 -12.805 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.18 0 Td [(.)]TJ -201.099 -13.55 Td [(The)-282(p)1(re)-1(cond)1(itioner)-282(data)-281(structure,)-292(con)28(taining)-282(the)-281(lo)-28(cal)-282(part)-281(of)]TJ/F22 10.9091 Tf 297.967 0 Td [(M)]TJ/F15 10.9091 Tf 11.773 0 Td [(.)-427(Note)]TJ -309.74 -13.549 Td [(that)]TJ/F18 10.9091 Tf 25.362 0 Td [(x)]TJ/F15 10.9091 Tf 11.737 0 Td [(m)28(ust)-492(b)-27(e)-492(c)28(hosen)-492(according)-491(to)-492(the)-491(real/com)-1(p)1(lex,)-532(single/dou)1(ble)]TJ -37.099 -13.549 Td [(precision)-333(v)28(e)-1(rsion)-333(of)-333(MLD2P4)-333(under)-334(use.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(x)]TJ/F18 10.9091 Tf 45.971 0 Td [(typ)51(e)]TJ/F44 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ +1 0 0 1 -198.399 -683.5417 cm +BT +/F46 10.9091 Tf 203.8536 683.5417 Td[(mld_precaply\050p,x,y,desc_a,info\051)]TJ -31.4997 -13.5492 Td[(mld_precaply\050p,x,y,desc_a,info,trans,work\051)]TJ/F15 10.9091 Tf -85.9541 -25.5044 Td[(This)-382(r)1(outin)1(e)-382(c)-1(ompu)1(te)-1(s)]TJ/F24 10.9091 Tf 112.644 0 Td[(y)]TJ/F15 10.9091 Tf 9.6497 0 Td[(=)]TJ/F24 10.9091 Tf 12.3947 0 Td[(op)]TJ/F15 10.9091 Tf 10.7765 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051)]TJ/F24 10.9091 Tf 6.0606 0 Td[(x)]TJ/F15 10.9091 Tf 6.2348 0 Td[(,)-394(wh)1(e)-1(r)1(e)]TJ/F24 10.9091 Tf 39.3996 0 Td[(M)]TJ/F15 10.9091 Tf 15.9368 0 Td[(is)-382(a)-382(p)1(reviou)1(s)-1(ly)-381(bu)1(ilt)-381(prec)-1(on)1(di)1(tioner,)]TJ -240.4308 -13.5492 Td[(stored)-424(i)1(n)28(to)]TJ/F46 10.9091 Tf 56.9069 0 Td[(p)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)-446(an)1(d)]TJ/F24 10.9091 Tf 30.0922 0 Td[(op)]TJ/F15 10.9091 Tf 15.3966 0 Td[(denot)1(e)-1(s)-424(th)1(e)-424(pr)1(e)-1(cond)1(ition)1(e)-1(r)-423(itse)-1(l)1(f)-424(or)-423(i)1(ts)-424(tran)1(s)-1(p)-27(os)-1(e,)-446(acc)-1(or)1(din)1(g)-424(to)]TJ -108.1229 -13.5492 Td[(th)1(e)-497(v)56(alue)-496(of)]TJ/F46 10.9091 Tf 64.7192 0 Td[(trans)]TJ/F15 10.9091 Tf 28.6361 0 Td[(.)-932(Note)-497(th)1(at,)-537(wh)1(e)-1(n)-495(MLD2P4)-496(i)1(s)-497(u)1(s)-1(ed)-496(with)-495(a)-496(Kryl)1(o)27(v)-496(solv)28(er)-496(f)1(rom)]TJ -93.3553 -13.5492 Td[(PS)1(BLAS,)]TJ/F46 10.9091 Tf 49.3635 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 72.7869 0 Td[(is)-372(c)-1(all)1(e)-1(d)-372(with)1(in)-372(th)1(e)-373(P)1(SBLAS)-372(rou)1(tin)1(e)]TJ/F46 10.9091 Tf 180.6653 0 Td[(mld_krylov)]TJ/F15 10.9091 Tf 61.3325 0 Td[(and)-371(hence)]TJ -364.1482 -13.5492 Td[(it)-333(is)-334(completely)-333(tran)1(s)-1(p)1(are)-1(n)29(t)-334(t)1(o)-334(th)1(e)-334(user.)]TJ/F19 11.9552 Tf 0 -40.6476 Td[(Arg)-1(umen)31(t)-1(s)]TJ/F46 10.9091 Tf 22.9141 -12.8052 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-282(p)1(rec)-1(on)1(diti)1(oner)-282(d)1(ata)-282(stru)1(c)-1(tu)1(re,)-292(con)28(tain)1(ing)-281(the)-282(l)1(o)-28(c)-1(al)-281(p)1(art)-282(of)]TJ/F24 10.9091 Tf 297.967 0 Td[(M)]TJ/F15 10.9091 Tf 11.7727 0 Td[(.)-427(Note)]TJ -309.7397 -13.5492 Td[(th)1(at)]TJ/F20 10.9091 Tf 25.3623 0 Td[(x)]TJ/F15 10.9091 Tf 11.7365 0 Td[(m)27(u)1(s)-1(t)-491(b)-27(e)-492(c)27(hosen)-492(accordi)1(ng)-492(t)1(o)-492(th)1(e)-492(real/c)-1(ompl)1(e)-1(x,)-530(s)-1(in)1(gle/doub)1(le)]TJ -37.0988 -13.5492 Td[(pr)1(e)-1(cision)-333(v)28(ers)-1(i)1(on)-333(of)-333(MLD2P)1(4)-334(u)1(nd)1(e)-1(r)-333(u)1(s)-1(e.)]TJ/F46 10.9091 Tf -45.9708 -13.5492 Td[(x)]TJ/F20 10.9091 Tf 45.9708 0 Td[(typ)51(e)]TJ/F46 10.9091 Tf 19.7771 0 Td[(\050)]TJ/F20 10.9091 Tf 5.7272 0 Td[(kind)]TJ ET +1 0 0 1 201.5306 482.6418 cm q -1 0 0 1 201.531 482.841 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -201.5306 -482.6418 cm BT -/F18 10.9091 Tf 204.876 482.642 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051,)-525(dimension\050:\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.635 0 Td [(.)]TJ -252.794 -13.549 Td [(The)-300(lo)-28(cal)-300(part)-301(of)-300(the)-300(v)28(ector)]TJ/F22 10.9091 Tf 133.655 0 Td [(x)]TJ/F15 10.9091 Tf 6.235 0 Td [(.)-433(Note)-301(that)]TJ/F18 10.9091 Tf 57.038 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 23.053 0 Td [(and)]TJ/F18 10.9091 Tf 20.851 0 Td [(kind)]TJ +/F20 10.9091 Tf 204.8761 482.6418 Td[(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.5678 0 Td[(\051,)-525(dimension\050:\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.6347 0 Td[(.)]TJ -252.7939 -13.5492 Td[(The)-301(l)1(o)-28(c)-1(al)-300(p)1(art)-300(of)-300(th)1(e)-301(v)28(ec)-1(tor)]TJ/F24 10.9091 Tf 133.6555 0 Td[(x)]TJ/F15 10.9091 Tf 6.2348 0 Td[(.)-433(Note)-301(th)1(at)]TJ/F20 10.9091 Tf 57.0377 0 Td[(typ)51(e)]TJ/F15 10.9091 Tf 23.053 0 Td[(and)]TJ/F20 10.9091 Tf 20.8517 0 Td[(kind)]TJ ET +1 0 0 1 416.859 469.0926 cm q -1 0 0 1 416.859 469.292 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -416.859 -469.0926 cm BT -/F18 10.9091 Tf 420.204 469.093 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.844 0 Td [(m)28(ust)]TJ -316.763 -13.55 Td [(b)-28(e)-263(c)28(hosen)-264(accordi)1(ng)-264(to)-263(the)-263(real/complex,)-277(single/double)-264(pr)1(e)-1(cision)-263(v)28(ersion)]TJ 0 -13.549 Td [(of)-333(MLD2P4)-334(u)1(nder)-334(use.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(y)]TJ/F18 10.9091 Tf 45.971 0 Td [(typ)51(e)]TJ/F44 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ +/F20 10.9091 Tf 420.2045 469.0926 Td[(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.8437 0 Td[(m)27(u)1(s)-1(t)]TJ -316.7635 -13.5492 Td[(b)-27(e)-264(c)27(h)1(os)-1(en)-263(acc)-1(or)1(din)1(g)-264(to)-263(th)1(e)-264(real/com)-1(p)1(lex,)-277(s)-1(i)1(ngle/dou)1(ble)-263(precis)-1(i)1(on)-263(v)28(e)-1(r)1(s)-1(ion)]TJ 0 -13.5492 Td[(of)-333(MLD)1(2P4)-333(un)1(der)-333(use)-1(.)]TJ/F46 10.9091 Tf -45.9708 -13.5492 Td[(y)]TJ/F20 10.9091 Tf 45.9708 0 Td[(typ)51(e)]TJ/F46 10.9091 Tf 19.7771 0 Td[(\050)]TJ/F20 10.9091 Tf 5.7272 0 Td[(kind)]TJ ET +1 0 0 1 201.5306 428.445 cm q -1 0 0 1 201.531 428.644 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -201.5306 -428.445 cm BT -/F18 10.9091 Tf 204.876 428.445 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051,)-525(dimension\050:\051,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.362 0 Td [(.)]TJ -258.521 -13.549 Td [(The)-304(lo)-28(cal)-304(part)-305(of)-304(the)-304(v)28(ector)]TJ/F22 10.9091 Tf 133.917 0 Td [(y)]TJ/F15 10.9091 Tf 5.74 0 Td [(.)-435(Note)-304(that)]TJ/F18 10.9091 Tf 57.14 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 23.096 0 Td [(and)]TJ/F18 10.9091 Tf 20.896 0 Td [(kind)]TJ +/F20 10.9091 Tf 204.8761 428.445 Td[(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.5678 0 Td[(\051,)-525(dimension\050:\051,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.3619 0 Td[(.)]TJ -258.5211 -13.5492 Td[(The)-305(l)1(o)-28(c)-1(al)-304(p)1(art)-304(of)-304(th)1(e)-305(v)28(ec)-1(tor)]TJ/F24 10.9091 Tf 133.9175 0 Td[(y)]TJ/F15 10.9091 Tf 5.7399 0 Td[(.)-435(Not)1(e)-305(that)]TJ/F20 10.9091 Tf 57.1396 0 Td[(typ)51(e)]TJ/F15 10.9091 Tf 23.0967 0 Td[(and)]TJ/F20 10.9091 Tf 20.8953 0 Td[(kind)]TJ ET +1 0 0 1 416.8153 414.8958 cm q -1 0 0 1 416.815 415.095 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -416.8153 -414.8958 cm BT -/F18 10.9091 Tf 420.161 414.896 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.887 0 Td [(m)28(ust)]TJ -316.763 -13.549 Td [(b)-28(e)-263(c)28(hosen)-264(accordi)1(ng)-264(to)-263(the)-263(real/complex,)-277(single/double)-264(pr)1(e)-1(cision)-263(v)28(ersion)]TJ 0 -13.55 Td [(of)-333(MLD2P4)-334(u)1(nder)-334(use.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.514 0 Td [(.)]TJ -177.543 -13.549 Td [(The)-319(c)-1(omm)28(unication)-319(descriptor)-320(asso)-28(ciated)-319(to)-320(th)1(e)-320(matrix)-319(to)-320(b)-28(e)-319(precondi-)]TJ 0 -13.549 Td [(tioned.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ +/F20 10.9091 Tf 420.1608 414.8958 Td[(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.8874 0 Td[(m)27(u)1(s)-1(t)]TJ -316.7635 -13.5492 Td[(b)-27(e)-264(c)27(h)1(os)-1(en)-263(acc)-1(or)1(din)1(g)-264(to)-263(th)1(e)-264(real/com)-1(p)1(lex,)-277(s)-1(i)1(ngle/dou)1(ble)-263(precis)-1(i)1(on)-263(v)28(e)-1(r)1(s)-1(ion)]TJ 0 -13.5492 Td[(of)-333(MLD)1(2P4)-333(un)1(der)-333(use)-1(.)]TJ/F46 10.9091 Tf -45.9708 -13.5492 Td[(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.5143 0 Td[(.)]TJ -177.5435 -13.5492 Td[(The)-320(com)-1(m)28(un)1(ication)-319(des)-1(cri)1(ptor)-319(as)-1(so)-28(ciated)-319(to)-320(th)1(e)-320(matrix)-319(to)-319(b)-28(e)-320(p)1(rec)-1(on)1(di-)]TJ 0 -13.5492 Td[(tion)1(e)-1(d)1(.)]TJ/F46 10.9091 Tf -45.9708 -13.5491 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-333(co)-28(de.)-444(If)-333(no)-333(e)-1(r)1(ror,)-333(0)-333(is)-334(r)1(e)-1(tu)1(rn)1(e)-1(d)1(.)-445(S)1(e)-1(e)-333(Sec)-1(tion)]TJ +ET +1 0 0 1 396.0424 320.0515 cm 0 0 1 rg 0 0 1 RG - [-333(7)]TJ +1 0 0 1 -396.0424 -320.0515 cm +BT +/F15 10.9091 Tf 396.0424 320.0515 Td[(7)]TJ +ET +1 0 0 1 401.497 320.0515 cm 0 g 0 G - [-333(for)-334(d)1(e)-1(tail)1(s)-1(.)]TJ/F44 10.9091 Tf -45.971 -13.55 Td [(trans)-1589(character\050len=1\051,)-525(optional,)-525(intent\050in\051.)]TJ/F15 10.9091 Tf 45.971 -13.549 Td [(If)]TJ/F44 10.9091 Tf 13.647 0 Td [(trans)]TJ/F15 10.9091 Tf 35.01 0 Td [(=)]TJ/F44 10.9091 Tf 14.86 0 Td [('N','n')]TJ/F15 10.9091 Tf 46.465 0 Td [(then)]TJ/F22 10.9091 Tf 27.586 0 Td [(op)]TJ/F15 10.9091 Tf 10.777 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 4.733 -3.959 Td [(\051)-696(=)]TJ/F22 10.9091 Tf 27.914 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(;)-710(if)]TJ/F44 10.9091 Tf 23.512 0 Td [(trans)]TJ/F15 10.9091 Tf 35.01 0 Td [(=)]TJ/F44 10.9091 Tf 14.86 0 Td [('T','t')]TJ/F15 10.9091 Tf -300.067 -13.549 Td [(then)]TJ/F22 10.9091 Tf 25.695 0 Td [(op)]TJ/F15 10.9091 Tf 10.777 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051)-407(=)]TJ/F22 10.9091 Tf 21.611 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F23 7.9701 Tf 6.587 0 Td [(T)]TJ/F15 10.9091 Tf 11.087 -3.959 Td [(\050transp)-28(ose)-411(of)]TJ/F22 10.9091 Tf 67.301 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051;)-450(if)]TJ/F44 10.9091 Tf 23.027 0 Td [(trans)]TJ/F15 10.9091 Tf 33.12 0 Td [(=)]TJ/F44 10.9091 Tf 12.968 0 Td [('C','c')]TJ/F15 10.9091 Tf 44.574 0 Td [(then)]TJ/F22 10.9091 Tf -318.945 -13.549 Td [(op)]TJ/F15 10.9091 Tf 10.776 0 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051)-278(=)]TJ/F22 10.9091 Tf 18.788 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F23 7.9701 Tf 6.586 0 Td [(C)]TJ/F15 10.9091 Tf 10.733 -3.959 Td [(\050conjugate)-333(transp)-28(ose)-333(of)]TJ/F22 10.9091 Tf 115.001 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051.)]TJ/F44 10.9091 Tf -270.053 -13.549 Td [(work)]TJ/F18 10.9091 Tf 45.971 0 Td [(typ)51(e)]TJ/F44 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ +1 0 0 1 -401.497 -320.0515 cm +BT +/F15 10.9091 Tf 405.1333 320.0515 Td[(for)-333(d)1(e)-1(t)1(ails.)]TJ/F46 10.9091 Tf -295.8195 -13.5492 Td[(trans)-1589(character\050len=1\051,)-525(optional,)-525(intent\050in\051.)]TJ/F15 10.9091 Tf 45.9709 -13.5492 Td[(If)]TJ/F46 10.9091 Tf 13.6472 0 Td[(trans)]TJ/F15 10.9091 Tf 35.0105 0 Td[(=)]TJ/F46 10.9091 Tf 14.8593 0 Td[('N','n')]TJ/F15 10.9091 Tf 46.4649 0 Td[(th)1(e)-1(n)]TJ/F24 10.9091 Tf 27.5867 0 Td[(op)]TJ/F15 10.9091 Tf 10.7765 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051)-696(=)]TJ/F24 10.9091 Tf 27.9147 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(;)-710(i)1(f)]TJ/F46 10.9091 Tf 23.5119 0 Td[(trans)]TJ/F15 10.9091 Tf 35.0105 0 Td[(=)]TJ/F46 10.9091 Tf 14.8593 0 Td[('T','t')]TJ/F15 10.9091 Tf -300.067 -13.5492 Td[(th)1(e)-1(n)]TJ/F24 10.9091 Tf 25.6956 0 Td[(op)]TJ/F15 10.9091 Tf 10.7766 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051)-407(=)]TJ/F24 10.9091 Tf 21.6115 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F25 7.9701 Tf 6.5865 0 Td[(T)]TJ/F15 10.9091 Tf 11.088 -3.9588 Td[(\050tr)1(ansp)-28(ose)-412(of)]TJ/F24 10.9091 Tf 67.3003 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051;)-449(if)]TJ/F46 10.9091 Tf 23.0269 0 Td[(trans)]TJ/F15 10.9091 Tf 33.1195 0 Td[(=)]TJ/F46 10.9091 Tf 12.9684 0 Td[('C','c')]TJ/F15 10.9091 Tf 44.5739 0 Td[(th)1(e)-1(n)]TJ/F24 10.9091 Tf -318.9453 -13.5492 Td[(op)]TJ/F15 10.9091 Tf 10.7765 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051)-278(=)]TJ/F24 10.9091 Tf 18.7878 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F25 7.9701 Tf 6.5865 0 Td[(C)]TJ/F15 10.9091 Tf 10.7332 -3.9588 Td[(\050conj)1(ugate)-334(tr)1(ansp)-28(ose)-334(of)]TJ/F24 10.9091 Tf 115.0001 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051.)]TJ/F46 10.9091 Tf -270.0532 -13.5492 Td[(work)]TJ/F20 10.9091 Tf 45.9709 0 Td[(typ)51(e)]TJ/F46 10.9091 Tf 19.7771 0 Td[(\050)]TJ/F20 10.9091 Tf 5.7272 0 Td[(kind)]TJ ET +1 0 0 1 201.5306 252.3056 cm q -1 0 0 1 201.531 252.505 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -201.5306 -252.3056 cm BT -/F18 10.9091 Tf 204.876 252.306 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051,)-525(dimension\050:\051,)-525(optional,)-525(target)]TJ/F15 10.9091 Tf 188.998 0 Td [(.)]TJ -287.157 -13.55 Td [(W)83(orkspace.)-1532(Its)-696(size)-697(shou)1(ld)-696(b)-28(e)-696(at)-696(least)]TJ/F44 10.9091 Tf 219.886 0 Td [(4)-525(*)-525(psb_cd_get_local_)]TJ -219.886 -13.549 Td [(cols\050desc_a\051)]TJ/F15 10.9091 Tf 73.906 0 Td [(\050see)-475(the)-475(PSBLAS)-474(User's)-475(Guide\051.)-869(Note)-475(th)1(at)]TJ/F18 10.9091 Tf 223.719 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 24.956 0 Td [(and)]TJ/F18 10.9091 Tf -322.581 -13.549 Td [(kind)]TJ +/F20 10.9091 Tf 204.8761 252.3056 Td[(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.5678 0 Td[(\051,)-525(dimension\050:\051,)-525(optional,)-525(target)]TJ/F15 10.9091 Tf 188.998 0 Td[(.)]TJ -287.1572 -13.5492 Td[(W)84(orkspace)-1(.)-1532(Its)-697(size)-697(shou)1(ld)-696(b)-27(e)-697(at)-696(l)1(e)-1(ast)]TJ/F46 10.9091 Tf 219.886 0 Td[(4)-525(*)-525(psb_cd_get_local_)]TJ -219.886 -13.5492 Td[(cols\050desc_a\051)]TJ/F15 10.9091 Tf 73.9059 0 Td[(\050se)-1(e)-475(th)1(e)-476(P)1(SBLAS)-474(Us)-1(er's)-475(Gu)1(id)1(e)-1(\051.)-868(Note)-475(that)]TJ/F20 10.9091 Tf 223.7193 0 Td[(typ)51(e)]TJ/F15 10.9091 Tf 24.9565 0 Td[(and)]TJ/F20 10.9091 Tf -322.5817 -13.5492 Td[(kind)]TJ ET +1 0 0 1 176.0263 211.658 cm q -1 0 0 1 176.026 211.857 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -176.0263 -211.658 cm BT -/F18 10.9091 Tf 179.372 211.658 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 54.627 0 Td [(m)28(ust)-556(b)-27(e)-556(c)28(hosen)-555(ac)-1(cordi)1(ng)-556(to)-555(the)-556(real/complex,)-611(sin-)]TJ -78.714 -13.549 Td [(gle/double)-333(precision)-334(v)28(ersion)-333(of)-333(MLD2P4)-334(und)1(e)-1(r)-333(use.)]TJ +/F20 10.9091 Tf 179.3718 211.658 Td[(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 54.6268 0 Td[(m)27(u)1(s)-1(t)-555(b)-27(e)-556(c)27(h)1(os)-1(en)-555(ac)-1(cord)1(ing)-555(to)-555(the)-556(r)1(e)-1(al/complex,)-611(sin)1(-)]TJ -78.7139 -13.5492 Td[(gle/dou)1(ble)-333(prec)-1(i)1(s)-1(ion)-332(v)28(e)-1(rsion)-333(of)-333(M)1(LD2P4)-333(un)1(der)-333(use)-1(.)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -452 0 obj << +487 0 obj << /Type /Page -/Contents 453 0 R -/Resources 451 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R -/Annots [ 450 0 R ] +/Contents 488 0 R +/Resources 486 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 473 0 R +/Annots [ 490 0 R ] >> endobj -450 0 obj << +490 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 314.99 402.493 328.624] +/Rect [395.0462 314.9904 402.4932 328.6235] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -454 0 obj << -/D [452 0 R /XYZ 86.4 740.002 null] +489 0 obj << +/D [487 0 R /XYZ 86.3998 740.0018 null] >> endobj 82 0 obj << -/D [452 0 R /XYZ 86.4 715.095 null] +/D [487 0 R /XYZ 86.3998 715.0952 null] >> endobj -451 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F17 111 0 R /F44 200 0 R /F22 175 0 R /F26 272 0 R /F20 273 0 R /F18 173 0 R /F23 271 0 R >> +486 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F19 113 0 R /F46 219 0 R /F24 186 0 R /F28 293 0 R /F22 296 0 R /F20 181 0 R /F25 290 0 R >> /ProcSet [ /PDF /Text ] >> endobj -459 0 obj << -/Length 1564 +493 0 obj << +/Length 2326 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(6)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(29)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(29)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.5)-1125(Subroutine)-375(mld)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 11.9552 Tf 93.6002 704.1363 Td[(6.)-1(5)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ ET +1 0 0 1 216.6225 704.1363 cm q -1 0 0 1 216.622 704.336 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -216.6225 -704.1363 cm BT -/F17 11.9552 Tf 220.657 704.136 Td [(precfree)]TJ +/F19 11.9552 Tf 220.6574 704.1363 Td[(pre)-1(cfree)]TJ +ET +1 0 0 1 237.0991 683.5417 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf 21.897 -20.594 Td [(mld_precfree\050p,info\051)]TJ/F15 10.9091 Tf -148.954 -25.505 Td [(This)-333(routine)-334(deallo)-27(cates)-334(the)-333(preconditioner)-333(data)-334(structur)1(e)-1(.)]TJ/F17 11.9552 Tf 0 -40.647 Td [(Argumen)31(ts)]TJ/F44 10.9091 Tf 22.914 -12.805 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.18 0 Td [(.)]TJ -201.099 -13.55 Td [(The)-267(preconditioner)-267(data)-268(stru)1(c)-1(tu)1(re.)-423(Note)-267(that)]TJ/F18 10.9091 Tf 216.639 0 Td [(x)]TJ/F15 10.9091 Tf 9.29 0 Td [(m)28(ust)-267(b)-28(e)-267(c)27(hosen)]TJ -225.929 -13.549 Td [(according)-352(to)-352(the)-352(real/complex,)-357(single/double)-352(precision)-352(v)28(ersion)]TJ 0 -13.549 Td [(of)-333(MLD2P4)-334(un)1(der)-334(use.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-308(co)-28(de.)-435(If)-308(no)-308(error,)-313(0)-308(is)-308(returned.)-436(See)-308(S)1(e)-1(ction)]TJ +1 0 0 1 -237.0991 -683.5417 cm +BT +/F46 10.9091 Tf 242.5537 683.5417 Td[(mld_precfree\050p,info\051)]TJ/F15 10.9091 Tf -148.9535 -25.5044 Td[(This)-333(rout)1(ine)-334(d)1(e)-1(al)1(lo)-28(cate)-1(s)-333(the)-334(p)1(rec)-1(on)1(diti)1(oner)-333(data)-333(s)-1(t)1(ructur)1(e)-1(.)]TJ/F19 11.9552 Tf 0 -40.6476 Td[(Arg)-1(umen)31(t)-1(s)]TJ/F46 10.9091 Tf 22.9141 -12.8052 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-267(prec)-1(on)1(di)1(tioner)-267(dat)1(a)-268(stru)1(c)-1(tu)1(re.)-422(Note)-268(th)1(at)]TJ/F20 10.9091 Tf 216.6391 0 Td[(x)]TJ/F15 10.9091 Tf 9.2894 0 Td[(m)27(u)1(s)-1(t)-267(b)-27(e)-268(c)28(hose)-1(n)]TJ -225.9285 -13.5492 Td[(acc)-1(ord)1(in)1(g)-352(to)-352(the)-352(real/c)-1(ompl)1(e)-1(x,)-356(single/dou)1(bl)1(e)-353(p)1(re)-1(cision)-352(v)28(ersion)]TJ 0 -13.5492 Td[(of)-333(MLD)1(2P4)-333(un)1(der)-333(use)-1(.)]TJ/F46 10.9091 Tf -45.9708 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-307(c)-1(o)-28(d)1(e)-1(.)-435(If)-308(n)1(o)-308(e)-1(r)1(ror,)-313(0)-307(is)-308(re)-1(t)1(urn)1(e)-1(d)1(.)-436(See)-308(Sec)-1(ti)1(on)]TJ +ET +1 0 0 1 400.8906 536.8386 cm 0 0 1 rg 0 0 1 RG - [-307(7)]TJ +1 0 0 1 -400.8906 -536.8386 cm +BT +/F15 10.9091 Tf 400.8906 536.8386 Td[(7)]TJ +ET +1 0 0 1 406.3452 536.8386 cm 0 g 0 G - [-308(for)-308(details.)]TJ +1 0 0 1 -406.3452 -536.8386 cm +BT +/F15 10.9091 Tf 409.7037 536.8386 Td[(for)-307(details.)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -458 0 obj << +492 0 obj << /Type /Page -/Contents 459 0 R -/Resources 457 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R -/Annots [ 456 0 R 455 0 R ] +/Contents 493 0 R +/Resources 491 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 473 0 R +/Annots [ 495 0 R 496 0 R ] >> endobj -456 0 obj << +495 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -455 0 obj << +496 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [399.894 531.778 407.341 545.411] +/Rect [399.8944 531.7775 407.3414 545.4106] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -460 0 obj << -/D [458 0 R /XYZ 93.6 740.002 null] +494 0 obj << +/D [492 0 R /XYZ 93.6002 740.0018 null] >> endobj 86 0 obj << -/D [458 0 R /XYZ 93.6 715.095 null] +/D [492 0 R /XYZ 93.6002 715.0952 null] >> endobj -457 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F44 200 0 R /F18 173 0 R >> +491 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F46 219 0 R /F20 181 0 R >> /ProcSet [ /PDF /Text ] >> endobj -464 0 obj << -/Length 2271 +499 0 obj << +/Length 3084 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(30)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(30)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.6)-1125(Subroutine)-375(mld)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F19 11.9552 Tf 86.3998 704.1363 Td[(6.)-1(6)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ ET +1 0 0 1 209.422 704.1363 cm q -1 0 0 1 209.422 704.336 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -209.422 -704.1363 cm BT -/F17 11.9552 Tf 213.457 704.136 Td [(precdescr)]TJ +/F19 11.9552 Tf 213.4569 704.1363 Td[(pre)-1(cdescr)]TJ +ET +1 0 0 1 227.0351 683.5417 cm 0 g 0 G 0 g 0 G -/F44 10.9091 Tf 19.033 -20.594 Td [(mld_precdescr\050p,info\051)]TJ -14.318 -13.549 Td [(mld_precdescr\050p,info,iout\051)]TJ/F15 10.9091 Tf -131.772 -25.505 Td [(This)-364(routine)-364(prin)28(ts)-365(a)-364(description)-364(of)-364(the)-365(preconditioner)-364(to)-364(the)-364(standard)-364(output)-365(or)-364(to)-364(a)]TJ 0 -13.549 Td [(\014le.)-444(It)-334(m)28(ust)-333(b)-28(e)-333(called)-334(after)]TJ/F44 10.9091 Tf 132.212 0 Td [(mld_precbld)]TJ/F15 10.9091 Tf 66.636 0 Td [(has)-333(b)-28(een)-333(called.)]TJ/F17 11.9552 Tf -198.848 -40.648 Td [(Argumen)31(ts)]TJ/F44 10.9091 Tf 22.914 -12.805 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 125.998 0 Td [(.)]TJ -183.917 -13.549 Td [(The)-478(preconditioner)-478(data)-478(structure.)-878(Note)-478(that)]TJ/F18 10.9091 Tf 233.108 0 Td [(x)]TJ/F15 10.9091 Tf 11.588 0 Td [(m)28(ust)-478(b)-28(e)-478(c)28(hosen)-478(ac-)]TJ -244.696 -13.549 Td [(cording)-269(to)-269(the)-270(real/complex,)-282(single/double)-269(precision)-269(v)27(ersion)-269(of)-269(MLD2P4)]TJ 0 -13.549 Td [(under)-333(use.)]TJ/F44 10.9091 Tf -45.971 -13.55 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ +1 0 0 1 -227.0351 -683.5417 cm +BT +/F46 10.9091 Tf 232.4896 683.5417 Td[(mld_precdescr\050p,info\051)]TJ -14.318 -13.5492 Td[(mld_precdescr\050p,info,iout\051)]TJ/F15 10.9091 Tf -131.7718 -25.5044 Td[(This)-364(rou)1(tine)-364(pri)1(n)28(ts)-365(a)-364(desc)-1(ri)1(ption)-363(of)-364(the)-364(prec)-1(on)1(di)1(tioner)-364(to)-364(the)-364(s)-1(tan)1(dar)1(d)-364(outp)1(ut)-364(or)-364(to)-364(a)]TJ 0 -13.5492 Td[(\014l)1(e)-1(.)-444(It)-333(m)27(u)1(s)-1(t)-333(b)-27(e)-334(c)-1(al)1(le)-1(d)-333(af)1(ter)]TJ/F46 10.9091 Tf 132.2122 0 Td[(mld_precbld)]TJ/F15 10.9091 Tf 66.6357 0 Td[(has)-333(b)-28(ee)-1(n)-332(c)-1(all)1(e)-1(d)1(.)]TJ/F19 11.9552 Tf -198.8479 -40.6476 Td[(Arg)-1(umen)31(t)-1(s)]TJ/F46 10.9091 Tf 22.9141 -12.8052 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F46 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 125.9986 0 Td[(.)]TJ -183.9177 -13.5492 Td[(The)-478(pr)1(e)-1(cond)1(ition)1(e)-1(r)-478(d)1(ata)-478(stru)1(c)-1(tu)1(re.)-879(Note)-478(th)1(at)]TJ/F20 10.9091 Tf 233.1081 0 Td[(x)]TJ/F15 10.9091 Tf 11.5884 0 Td[(m)27(u)1(s)-1(t)-477(b)-28(e)-478(c)27(h)1(os)-1(en)-478(ac-)]TJ -244.6965 -13.5492 Td[(cordi)1(ng)-269(to)-269(the)-270(r)1(e)-1(al/complex,)-282(singl)1(e)-1(/d)1(oub)1(le)-270(pr)1(e)-1(cision)-269(v)28(ers)-1(i)1(on)-269(of)-269(MLD2P)1(4)]TJ 0 -13.5492 Td[(un)1(der)-333(use)-1(.)]TJ/F46 10.9091 Tf -45.9708 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-333(co)-28(de.)-444(If)-333(no)-333(e)-1(r)1(ror,)-333(0)-333(is)-334(r)1(e)-1(tu)1(rn)1(e)-1(d)1(.)-445(S)1(e)-1(e)-333(Sec)-1(tion)]TJ +ET +1 0 0 1 396.0424 509.7402 cm 0 0 1 rg 0 0 1 RG - [-333(7)]TJ +1 0 0 1 -396.0424 -509.7402 cm +BT +/F15 10.9091 Tf 396.0424 509.7402 Td[(7)]TJ +ET +1 0 0 1 401.497 509.7402 cm 0 g 0 G - [-333(for)-334(d)1(e)-1(tail)1(s)-1(.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(iout)-2114(integer,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(The)-376(id)-376(of)-375(the)-376(\014le)-376(where)-376(the)-376(p)1(rec)-1(on)1(ditioner)-376(description)-376(will)-376(b)-27(e)-376(prin)28(ted;)]TJ 0 -13.549 Td [(the)-333(default)-334(i)1(s)-334(the)-333(standard)-333(output.)]TJ +1 0 0 1 -401.497 -509.7402 cm +BT +/F15 10.9091 Tf 405.1333 509.7402 Td[(for)-333(d)1(e)-1(t)1(ails.)]TJ/F46 10.9091 Tf -295.8195 -13.5492 Td[(iout)-2114(integer,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 212.06 0 Td[(.)]TJ -166.0891 -13.5492 Td[(The)-376(id)-375(of)-376(t)1(he)-376(\014le)-376(where)-376(th)1(e)-377(p)1(rec)-1(on)1(diti)1(oner)-376(d)1(e)-1(sc)-1(r)1(ipti)1(on)-376(wil)1(l)-376(b)-27(e)-377(p)1(rin)29(te)-1(d)1(;)]TJ 0 -13.5492 Td[(th)1(e)-334(defau)1(lt)-333(is)-334(th)1(e)-334(s)-1(t)1(andar)1(d)-333(outp)1(ut.)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -463 0 obj << +498 0 obj << /Type /Page -/Contents 464 0 R -/Resources 462 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R -/Annots [ 461 0 R ] +/Contents 499 0 R +/Resources 497 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 473 0 R +/Annots [ 501 0 R ] >> endobj -461 0 obj << +501 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 504.679 402.493 518.312] +/Rect [395.0462 504.6791 402.4932 518.3122] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -465 0 obj << -/D [463 0 R /XYZ 86.4 740.002 null] +500 0 obj << +/D [498 0 R /XYZ 86.3998 740.0018 null] >> endobj 90 0 obj << -/D [463 0 R /XYZ 86.4 715.095 null] +/D [498 0 R /XYZ 86.3998 715.0952 null] >> endobj -462 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F17 111 0 R /F44 200 0 R /F18 173 0 R >> +497 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F19 113 0 R /F46 219 0 R /F20 181 0 R >> /ProcSet [ /PDF /Text ] >> endobj -470 0 obj << -/Length 1804 +504 0 obj << +/Length 2634 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(7)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(7)]TJ +ET +1 0 0 1 99.6305 740.0018 cm 0 g 0 G - [-378(Err)22(o)1(r)-378(handling)]TJ/F15 10.9091 Tf 401.542 0 Td [(31)]TJ +1 0 0 1 -99.6305 -740.0018 cm +BT +/F43 10.9091 Tf 103.7516 740.0018 Td[(Err)22(o)1(r)-378(h)-1(and)-1(lin)-1(g)]TJ/F15 10.9091 Tf 391.3906 0 Td[(31)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(7)-1125(Error)-375(Handling)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)-416(error)-416(handling)-416(in)-417(MLD2P)1(4)-417(is)-416(based)-416(on)-416(the)-417(PS)1(B)-1(LAS)-416(\050v)28(ersion)-416(2\051)-416(error)-416(handling.)]TJ 0 -13.549 Td [(Error)-249(conditions)-249(are)-249(signaled)-249(via)-249(an)-249(in)28(teger)-249(argumen)28(t)]TJ/F44 10.9091 Tf 252.188 0 Td [(info)]TJ/F15 10.9091 Tf 22.908 0 Td [(;)-277(whenev)28(er)-249(an)-249(error)-249(condition)]TJ -275.096 -13.549 Td [(is)-315(dete)-1(cted,)-319(an)-315(error)-315(trace)-316(stac)28(k)-315(is)-316(built)-315(b)28(y)-316(the)-315(library)-315(up)-316(to)-315(the)-316(top-lev)28(el,)-319(user-callable)]TJ 0 -13.549 Td [(routine.)-552(This)-370(routin)1(e)-370(will)-369(then)-369(decide,)-379(according)-369(to)-369(the)-370(user)-369(preferences,)-378(whether)-370(the)]TJ 0 -13.55 Td [(error)-275(should)-275(b)-28(e)-275(han)1(dled)-275(b)27(y)-275(t)1(e)-1(rmin)1(ating)-275(the)-275(program)-275(or)-275(b)28(y)-275(returning)-275(the)-275(error)-275(condition)]TJ 0 -13.549 Td [(to)-335(the)-334(use)-1(r)-334(co)-28(de,)-335(whic)28(h)-335(will)-335(then)-334(tak)27(e)-334(action,)-335(and)-335(whether)-335(an)-335(error)-334(message)-335(should)-335(b)-28(e)]TJ 0 -13.549 Td [(prin)28(ted.)-568(These)-375(options)-374(ma)28(y)-375(b)-28(e)-374(set)-375(b)28(y)-375(using)-374(the)-375(PS)1(B)-1(LAS)-374(error)-374(handling)-375(routines;)-395(for)]TJ 0 -13.549 Td [(further)-333(details)-334(see)-333(the)-333(PSBLAS)-334(User's)-333(Guide)-333([)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 14.3462 Tf 93.6002 704.1363 Td[(7)-1125(E)-1(rr)-1(or)-376(Ha)1(ndl)-1(ing)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(The)-416(e)-1(rr)1(or)-416(han)1(dli)1(ng)-416(in)-416(M)1(LD2P4)-416(is)-416(base)-1(d)-416(on)-415(the)-417(P)1(SBLAS)-416(\050v)28(ersion)-416(2\051)-416(error)-415(hand)1(lin)1(g.)]TJ 0 -13.5492 Td[(Er)1(ror)-249(cond)1(ition)1(s)-250(ar)1(e)-250(signal)1(e)-1(d)-248(via)-249(an)-248(in)28(tege)-1(r)-248(argumen)28(t)]TJ/F46 10.9091 Tf 252.1874 0 Td[(info)]TJ/F15 10.9091 Tf 22.9088 0 Td[(;)-277(whenev)28(e)-1(r)-248(an)-249(error)-248(c)-1(on)1(diti)1(on)]TJ -275.0962 -13.5492 Td[(is)-316(d)1(e)-1(tecte)-1(d)1(,)-319(an)-315(e)-1(r)1(ror)-315(trace)-316(stac)27(k)-315(is)-316(b)1(uil)1(t)-316(b)29(y)-316(th)1(e)-316(lib)1(rar)1(y)-316(u)1(p)-315(to)-315(the)-316(top)1(-)-1(l)1(e)-1(v)28(el,)-319(u)1(s)-1(er-c)-1(al)1(lable)]TJ 0 -13.5492 Td[(rou)1(tin)1(e)-1(.)-552(This)-369(routi)1(ne)-370(wil)1(l)-370(t)1(hen)-369(dec)-1(id)1(e)-1(,)-378(acc)-1(or)1(din)1(g)-369(to)-370(t)1(he)-370(u)1(s)-1(er)-369(pr)1(e)-1(f)1(e)-1(rences)-1(,)-378(whether)-369(the)]TJ 0 -13.5492 Td[(error)-274(s)-1(h)1(ould)-274(b)-28(e)-275(han)1(dl)1(e)-1(d)-274(b)28(y)-275(terminati)1(ng)-275(th)1(e)-276(p)1(rogram)-275(or)-275(b)29(y)-275(retur)1(nin)1(g)-275(the)-275(error)-274(c)-1(on)1(diti)1(on)]TJ 0 -13.5492 Td[(to)-335(th)1(e)-335(use)-1(r)-334(c)-1(o)-27(de,)-335(whic)28(h)-335(will)-334(then)-334(tak)28(e)-335(ac)-1(ti)1(on,)-335(an)1(d)-335(wheth)1(e)-1(r)-334(an)-335(err)1(or)-335(me)-1(ssage)-336(shou)1(ld)-334(b)-28(e)]TJ 0 -13.5492 Td[(pr)1(in)28(ted.)-567(T)-1(h)1(e)-1(se)-375(opti)1(ons)-375(ma)28(y)-375(b)-27(e)-375(s)-1(et)-374(b)28(y)-374(using)-374(the)-375(P)1(SBLAS)-374(e)-1(r)1(ror)-374(han)1(dli)1(ng)-375(r)1(outi)1(nes)-1(;)-395(f)1(or)]TJ 0 -13.5492 Td[(fu)1(rth)1(e)-1(r)-333(d)1(e)-1(tai)1(ls)-334(se)-1(e)-334(t)1(he)-334(P)1(SBLAS)-333(Us)-1(er')1(s)-334(Gui)1(de)-334([)]TJ +ET +1 0 0 1 315.0702 584.9397 cm 1 0 0 rg 1 0 0 RG - [(14)]TJ +1 0 0 1 -315.0702 -584.9397 cm +BT +/F15 10.9091 Tf 315.0702 584.9397 Td[(14)]TJ +ET +1 0 0 1 325.9793 584.9397 cm 0 g 0 G - [(].)]TJ +1 0 0 1 -325.9793 -584.9397 cm +BT +/F15 10.9091 Tf 325.9793 584.9397 Td[(].)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -469 0 obj << +503 0 obj << /Type /Page -/Contents 470 0 R -/Resources 468 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 472 0 R -/Annots [ 467 0 R 466 0 R ] +/Contents 504 0 R +/Resources 502 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 508 0 R +/Annots [ 506 0 R 507 0 R ] >> endobj -467 0 obj << +506 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] +/Rect [92.604 739.0056 100.6267 748.4526] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -466 0 obj << +507 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [314.074 583.943 326.976 592.966] +/Rect [314.0739 583.9435 326.9755 592.9663] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -471 0 obj << -/D [469 0 R /XYZ 93.6 740.002 null] +505 0 obj << +/D [503 0 R /XYZ 93.6002 740.0018 null] >> endobj 94 0 obj << -/D [469 0 R /XYZ 93.6 715.095 null] +/D [503 0 R /XYZ 93.6002 715.0952 null] >> endobj -468 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F44 200 0 R >> +502 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -475 0 obj << -/Length 3999 +511 0 obj << +/Length 4335 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(32)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(32)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -203.265 -35.866 Td [(A)-1125(License)]TJ/F15 10.9091 Tf 0 -22.758 Td [(The)-333(MLD2P4)-334(is)-333(freely)-333(distributable)-333(under)-334(the)-333(follo)28(wing)-333(cop)27(yri)1(gh)27(t)-333(terms:)]TJ +1 0 0 1 -498.8509 -740.0018 cm +BT +/F19 14.3462 Tf 86.3998 704.1363 Td[(A)-1125(L)1(i)-1(cense)]TJ/F15 10.9091 Tf 0 -22.7582 Td[(The)-334(M)1(LD2P4)-333(is)-334(f)1(ree)-1(l)1(y)-334(d)1(istrib)1(utab)1(le)-334(u)1(nd)1(e)-1(r)-333(th)1(e)-334(fol)1(lo)28(w)-1(i)1(ng)-333(c)-1(op)28(y)1(righ)28(t)-333(terms)-1(:)]TJ +ET +1 0 0 1 80.9452 660.4566 cm 0 g 0 G 0 g 0 G -/F44 9.9626 Tf 130.758 -20.921 Td [(MLD2P4)-1050(version)-525(1.0)]TJ -130.758 -11.956 Td [(MultiLevel)-525(Domain)-525(Decomposition)-525(Parallel)-525(Preconditioners)-525(Package)]TJ 57.534 -11.955 Td [(based)-525(on)-525(PSBLAS)-525(\050Parallel)-525(Sparse)-525(BLAS)-525(version)-525(2.3\051)]TJ -57.534 -23.91 Td [(\050C\051)-525(Copyright)-525(2008)]TJ 104.607 -23.91 Td [(Salvatore)-525(Filippone)-1050(University)-525(of)-525(Rome)-525(Tor)-525(Vergata)]TJ 0 -11.956 Td [(Alfredo)-525(Buttari)-3150(University)-525(of)-525(Rome)-525(Tor)-525(Vergata)]TJ 0 -11.955 Td [(Pasqua)-525(D'Ambra)-3675(ICAR-CNR,)-525(Naples)]TJ 0 -11.955 Td [(Daniela)-525(di)-525(Serafino)-1050(Second)-525(University)-525(of)-525(Naples)]TJ -104.607 -35.865 Td [(Redistribution)-525(and)-525(use)-525(in)-525(source)-525(and)-525(binary)-525(forms,)-525(with)-525(or)-525(without)]TJ 0 -11.956 Td [(modification,)-525(are)-525(permitted)-525(provided)-525(that)-525(the)-525(following)-525(conditions)]TJ 0 -11.955 Td [(are)-525(met:)]TJ 10.46 -11.955 Td [(1.)-525(Redistributions)-525(of)-525(source)-525(code)-525(must)-525(retain)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.955 Td [(notice,)-525(this)-525(list)-525(of)-525(conditions)-525(and)-525(the)-525(following)-525(disclaimer.)]TJ -15.691 -11.955 Td [(2.)-525(Redistributions)-525(in)-525(binary)-525(form)-525(must)-525(reproduce)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.955 Td [(notice,)-525(this)-525(list)-525(of)-525(conditions,)-525(and)-525(the)-525(following)-525(disclaimer)-525(in)-525(the)]TJ 0 -11.956 Td [(documentation)-525(and/or)-525(other)-525(materials)-525(provided)-525(with)-525(the)-525(distribution.)]TJ -15.691 -11.955 Td [(3.)-525(The)-525(name)-525(of)-525(the)-525(MLD2P4)-525(group)-525(or)-525(the)-525(names)-525(of)-525(its)-525(contributors)-525(may)]TJ 15.691 -11.955 Td [(not)-525(be)-525(used)-525(to)-525(endorse)-525(or)-525(promote)-525(products)-525(derived)-525(from)-525(this)]TJ 0 -11.955 Td [(software)-525(without)-525(specific)-525(written)-525(permission.)]TJ -26.151 -23.911 Td [(THIS)-525(SOFTWARE)-525(IS)-525(PROVIDED)-525(BY)-525(THE)-525(COPYRIGHT)-525(HOLDERS)-525(AND)-525(CONTRIBUTORS)]TJ 0 -11.955 Td [(``AS)-525(IS'')-525(AND)-525(ANY)-525(EXPRESS)-525(OR)-525(IMPLIED)-525(WARRANTIES,)-525(INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)]TJ 0 -11.955 Td [(TO,)-525(THE)-525(IMPLIED)-525(WARRANTIES)-525(OF)-525(MERCHANTABILITY)-525(AND)-525(FITNESS)-525(FOR)-525(A)-525(PARTICULAR)]TJ 0 -11.955 Td [(PURPOSE)-525(ARE)-525(DISCLAIMED.)-525(IN)-525(NO)-525(EVENT)-525(SHALL)-525(THE)-525(MLD2P4)-525(GROUP)-525(OR)-525(ITS)-525(CONTRIBUTORS)]TJ 0 -11.955 Td [(BE)-525(LIABLE)-525(FOR)-525(ANY)-525(DIRECT,)-525(INDIRECT,)-525(INCIDENTAL,)-525(SPECIAL,)-525(EXEMPLARY,)-525(OR)]TJ 0 -11.955 Td [(CONSEQUENTIAL)-525(DAMAGES)-525(\050INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)-525(TO,)-525(PROCUREMENT)-525(OF)]TJ 0 -11.956 Td [(SUBSTITUTE)-525(GOODS)-525(OR)-525(SERVICES;)-525(LOSS)-525(OF)-525(USE,)-525(DATA,)-525(OR)-525(PROFITS;)-525(OR)-525(BUSINESS)]TJ 0 -11.955 Td [(INTERRUPTION\051)-525(HOWEVER)-525(CAUSED)-525(AND)-525(ON)-525(ANY)-525(THEORY)-525(OF)-525(LIABILITY,)-525(WHETHER)-525(IN)]TJ 0 -11.955 Td [(CONTRACT,)-525(STRICT)-525(LIABILITY,)-525(OR)-525(TORT)-525(\050INCLUDING)-525(NEGLIGENCE)-525(OR)-525(OTHERWISE\051)]TJ 0 -11.955 Td [(ARISING)-525(IN)-525(ANY)-525(WAY)-525(OUT)-525(OF)-525(THE)-525(USE)-525(OF)-525(THIS)-525(SOFTWARE,)-525(EVEN)-525(IF)-525(ADVISED)-525(OF)-525(THE)]TJ 0 -11.955 Td [(POSSIBILITY)-525(OF)-525(SUCH)-525(DAMAGE.)]TJ +1 0 0 1 -80.9452 -660.4566 cm +BT +/F46 9.9626 Tf 217.1583 660.4566 Td[(MLD2P4)-1050(version)-525(1.0)]TJ -130.7585 -11.9552 Td[(MultiLevel)-525(Domain)-525(Decomposition)-525(Parallel)-525(Preconditioners)-525(Package)]TJ 57.5337 -11.9551 Td[(based)-525(on)-525(PSBLAS)-525(\050Parallel)-525(Sparse)-525(BLAS)-525(version)-525(2.3\051)]TJ -57.5337 -23.9104 Td[(\050C\051)-525(Copyright)-525(2008)]TJ 104.6068 -23.9103 Td[(Salvatore)-525(Filippone)-1050(University)-525(of)-525(Rome)-525(Tor)-525(Vergata)]TJ 0 -11.9552 Td[(Alfredo)-525(Buttari)-3150(University)-525(of)-525(Rome)-525(Tor)-525(Vergata)]TJ 0 -11.9551 Td[(Pasqua)-525(D'Ambra)-3675(ICAR-CNR,)-525(Naples)]TJ 0 -11.9552 Td[(Daniela)-525(di)-525(Serafino)-1050(Second)-525(University)-525(of)-525(Naples)]TJ -104.6068 -35.8655 Td[(Redistribution)-525(and)-525(use)-525(in)-525(source)-525(and)-525(binary)-525(forms,)-525(with)-525(or)-525(without)]TJ 0 -11.9552 Td[(modification,)-525(are)-525(permitted)-525(provided)-525(that)-525(the)-525(following)-525(conditions)]TJ 0 -11.9551 Td[(are)-525(met:)]TJ 10.4607 -11.9552 Td[(1.)-525(Redistributions)-525(of)-525(source)-525(code)-525(must)-525(retain)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.9552 Td[(notice,)-525(this)-525(list)-525(of)-525(conditions)-525(and)-525(the)-525(following)-525(disclaimer.)]TJ -15.691 -11.9551 Td[(2.)-525(Redistributions)-525(in)-525(binary)-525(form)-525(must)-525(reproduce)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.9552 Td[(notice,)-525(this)-525(list)-525(of)-525(conditions,)-525(and)-525(the)-525(following)-525(disclaimer)-525(in)-525(the)]TJ 0 -11.9552 Td[(documentation)-525(and/or)-525(other)-525(materials)-525(provided)-525(with)-525(the)-525(distribution.)]TJ -15.691 -11.9551 Td[(3.)-525(The)-525(name)-525(of)-525(the)-525(MLD2P4)-525(group)-525(or)-525(the)-525(names)-525(of)-525(its)-525(contributors)-525(may)]TJ 15.691 -11.9552 Td[(not)-525(be)-525(used)-525(to)-525(endorse)-525(or)-525(promote)-525(products)-525(derived)-525(from)-525(this)]TJ 0 -11.9552 Td[(software)-525(without)-525(specific)-525(written)-525(permission.)]TJ -26.1517 -23.9103 Td[(THIS)-525(SOFTWARE)-525(IS)-525(PROVIDED)-525(BY)-525(THE)-525(COPYRIGHT)-525(HOLDERS)-525(AND)-525(CONTRIBUTORS)]TJ 0 -11.9552 Td[(``AS)-525(IS'')-525(AND)-525(ANY)-525(EXPRESS)-525(OR)-525(IMPLIED)-525(WARRANTIES,)-525(INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)]TJ 0 -11.9551 Td[(TO,)-525(THE)-525(IMPLIED)-525(WARRANTIES)-525(OF)-525(MERCHANTABILITY)-525(AND)-525(FITNESS)-525(FOR)-525(A)-525(PARTICULAR)]TJ 0 -11.9552 Td[(PURPOSE)-525(ARE)-525(DISCLAIMED.)-525(IN)-525(NO)-525(EVENT)-525(SHALL)-525(THE)-525(MLD2P4)-525(GROUP)-525(OR)-525(ITS)-525(CONTRIBUTORS)]TJ 0 -11.9552 Td[(BE)-525(LIABLE)-525(FOR)-525(ANY)-525(DIRECT,)-525(INDIRECT,)-525(INCIDENTAL,)-525(SPECIAL,)-525(EXEMPLARY,)-525(OR)]TJ 0 -11.9551 Td[(CONSEQUENTIAL)-525(DAMAGES)-525(\050INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)-525(TO,)-525(PROCUREMENT)-525(OF)]TJ 0 -11.9552 Td[(SUBSTITUTE)-525(GOODS)-525(OR)-525(SERVICES;)-525(LOSS)-525(OF)-525(USE,)-525(DATA,)-525(OR)-525(PROFITS;)-525(OR)-525(BUSINESS)]TJ 0 -11.9552 Td[(INTERRUPTION\051)-525(HOWEVER)-525(CAUSED)-525(AND)-525(ON)-525(ANY)-525(THEORY)-525(OF)-525(LIABILITY,)-525(WHETHER)-525(IN)]TJ 0 -11.9551 Td[(CONTRACT,)-525(STRICT)-525(LIABILITY,)-525(OR)-525(TORT)-525(\050INCLUDING)-525(NEGLIGENCE)-525(OR)-525(OTHERWISE\051)]TJ 0 -11.9552 Td[(ARISING)-525(IN)-525(ANY)-525(WAY)-525(OUT)-525(OF)-525(THE)-525(USE)-525(OF)-525(THIS)-525(SOFTWARE,)-525(EVEN)-525(IF)-525(ADVISED)-525(OF)-525(THE)]TJ 0 -11.9552 Td[(POSSIBILITY)-525(OF)-525(SUCH)-525(DAMAGE.)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -474 0 obj << +510 0 obj << /Type /Page -/Contents 475 0 R -/Resources 473 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 472 0 R +/Contents 511 0 R +/Resources 509 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 508 0 R >> endobj -476 0 obj << -/D [474 0 R /XYZ 86.4 740.002 null] +512 0 obj << +/D [510 0 R /XYZ 86.3998 740.0018 null] >> endobj 98 0 obj << -/D [474 0 R /XYZ 86.4 715.095 null] +/D [510 0 R /XYZ 86.3998 715.0952 null] >> endobj -473 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F17 111 0 R /F44 200 0 R >> +509 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F19 113 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -479 0 obj << -/Length 6658 +515 0 obj << +/Length 9878 >> stream +1 0 0 1 93.6002 740.0018 cm 0 g 0 G +1 0 0 1 -93.6002 -740.0018 cm BT -/F41 10.9091 Tf 93.6 740.002 Td [(References)]TJ/F15 10.9091 Tf 401.542 0 Td [(33)]TJ +/F43 10.9091 Tf 93.6002 740.0018 Td[(Ref)1(erenc)-1(e)1(s)]TJ/F15 10.9091 Tf 401.542 0 Td[(33)]TJ +ET +1 0 0 1 506.0513 740.0018 cm 0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(References)]TJ +1 0 0 1 -506.0513 -740.0018 cm +BT +/F19 14.3462 Tf 93.6002 704.1363 Td[(Refer)-1(ence)-1(s)]TJ +ET +1 0 0 1 93.6002 679.7841 cm 0 g 0 G -/F15 10.9091 Tf 5.455 -24.352 Td [([1])]TJ +1 0 0 1 -93.6002 -679.7841 cm +BT +/F15 10.9091 Tf 99.0548 679.7841 Td[([1])]TJ +ET +1 0 0 1 110.5699 679.7841 cm 0 g 0 G - [-500(M.)-272(Brezina,)-284(P)83(.)-272(V)84(an)27(\024)473(ek,)]TJ/F18 10.9091 Tf 123.379 0 Td [(A)-301(Black-Box)-302(I)1(ter)51(ative)-302(Solver)-301(Base)51(d)-301(on)-302(a)-301(Two-L)51(evel)-301(Schwarz)]TJ -106.41 -13.549 Td [(Metho)51(d)]TJ/F15 10.9091 Tf 34.594 0 Td [(,)-333(Computing,)-334(63,)-333(1999,)-333(233{263.)]TJ +1 0 0 1 -110.5699 -679.7841 cm +BT +/F15 10.9091 Tf 116.0245 679.7841 Td[(M.)-271(B)-1(r)1(e)-1(zina,)-284(P)84(.)-272(V)84(an)28(\024)472(ek,)]TJ/F20 10.9091 Tf 106.4092 0 Td[(A)-302(Bl)1(ack-Box)-301(Iter)52(a)-1(ti)1(ve)-302(Solver)-301(Base)52(d)-302(on)-302(a)-301(Two-L)51(evel)-301(Schw)-1(ar)1(z)]TJ -106.4092 -13.5492 Td[(Metho)51(d)]TJ/F15 10.9091 Tf 34.5937 0 Td[(,)-333(Com)-1(p)1(uti)1(ng,)-333(63,)-333(1999,)-333(233{263.)]TJ +ET +1 0 0 1 93.6002 645.0456 cm 0 g 0 G - -51.563 -21.189 Td [([2])]TJ +1 0 0 1 -93.6002 -645.0456 cm +BT +/F15 10.9091 Tf 99.0548 645.0456 Td[([2])]TJ +ET +1 0 0 1 110.5699 645.0456 cm 0 g 0 G - [-500(A.)-306(Buttari,)-312(P)84(.)-306(D'Am)27(bra,)-311(D.)-306(di)-306(Sera\014no,)-312(S.)-306(Filipp)-28(one,)]TJ/F18 10.9091 Tf 272.057 0 Td [(Extending)-333(PSBLAS)-333(to)-333(Bui)1(ld)]TJ -255.088 -13.55 Td [(Par)51(al)-51(lel)-472(Schwarz)-473(Pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 159.206 0 Td [(,)-489(in)-458(,)-489(J.)-458(Dongarra,)-490(K.)-458(Mad)1(s)-1(en,)-489(J.)-458(W)84(asniewski,)]TJ -159.206 -13.549 Td [(editors,)-319(Pro)-27(ce)-1(edin)1(gs)-316(of)-315(P)84(ARA)-315(04)-315(W)83(orkshop)-315(on)-315(State)-315(of)-315(the)-315(Art)-315(in)-315(Scien)28(ti\014c)-316(Com-)]TJ 0 -13.549 Td [(puting,)-333(Lecture)-334(Notes)-333(in)-333(Computer)-334(Science,)-333(Springer,)-333(2005,)-333(593{602.)]TJ +1 0 0 1 -110.5699 -645.0456 cm +BT +/F15 10.9091 Tf 116.0245 645.0456 Td[(A.)-306(Buttar)1(i,)-311(P)83(.)-306(D')1(Am)27(b)1(ra,)-312(D)1(.)-306(di)-306(S)1(e)-1(ra\014)1(no,)-311(S.)-306(F)1(ilip)1(p)-28(on)1(e)-1(,)]TJ/F20 10.9091 Tf 255.0876 0 Td[(Exten)-1(di)1(n)-1(g)-332(P)-1(SBLAS)-333(t)-1(o)-333(B)1(uil)1(d)]TJ -255.0876 -13.5492 Td[(Par)51(al)-51(l)1(el)-472(S)-1(chwarz)-472(P)-1(r)52(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 159.2054 0 Td[(,)-489(in)-457(,)-489(J.)-458(Dongar)1(ra,)-489(K.)-458(M)1(adse)-1(n)1(,)-489(J.)-458(W)84(as)-1(n)1(ie)-1(wski,)]TJ -159.2054 -13.5492 Td[(editor)1(s)-1(,)-318(Pro)-27(c)-1(ee)-1(d)1(ings)-315(of)-315(P)84(ARA)-315(04)-315(W)83(or)1(ks)-1(h)1(op)-315(on)-314(State)-315(of)-315(th)1(e)-316(Ar)1(t)-315(in)-315(S)1(c)-1(ien)28(ti\014)1(c)-316(Com-)]TJ 0 -13.5492 Td[(pu)1(tin)1(g,)-333(Le)-1(ctur)1(e)-334(Note)-1(s)-333(in)-333(Com)-1(p)1(uter)-333(Science)-1(,)-333(S)1(pri)1(nger,)-333(2005,)-333(593{602.)]TJ +ET +1 0 0 1 93.6002 583.2087 cm 0 g 0 G - -16.969 -21.189 Td [([3])]TJ +1 0 0 1 -93.6002 -583.2087 cm +BT +/F15 10.9091 Tf 99.0548 583.2087 Td[([3])]TJ +ET +1 0 0 1 110.5699 583.2087 cm 0 g 0 G - [-500(A.)-380(Buttari,)-392(P)84(.)-381(D')1(Am)27(bra,)-391(D.)-381(di)-380(Sera\014no,)-391(S.)-380(Filipp)-28(one,)]TJ/F18 10.9091 Tf 279.591 0 Td [(2LEV-D2P4:)-546(a)-401(p)51(ackage)-401(of)]TJ -262.622 -13.549 Td [(high-p)51(erformanc)51(e)-423(pr)51(e)51(c)51(onditioners)-424(for)-423(scienti\014c)-424(and)-424(engine)52(ering)-424(applic)51(ations)]TJ/F15 10.9091 Tf 364.505 0 Td [(,)-423(Ap-)]TJ -364.505 -13.55 Td [(plicable)-462(Algebra)-461(in)-462(Engineering,)-493(Comm)27(uni)1(c)-1(ation)1(s)-462(and)-462(Computing,)-493(18,)-494(3,)-494(2007,)]TJ 0 -13.549 Td [(223{239.)]TJ +1 0 0 1 -110.5699 -583.2087 cm +BT +/F15 10.9091 Tf 116.0245 583.2087 Td[(A.)-380(Buttar)1(i,)-392(P)84(.)-380(D')1(Am)27(br)1(a,)-392(D.)-380(d)1(i)-380(Sera\014)1(no,)-392(S)1(.)-380(Fil)1(ipp)-27(one,)]TJ/F20 10.9091 Tf 262.6214 0 Td[(2LE)-1(V-D2P4:)-546(a)-401(p)51(ackage)-401(of)]TJ -262.6214 -13.5492 Td[(high-p)51(er)1(formanc)51(e)-423(p)-1(r)52(e)51(c)51(onditioners)-423(for)-423(scienti\014c)-424(and)-424(engine)51(eri)1(n)-1(g)-423(ap)-1(pl)1(ic)51(ations)]TJ/F15 10.9091 Tf 364.5046 0 Td[(,)-423(Ap)1(-)]TJ -364.5046 -13.5492 Td[(pl)1(ic)-1(ab)1(le)-462(Algebr)1(a)-462(in)-461(En)1(gin)1(e)-1(erin)1(g,)-494(Comm)27(un)1(ications)-462(an)1(d)-461(C)-1(omp)1(utin)1(g,)-494(18,)-493(3,)-494(2007,)]TJ 0 -13.5492 Td[(223{239.)]TJ +ET +1 0 0 1 93.6002 521.3718 cm 0 g 0 G - -16.969 -21.189 Td [([4])]TJ +1 0 0 1 -93.6002 -521.3718 cm +BT +/F15 10.9091 Tf 99.0548 521.3718 Td[([4])]TJ +ET +1 0 0 1 110.5699 521.3718 cm 0 g 0 G - [-500(P)83(.)-366(D'Am)28(bra,)-375(S.)-367(Filipp)-27(one,)-375(D.)-367(di)-366(Sera\014no,)]TJ/F18 10.9091 Tf 220.753 0 Td [(On)-388(the)-389(Development)-388(of)-388(PS)-1(B)1(L)-1(AS-b)52(ase)51(d)]TJ -203.784 -13.549 Td [(Par)51(al)-51(lel)-380(Two-level)-379(Schwarz)-380(Pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 206.489 0 Td [(,)-363(Applied)-357(Numerical)-358(Mathematics,)-363(El-)]TJ -206.489 -13.55 Td [(sevier)-333(Science)-1(,)-333(57,)-333(11-12,)-333(2007,)-334(1181-1196.)]TJ +1 0 0 1 -110.5699 -521.3718 cm +BT +/F15 10.9091 Tf 116.0245 521.3718 Td[(P)84(.)-367(D)1('Am)27(b)1(ra,)-375(S)1(.)-367(F)1(ilip)1(p)-28(on)1(e)-1(,)-374(D.)-367(d)1(i)-367(S)1(e)-1(r)1(a\014n)1(o,)]TJ/F20 10.9091 Tf 203.7832 0 Td[(On)-388(th)-1(e)-388(Development)-388(of)-388(P)-1(SBLAS)-1(-)1(b)51(ase)51(d)]TJ -203.7832 -13.5492 Td[(Par)51(al)-51(l)1(el)-380(T)1(w)-1(o-l)1(evel)-379(S)-1(chwarz)-380(Pr)52(e)51(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)1(s)]TJ/F15 10.9091 Tf 206.4885 0 Td[(,)-363(App)1(lied)-357(Numerical)-357(Math)1(e)-1(matics)-1(,)-363(E)1(l-)]TJ -206.4885 -13.5492 Td[(se)-1(vi)1(e)-1(r)-333(S)1(c)-1(ience)-1(,)-333(57,)-333(11-12,)-333(2007,)-333(1181-)-1(1196.)]TJ +ET +1 0 0 1 93.6002 473.0841 cm 0 g 0 G - -16.969 -21.189 Td [([5])]TJ +1 0 0 1 -93.6002 -473.0841 cm +BT +/F15 10.9091 Tf 99.0548 473.0841 Td[([5])]TJ +ET +1 0 0 1 110.5699 473.0841 cm 0 g 0 G - [-500(X.)-410(C.)-410(Cai,)-430(M.)-410(Sarkis,)]TJ/F18 10.9091 Tf 126.22 0 Td [(A)-428(R)51(estricte)51(d)-429(A)51(dditive)-428(Schwarz)-429(Pr)51(e)52(c)51(onditioner)-429(for)-428(Gener)51(al)]TJ -109.251 -13.549 Td [(Sp)51(arse)-378(Line)51(ar)-379(Systems)]TJ/F15 10.9091 Tf 107.936 0 Td [(,)-361(SIAM)-356(Journal)-356(on)-356(Scien)28(ti\014c)-356(Computing,)-361(21,)-361(2,)-362(1999,)-361(792{)]TJ -107.936 -13.549 Td [(797.)]TJ +1 0 0 1 -110.5699 -473.0841 cm +BT +/F15 10.9091 Tf 116.0245 473.0841 Td[(X.)-410(C.)-410(Cai,)-429(M.)-410(Sar)1(kis,)]TJ/F20 10.9091 Tf 109.2505 0 Td[(A)-429(R)51(estricte)51(d)-428(A)51(d)-1(di)1(t)-1(i)1(ve)-429(Schw)-1(ar)1(z)-429(Pr)51(e)52(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)-428(for)-428(G)1(en)-1(er)52(al)]TJ -109.2505 -13.5492 Td[(Sp)51(arse)-378(L)-1(i)1(ne)51(ar)-379(Sy)1(stems)]TJ/F15 10.9091 Tf 107.9356 0 Td[(,)-361(SIAM)-355(Jour)1(nal)-356(on)-355(Scien)28(ti\014)1(c)-357(Compu)1(tin)1(g,)-362(21,)-361(2,)-361(1999,)-361(792{)]TJ -107.9356 -13.5492 Td[(797.)]TJ +ET +1 0 0 1 93.6002 424.7964 cm 0 g 0 G - -16.969 -21.19 Td [([6])]TJ +1 0 0 1 -93.6002 -424.7964 cm +BT +/F15 10.9091 Tf 99.0548 424.7964 Td[([6])]TJ +ET +1 0 0 1 110.5699 424.7964 cm 0 g 0 G - [-500(X.)-234(C.)-234(Cai,)-254(O.)-234(B.)-234(Widlund,)]TJ/F18 10.9091 Tf 141.054 0 Td [(Domain)-266(De)51(c)51(omp)51(osition)-266(A)25(lgorithms)-266(for)-267(I)1(n)-1(de\014nite)-266(El)-51(liptic)]TJ -124.085 -13.549 Td [(Pr)51(oblems)]TJ/F15 10.9091 Tf 43.224 0 Td [(,)-293(SIAM)-282(Journal)-282(on)-282(Scien)27(ti\014)1(c)-283(and)-282(Statistical)-282(Com)-1(p)1(uting,)-293(13,)-292(1,)-293(1992,)-293(243{)]TJ -43.224 -13.549 Td [(258.)]TJ +1 0 0 1 -110.5699 -424.7964 cm +BT +/F15 10.9091 Tf 116.0245 424.7964 Td[(X.)-234(C.)-234(Cai,)-254(O)1(.)-234(B.)-234(Wid)1(lun)1(d,)]TJ/F20 10.9091 Tf 124.0849 0 Td[(Domain)-266(De)51(c)51(omp)51(ositi)1(o)-1(n)-266(A)25(lgor)1(ithms)-266(for)-266(Inde\014n)-1(i)1(te)-267(El)-51(l)1(iptic)]TJ -124.0849 -13.5492 Td[(Pr)51(oblem)1(s)]TJ/F15 10.9091 Tf 43.2239 0 Td[(,)-292(SIAM)-282(Jou)1(rnal)-282(on)-282(S)1(c)-1(i)1(e)-1(n)28(ti)1(\014c)-283(an)1(d)-282(Stati)1(s)-1(ti)1(c)-1(al)-282(Com)-1(p)1(uti)1(ng,)-292(13,)-293(1,)-292(1992,)-292(243{)]TJ -43.2239 -13.5492 Td[(258.)]TJ +ET +1 0 0 1 93.6002 376.5086 cm 0 g 0 G - -16.969 -21.189 Td [([7])]TJ +1 0 0 1 -93.6002 -376.5086 cm +BT +/F15 10.9091 Tf 99.0548 376.5086 Td[([7])]TJ +ET +1 0 0 1 110.5699 376.5086 cm 0 g 0 G - [-500(T.)-316(Chan)-315(and)-316(T.)-315(Mathew,)]TJ/F18 10.9091 Tf 140.588 0 Td [(Domain)-341(De)51(c)51(omp)51(osition)-342(A)26(lgorithms)]TJ/F15 10.9091 Tf 165.71 0 Td [(,)-319(in)-316(A.)-315(Iserles,)-320(editor,)]TJ -289.329 -13.55 Td [(Acta)-333(Numerica)-334(1994,)-333(61{143.)-333(Cam)27(bridge)-333(Univ)28(ersit)28(y)-334(Press.)]TJ +1 0 0 1 -110.5699 -376.5086 cm +BT +/F15 10.9091 Tf 116.0245 376.5086 Td[(T.)-316(Ch)1(an)-316(an)1(d)-315(T)-1(.)-315(Math)1(e)-1(w,)]TJ/F20 10.9091 Tf 123.6183 0 Td[(Domain)-341(De)51(c)51(omp)51(osition)-341(A)25(lgor)1(ithms)]TJ/F15 10.9091 Tf 165.71 0 Td[(,)-319(in)-315(A.)-315(Is)-1(erles)-1(,)-319(edi)1(tor,)]TJ -289.3283 -13.5492 Td[(Acta)-334(Nu)1(m)-1(eri)1(c)-1(a)-333(1994,)-333(61{143.)-333(C)-1(am)28(br)1(idge)-334(Un)1(iv)28(ersit)28(y)-333(Pres)-1(s.)]TJ +ET +1 0 0 1 93.6002 341.7701 cm 0 g 0 G - -16.969 -21.189 Td [([8])]TJ +1 0 0 1 -93.6002 -341.7701 cm +BT +/F15 10.9091 Tf 99.0548 341.7701 Td[([8])]TJ +ET +1 0 0 1 110.5699 341.7701 cm 0 g 0 G - [-500(T.A.)-444(Da)28(vis,)]TJ/F18 10.9091 Tf 78.69 0 Td [(A)25(l)1(gorithm)-460(832:)-664(UMFP)77(A)25(CK)-460(-)-459(an)-460(Unsymmetric-p)51(attern)-460(Mu)1(ltifr)51(ontal)]TJ -61.721 -13.549 Td [(Metho)51(d)-307(with)-307(a)-308(Col)1(umn)-308(Pr)52(e-or)51(dering)-307(St)-1(r)52(ate)51(gy)]TJ/F15 10.9091 Tf 211.246 0 Td [(,)-289(A)27(CM)-278(T)83(ran)1(s)-1(action)1(s)-279(on)-278(Mathematical)]TJ -211.246 -13.549 Td [(Soft)28(w)28(are,)-334(30,)-333(2004,)-333(196{199.)-334(\050See)-333(also)]TJ/F44 10.9091 Tf 184.031 0 Td [(http://www.cise.ufl.edu/)-525(davis/)]TJ/F15 10.9091 Tf 177.543 0 Td [(\051)]TJ +1 0 0 1 -110.5699 -341.7701 cm +BT +/F15 10.9091 Tf 116.0245 341.7701 Td[(T.A.)-444(Da)28(vis,)]TJ/F20 10.9091 Tf 61.721 0 Td[(A)25(l)1(gorithm)-460(832:)-664(UMF)1(P)76(A)25(C)1(K)-460(-)-459(a)-1(n)-459(U)-1(nsy)1(mmetric-)1(p)51(at)-1(tern)-460(M)1(ul)1(t)-1(i)1(fr)52(o)-1(ntal)]TJ -61.721 -13.5492 Td[(Metho)51(d)-307(w)-1(i)1(t)-1(h)-307(a)-307(Col)1(umn)-307(P)-1(r)52(e-or)51(der)1(ing)-307(S)-1(tr)52(a)-1(te)51(gy)]TJ/F15 10.9091 Tf 211.2457 0 Td[(,)-289(A)28(C)-1(M)-278(T)84(ransac)-1(t)1(ions)-279(on)-277(Mathematical)]TJ -211.2457 -13.5492 Td[(Sof)1(t)28(w)27(ar)1(e)-1(,)-333(30,)-333(2004,)-333(196{199.)-333(\050See)-334(also)]TJ/F46 10.9091 Tf 184.0304 0 Td[(http://www.cise.ufl.edu/)-525(davis/)]TJ/F15 10.9091 Tf 177.5436 0 Td[(\051)]TJ +ET +1 0 0 1 93.6002 293.4824 cm 0 g 0 G - -378.543 -21.19 Td [([9])]TJ +1 0 0 1 -93.6002 -293.4824 cm +BT +/F15 10.9091 Tf 99.0548 293.4824 Td[([9])]TJ +ET +1 0 0 1 110.5699 293.4824 cm 0 g 0 G - [-500(J.W.)-423(Demmel,)-446(S.C.)-423(Eisenstat,)-445(J.R.)-424(Gilb)-27(ert,)-446(X.S.)-423(Li)-423(and)-423(J.W.H.)-423(Liu,)-446(A)-423(sup)-28(ern-)]TJ 16.969 -13.549 Td [(o)-28(dal)-398(approac)28(h)-398(to)-399(sparse)-398(partial)-398(piv)28(oting,)-415(S)1(IAM)-399(Journal)-398(on)-398(Matrix)-398(Analysis)-398(and)]TJ 0 -13.549 Td [(Applications,)-333(20,)-334(3,)-333(1999,)-333(720{755.)]TJ +1 0 0 1 -110.5699 -293.4824 cm +BT +/F15 10.9091 Tf 116.0245 293.4824 Td[(J.W)1(.)-423(De)-1(mme)-1(l,)-445(S.)1(C)-1(.)-423(E)1(ise)-1(n)1(s)-1(tat,)-445(J.R.)-423(G)1(ilb)-27(e)-1(r)1(t,)-446(X.)1(S.)-423(Li)-423(an)1(d)-423(J.W.)1(H.)-423(Liu,)-445(A)-423(s)-1(u)1(p)-27(e)-1(rn)1(-)]TJ 0 -13.5492 Td[(o)-28(d)1(al)-398(app)1(roac)27(h)-398(t)1(o)-399(spar)1(s)-1(e)-399(p)1(arti)1(al)-398(piv)28(oti)1(ng,)-414(SIAM)-398(Jou)1(rn)1(al)-398(on)-398(Matri)1(x)-398(Analy)1(s)-1(is)-398(and)]TJ 0 -13.5492 Td[(App)1(lication)1(s)-1(,)-333(20,)-333(3,)-333(1999,)-333(720{755.)]TJ +ET +1 0 0 1 93.6002 245.1947 cm 0 g 0 G - -22.424 -21.189 Td [([10])]TJ +1 0 0 1 -93.6002 -245.1947 cm +BT +/F15 10.9091 Tf 93.6002 245.1947 Td[([10])]TJ +ET +1 0 0 1 110.5699 245.1947 cm 0 g 0 G - [-500(J.)-443(J.)-444(Dongarra,)-470(J.)-444(Du)-443(Croz,)-471(I.)-443(S.)-444(Du\013,)-471(S.)-443(Hammarling,)]TJ/F18 10.9091 Tf 301.5 0 Td [(A)-459(set)-459(of)-459(L)51(evel)-459(3)-459(Basic)]TJ -279.076 -13.549 Td [(Line)51(ar)-460(A)26(lgebr)51(a)-459(Subpr)51(o)51(gr)51(ams)]TJ/F15 10.9091 Tf 135.936 0 Td [(,)-472(A)28(CM)-444(T)83(ran)1(s)-1(action)1(s)-445(on)-444(Math)1(e)-1(matical)-444(Sof)1(t)27(w)28(are,)-472(16,)]TJ -135.936 -13.55 Td [(1990,)-333(1{17.)]TJ +1 0 0 1 -110.5699 -245.1947 cm +BT +/F15 10.9091 Tf 116.0245 245.1947 Td[(J.)-443(J.)-443(Dongar)1(ra,)-471(J)1(.)-444(Du)-443(Cr)1(oz)-1(,)-471(I.)-443(S)1(.)-444(D)1(u\013,)-471(S.)-443(Hammarlin)1(g,)]TJ/F20 10.9091 Tf 279.0753 0 Td[(A)-459(set)-459(of)-459(L)51(evel)-459(3)-459(Basic)]TJ -279.0753 -13.5492 Td[(Line)51(ar)-459(A)25(lgebr)52(a)-460(Subpr)51(o)52(gr)51(ams)]TJ/F15 10.9091 Tf 135.9361 0 Td[(,)-471(A)27(CM)-444(T)84(ransac)-1(t)1(ions)-444(on)-444(M)1(athem)-1(ati)1(c)-1(al)-444(S)1(oft)28(w)28(are,)-472(16,)]TJ -135.9361 -13.5492 Td[(1990,)-333(1{17.)]TJ +ET +1 0 0 1 93.6002 196.907 cm 0 g 0 G - -22.424 -21.189 Td [([11])]TJ +1 0 0 1 -93.6002 -196.907 cm +BT +/F15 10.9091 Tf 93.6002 196.907 Td[([11])]TJ +ET +1 0 0 1 110.5699 196.907 cm 0 g 0 G - [-500(J.)-450(J.)-450(Dongarra,)-479(J.)-450(Du)-450(Croz,)-480(S.)-450(Hammarling,)-479(R.)-450(J.)-450(Hanson,)]TJ/F18 10.9091 Tf 320.772 0 Td [(A)26(n)-466(extende)51(d)-465(set)-465(of)]TJ -298.348 -13.549 Td [(F)26(OR)76(TRAN)-355(Basic)-355(L)-1(i)1(ne)51(ar)-356(A)26(lgebr)51(a)-355(Subpr)51(o)51(gr)51(ams)]TJ/F15 10.9091 Tf 221.802 0 Td [(,)-331(A)28(CM)-331(T)83(ransactions)-331(on)-330(Mathemat-)]TJ -221.802 -13.549 Td [(ical)-333(Soft)28(w)27(are,)-333(14,)-333(1988,)-334(1{17.)]TJ +1 0 0 1 -110.5699 -196.907 cm +BT +/F15 10.9091 Tf 116.0245 196.907 Td[(J.)-450(J.)-450(D)1(ongarr)1(a,)-479(J.)-450(Du)-450(Croz,)-479(S.)-450(Hammarlin)1(g,)-479(R.)-450(J.)-450(Han)1(s)-1(on)1(,)]TJ/F20 10.9091 Tf 298.3479 0 Td[(A)25(n)-465(exten)-1(de)51(d)-465(set)-465(of)]TJ -298.3479 -13.5492 Td[(F)26(OR)76(T)1(R)-1(AN)-356(Basi)1(c)-356(Li)1(n)-1(e)51(ar)-355(A)26(lgebr)51(a)-355(Subpr)51(o)51(gr)52(ams)]TJ/F15 10.9091 Tf 221.8021 0 Td[(,)-331(A)28(CM)-331(T)83(r)1(ansac)-1(tion)1(s)-331(on)-330(Mathemat-)]TJ -221.8021 -13.5492 Td[(ical)-333(Sof)1(t)27(w)28(are,)-333(14,)-333(1988,)-333(1{17.)]TJ +ET +1 0 0 1 93.6002 148.6193 cm 0 g 0 G - -22.424 -21.19 Td [([12])]TJ +1 0 0 1 -93.6002 -148.6193 cm +BT +/F15 10.9091 Tf 93.6002 148.6193 Td[([12])]TJ +ET +1 0 0 1 110.5699 148.6193 cm 0 g 0 G - [-500(J.)-379(J.)-380(Dongarra)-379(and)-380(R.)-379(C.)-380(Whaley)84(,)]TJ/F18 10.9091 Tf 191.593 0 Td [(A)-400(User's)-400(Guide)-401(to)-400(the)-400(BLA)25(CS)-400(v.)-400(1.1)]TJ/F15 10.9091 Tf 179.471 0 Td [(,)-391(Lapac)28(k)]TJ -348.64 -13.549 Td [(W)83(orking)-314(Note)-315(94,)-318(T)83(ec)28(h.)-315(Rep.)-315(UT-CS-95-281,)-318(Univ)28(ersit)28(y)-315(of)-315(T)84(e)-1(n)1(nes)-1(see,)-318(Marc)28(h)-315(1995)]TJ 0 -13.549 Td [(\050up)-28(dated)-333(Ma)28(y)-333(1997\051.)]TJ +1 0 0 1 -110.5699 -148.6193 cm +BT +/F15 10.9091 Tf 116.0245 148.6193 Td[(J.)-379(J.)-379(Dongarr)1(a)-380(an)1(d)-379(R.)-380(C.)-379(Whal)1(e)-1(y)84(,)]TJ/F20 10.9091 Tf 169.1689 0 Td[(A)-401(User)1('s)-400(Gui)1(de)-401(to)-400(the)-401(BLA)25(C)1(S)-401(v.)-400(1.)1(1)]TJ/F15 10.9091 Tf 179.4704 0 Td[(,)-391(Lap)1(ac)27(k)]TJ -348.6393 -13.5492 Td[(W)84(orkin)1(g)-315(Note)-315(94,)-318(T)83(ec)27(h.)-314(Re)-1(p)1(.)-315(UT-CS-95-)-1(281,)-318(Un)1(iv)28(e)-1(r)1(s)-1(it)28(y)-314(of)-314(T)83(e)-1(n)1(nes)-1(se)-1(e,)-318(Marc)28(h)-314(1995)]TJ 0 -13.5492 Td[(\050u)1(p)-28(d)1(ate)-1(d)-333(M)1(a)28(y)-334(1997\051)1(.)]TJ +ET +1 0 0 1 93.6002 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -478 0 obj << +514 0 obj << /Type /Page -/Contents 479 0 R -/Resources 477 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 472 0 R +/Contents 515 0 R +/Resources 513 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 508 0 R >> endobj -480 0 obj << -/D [478 0 R /XYZ 93.6 740.002 null] +516 0 obj << +/D [514 0 R /XYZ 93.6002 740.0018 null] >> endobj 102 0 obj << -/D [478 0 R /XYZ 93.6 693.333 null] +/D [514 0 R /XYZ 93.6002 693.3333 null] >> endobj -179 0 obj << -/D [478 0 R /XYZ 93.6 697.153 null] +197 0 obj << +/D [514 0 R /XYZ 93.6002 697.1534 null] >> endobj -281 0 obj << -/D [478 0 R /XYZ 93.6 660.294 null] +309 0 obj << +/D [514 0 R /XYZ 93.6002 660.2937 null] >> endobj -282 0 obj << -/D [478 0 R /XYZ 93.6 598.457 null] +310 0 obj << +/D [514 0 R /XYZ 93.6002 598.4567 null] >> endobj -283 0 obj << -/D [478 0 R /XYZ 93.6 538.741 null] +311 0 obj << +/D [514 0 R /XYZ 93.6002 538.741 null] >> endobj -292 0 obj << -/D [478 0 R /XYZ 93.6 488.332 null] +322 0 obj << +/D [514 0 R /XYZ 93.6002 488.3321 null] >> endobj -254 0 obj << -/D [478 0 R /XYZ 93.6 442.166 null] +273 0 obj << +/D [514 0 R /XYZ 93.6002 442.1656 null] >> endobj -255 0 obj << -/D [478 0 R /XYZ 93.6 393.878 null] +274 0 obj << +/D [514 0 R /XYZ 93.6002 393.8779 null] >> endobj -226 0 obj << -/D [478 0 R /XYZ 93.6 357.018 null] +246 0 obj << +/D [514 0 R /XYZ 93.6002 357.0182 null] >> endobj -227 0 obj << -/D [478 0 R /XYZ 93.6 308.124 null] +247 0 obj << +/D [514 0 R /XYZ 93.6002 308.1244 null] >> endobj -213 0 obj << -/D [478 0 R /XYZ 93.6 260.443 null] +233 0 obj << +/D [514 0 R /XYZ 93.6002 260.4427 null] >> endobj -214 0 obj << -/D [478 0 R /XYZ 93.6 212.155 null] +234 0 obj << +/D [514 0 R /XYZ 93.6002 212.155 null] >> endobj -217 0 obj << -/D [478 0 R /XYZ 93.6 163.867 null] +237 0 obj << +/D [514 0 R /XYZ 93.6002 163.8673 null] >> endobj -477 0 obj << -/Font << /F41 124 0 R /F15 123 0 R /F17 111 0 R /F18 173 0 R /F44 200 0 R >> +513 0 obj << +/Font << /F43 134 0 R /F15 131 0 R /F19 113 0 R /F20 181 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -483 0 obj << -/Length 6077 +519 0 obj << +/Length 9047 >> stream +1 0 0 1 86.3998 740.0018 cm 0 g 0 G +1 0 0 1 -86.3998 -740.0018 cm BT -/F15 10.9091 Tf 86.4 740.002 Td [(34)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ +/F15 10.9091 Tf 86.3998 740.0018 Td[(34)]TJ/F43 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ +ET +1 0 0 1 498.8509 740.0018 cm 0 g 0 G +1 0 0 1 -412.4511 -35.8655 cm 0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [([13])]TJ +1 0 0 1 -86.3998 -704.1363 cm +BT +/F15 10.9091 Tf 86.3998 704.1363 Td[([13])]TJ +ET +1 0 0 1 103.3695 704.1363 cm 0 g 0 G - [-500(E.)-392(Efstathiou,)-407(J.)-393(G.)-392(Gander,)]TJ/F18 10.9091 Tf 165.756 0 Td [(Why)-412(R)51(estricte)51(d)-412(A)51(dditive)-412(Schwarz)-412(Conver)51(ges)-412(F)77(aster)]TJ -143.332 -13.549 Td [(than)-358(A)51(dditive)-357(Sch)-1(warz)]TJ/F15 10.9091 Tf 106.381 0 Td [(,)-333(BIT)-334(Numerical)-333(Mathematics,)-333(43,)-334(2003,)-333(945{959.)]TJ +1 0 0 1 -103.3695 -704.1363 cm +BT +/F15 10.9091 Tf 108.824 704.1363 Td[(E.)-392(E)1(fstathi)1(ou,)-407(J.)-392(G.)-392(Gan)1(der,)]TJ/F20 10.9091 Tf 143.3316 0 Td[(Why)-412(R)51(estri)1(ct)-1(e)51(d)-412(A)51(dditive)-412(Schw)-1(ar)1(z)-412(Conver)51(ges)-412(F)77(aster)]TJ -143.3316 -13.5492 Td[(than)-358(A)50(dditi)1(ve)-358(Schw)-1(arz)]TJ/F15 10.9091 Tf 106.3811 0 Td[(,)-333(BI)-1(T)-333(Numerical)-333(Mathematics)-1(,)-333(43,)-333(2003,)-333(945{959.)]TJ +ET +1 0 0 1 86.3998 668.0716 cm 0 g 0 G - -128.805 -22.515 Td [([14])]TJ +1 0 0 1 -86.3998 -668.0716 cm +BT +/F15 10.9091 Tf 86.3998 668.0716 Td[([14])]TJ +ET +1 0 0 1 103.3695 668.0716 cm 0 g 0 G - [-500(S.)-1203(Filipp)-28(one,)-1421(A.)-1204(Buttar)1(i,)]TJ/F18 10.9091 Tf 186.082 0 Td [(PSBLAS-2.3)-1158(User's)-1159(Guide.)-1158(A)-1157(R)51(efer)51(enc)51(e)]TJ -163.658 -13.55 Td [(Guide)-1084(for)-1084(the)-1084(Par)51(al)-51(lel)-1084(Sp)51(ar)1(se)-1084(BLAS)-1084(Libr)51(ar)1(y)]TJ/F15 10.9091 Tf 257.737 0 Td [(,)-1320(2008,)-1320(a)28(v)55(ailable)-1122(from)]TJ/F44 10.9091 Tf -257.737 -13.549 Td [(http://www.ce.uniroma2.it/psblas/)]TJ/F15 10.9091 Tf 188.998 0 Td [(.)]TJ +1 0 0 1 -103.3695 -668.0716 cm +BT +/F15 10.9091 Tf 108.824 668.0716 Td[(S.)-1203(Fi)1(lipp)-27(on)1(e)-1(,)-1421(A.)-1203(Buttar)1(i,)]TJ/F20 10.9091 Tf 163.6578 0 Td[(PS)-1(B)1(L)-1(AS-2.3)-1158(U)-1(s)1(er's)-1158(Gu)1(ide.)-1158(A)-1158(R)51(efer)52(en)-1(c)51(e)]TJ -163.6578 -13.5492 Td[(Gu)1(ide)-1084(for)-1083(t)-1(he)-1084(Par)51(al)-50(lel)-1083(S)-1(p)51(ar)1(se)-1084(BLA)-1(S)-1083(Libr)51(ar)1(y)]TJ/F15 10.9091 Tf 257.7373 0 Td[(,)-1320(2008,)-1320(a)28(v)56(ailab)1(le)-1123(fr)1(om)]TJ/F46 10.9091 Tf -257.7373 -13.5492 Td[(http://www.ce.uniroma2.it/psblas/)]TJ/F15 10.9091 Tf 188.998 0 Td[(.)]TJ +ET +1 0 0 1 86.3998 618.4576 cm 0 g 0 G - -211.422 -22.515 Td [([15])]TJ +1 0 0 1 -86.3998 -618.4576 cm +BT +/F15 10.9091 Tf 86.3998 618.4576 Td[([15])]TJ +ET +1 0 0 1 103.3695 618.4576 cm 0 g 0 G - [-500(S.)-312(Filip)1(p)-28(one,)-316(M.)-312(Cola)-56(j)1(anni,)]TJ/F18 10.9091 Tf 155.667 0 Td [(PSBLAS:)-338(A)-338(Libr)51(ary)-338(for)-337(Par)51(al)-51(lel)-338(Line)51(ar)-338(A)26(lgebr)51(a)-338(Com-)]TJ -133.243 -13.55 Td [(putation)-333(on)-332(Sp)51(arse)-333(Matric)52(es)]TJ/F15 10.9091 Tf 133.575 0 Td [(,)-311(A)27(CM)-306(T)84(ransactions)-306(on)-306(Mathematical)-306(Soft)28(w)28(are,)-312(26,)-311(4,)]TJ -133.575 -13.549 Td [(2000,)-333(527{550.)]TJ +1 0 0 1 -103.3695 -618.4576 cm +BT +/F15 10.9091 Tf 108.824 618.4576 Td[(S.)-311(Fil)1(ipp)-27(one,)-316(M.)-311(Cola)-56(j)1(ann)1(i,)]TJ/F20 10.9091 Tf 133.243 0 Td[(PS)-1(B)1(L)-1(AS:)-338(A)-338(Libr)52(a)-1(r)1(y)-338(f)1(or)-338(Par)51(al)-51(l)1(el)-338(Line)51(ar)-337(A)25(lgebr)52(a)-338(Com-)]TJ -133.243 -13.5492 Td[(putation)-333(on)-333(Sp)51(arse)-332(Matric)52(es)]TJ/F15 10.9091 Tf 133.5747 0 Td[(,)-311(A)28(C)-1(M)-305(T)83(ran)1(s)-1(action)1(s)-307(on)-305(Mathematical)-306(Sof)1(t)28(w)27(ar)1(e)-1(,)-311(26,)-311(4,)]TJ -133.5747 -13.5492 Td[(2000,)-333(527{550.)]TJ +ET +1 0 0 1 86.3998 568.8436 cm 0 g 0 G - -22.424 -22.515 Td [([16])]TJ +1 0 0 1 -86.3998 -568.8436 cm +BT +/F15 10.9091 Tf 86.3998 568.8436 Td[([16])]TJ +ET +1 0 0 1 103.3695 568.8436 cm 0 g 0 G - [-500(W.)-413(Gropp,)-433(S.)-413(Huss-Lederman,)-433(A.)-413(Lumsdaine,)-433(E)1(.)-413(Lusk,)-433(B.)-413(Nitzb)-28(erg,)-433(W.)-413(Saphir,)]TJ 22.424 -13.55 Td [(M.)-349(Snir,)]TJ/F18 10.9091 Tf 43.142 0 Td [(MPI:)-372(The)-372(Complete)-372(R)51(efer)51(enc)51(e.)-372(V)77(olume)-372(2)-373(-)-372(The)-372(MPI-2)-372(Extensions)]TJ/F15 10.9091 Tf 318.187 0 Td [(,)-353(MIT)]TJ -361.329 -13.549 Td [(Press,)-333(1998.)]TJ +1 0 0 1 -103.3695 -568.8436 cm +BT +/F15 10.9091 Tf 108.824 568.8436 Td[(W.)-413(G)1(ropp)1(,)-433(S)1(.)-413(Huss)-1(-Lederman,)-433(A.)-412(Lums)-1(d)1(aine,)-433(E)1(.)-413(Lusk,)-433(B.)-413(Nit)1(z)-1(b)-27(e)-1(r)1(g,)-433(W.)-413(S)1(aph)1(ir,)]TJ 0 -13.5492 Td[(M.)-348(Sni)1(r,)]TJ/F20 10.9091 Tf 43.1417 0 Td[(MPI:)-371(The)-372(Compl)1(et)-1(e)-372(R)51(efer)52(enc)51(e.)-372(V)76(ol)1(ume)-372(2)-372(-)-372(The)-372(MPI-)1(2)-373(Extensions)]TJ/F15 10.9091 Tf 318.1869 0 Td[(,)-353(M)1(IT)]TJ -361.3286 -13.5492 Td[(Pr)1(e)-1(ss)-1(,)-333(1998.)]TJ +ET +1 0 0 1 86.3998 519.2297 cm 0 g 0 G - -22.424 -22.515 Td [([17])]TJ +1 0 0 1 -86.3998 -519.2297 cm +BT +/F15 10.9091 Tf 86.3998 519.2297 Td[([17])]TJ +ET +1 0 0 1 103.3695 519.2297 cm 0 g 0 G - [-500(C.)-347(L.)-347(La)28(wson,)-351(R.)-347(J.)-347(Hanson,)-350(D.)-347(Kincaid,)-350(F.)-347(T.)-347(Krogh,)]TJ/F18 10.9091 Tf 287.094 0 Td [(Basic)-370(Line)51(ar)-371(A)26(lgebr)51(a)-370(Sub-)]TJ -264.67 -13.55 Td [(pr)51(o)51(gr)51(ams)-368(for)-367(F)25(OR)77(TRAN)-368(usage)]TJ/F15 10.9091 Tf 148.454 0 Td [(,)-347(A)28(CM)-345(T)84(ransactions)-345(on)-344(Mathematical)-345(Sof)1(t)27(w)28(are,)-347(5,)]TJ -148.454 -13.549 Td [(1979,)-333(308{323.)]TJ +1 0 0 1 -103.3695 -519.2297 cm +BT +/F15 10.9091 Tf 108.824 519.2297 Td[(C.)-347(L.)-347(La)28(ws)-1(on)1(,)-350(R)-1(.)-346(J.)-347(Hanson,)-350(D.)-347(K)1(incaid)1(,)-351(F)1(.)-347(T.)-347(Krogh)1(,)]TJ/F20 10.9091 Tf 264.6704 0 Td[(Basic)-370(Line)51(ar)-370(A)25(l)1(gebr)51(a)-370(S)-1(u)1(b-)]TJ -264.6704 -13.5492 Td[(pr)51(o)51(gr)52(ams)-368(for)-367(F)25(O)1(R)76(TRAN)-369(u)1(sage)]TJ/F15 10.9091 Tf 148.4536 0 Td[(,)-347(A)28(CM)-344(T)83(ransactions)-345(on)-344(M)1(athematic)-1(al)-344(S)1(oft)28(w)28(are,)-347(5,)]TJ -148.4536 -13.5492 Td[(1979,)-333(308{323.)]TJ +ET +1 0 0 1 86.3998 469.6157 cm 0 g 0 G - -22.424 -22.515 Td [([18])]TJ +1 0 0 1 -86.3998 -469.6157 cm +BT +/F15 10.9091 Tf 86.3998 469.6157 Td[([18])]TJ +ET +1 0 0 1 103.3695 469.6157 cm 0 g 0 G - [-500(X.)-408(S.)-408(Li,)-427(J.)-408(W)1(.)-408(De)-1(mmel,)]TJ/F18 10.9091 Tf 147.871 0 Td [(Sup)51(erLU)]TJ +1 0 0 1 -103.3695 -469.6157 cm +BT +/F15 10.9091 Tf 108.824 469.6157 Td[(X.)-408(S)1(.)-408(Li,)-426(J.)-408(W.)-408(Demm)-1(el,)]TJ/F20 10.9091 Tf 125.4472 0 Td[(Sup)51(erLU)]TJ ET +1 0 0 1 276.5157 469.6157 cm q -1 0 0 1 276.516 469.815 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.3455 0.1992 l +S Q +1 0 0 1 -276.5157 -469.6157 cm BT -/F18 10.9091 Tf 279.861 469.616 Td [(DIST:)-426(A)-427(Sc)51(alable)-426(Distribute)51(d-memory)-426(Sp)51(arse)]TJ -171.037 -13.549 Td [(Dir)51(e)51(ct)-342(Solver)-343(for)-342(Unsymmetric)-342(Line)51(ar)-343(Systems)]TJ/F15 10.9091 Tf 222.383 0 Td [(,)-320(A)28(CM)-317(T)83(ran)1(s)-1(actions)-316(on)-317(Mathemat-)]TJ -222.383 -13.55 Td [(ical)-333(Soft)28(w)27(are,)-333(29,)-333(2,)-334(2003,)-333(110{140.)]TJ +/F20 10.9091 Tf 279.8612 469.6157 Td[(DIST)1(:)-426(A)-427(Sc)51(alable)-426(Distri)1(bute)51(d-mem)1(ory)-426(Sp)51(a)-1(r)1(se)]TJ -171.0372 -13.5492 Td[(Dir)52(e)51(ct)-343(Solver)-342(f)1(o)-1(r)-342(Unsymm)1(etric)-342(L)-1(i)1(ne)51(ar)-343(Sy)1(stems)]TJ/F15 10.9091 Tf 222.3826 0 Td[(,)-320(A)28(CM)-317(T)83(r)1(ansac)-1(ti)1(ons)-317(on)-316(Math)1(e)-1(mat-)]TJ -222.3825 -13.5492 Td[(ical)-333(Sof)1(t)27(w)28(are,)-333(29,)-333(2,)-333(2003,)-334(110{140.)]TJ +ET +1 0 0 1 86.3998 420.0017 cm 0 g 0 G - -22.424 -22.515 Td [([19])]TJ +1 0 0 1 -86.3998 -420.0017 cm +BT +/F15 10.9091 Tf 86.3998 420.0017 Td[([19])]TJ +ET +1 0 0 1 103.3695 420.0017 cm 0 g 0 G - [-500(Y.)-333(Saad,)]TJ/F18 10.9091 Tf 66.97 0 Td [(Iter)51(ative)-358(metho)52(ds)-358(for)-358(sp)51(arse)-358(l)1(ine)51(ar)-358(systems)]TJ/F15 10.9091 Tf 202.98 0 Td [(,)-333(2nd)-334(editi)1(on,)-334(SIAM,)-333(2003)]TJ +1 0 0 1 -103.3695 -420.0017 cm +BT +/F15 10.9091 Tf 108.824 420.0017 Td[(Y.)-333(Saad)1(,)]TJ/F20 10.9091 Tf 44.5455 0 Td[(Iter)52(at)-1(i)1(ve)-358(metho)51(ds)-358(for)-357(sp)51(arse)-357(line)51(ar)-357(systems)]TJ/F15 10.9091 Tf 202.9804 0 Td[(,)-333(2nd)-333(edi)1(tion,)-333(S)1(IAM,)-333(2003)]TJ +ET +1 0 0 1 86.3998 397.4862 cm 0 g 0 G - -269.95 -22.516 Td [([20])]TJ +1 0 0 1 -86.3998 -397.4862 cm +BT +/F15 10.9091 Tf 86.3998 397.4862 Td[([20])]TJ +ET +1 0 0 1 103.3695 397.4862 cm 0 g 0 G - [-500(B.)-505(Smith,)-549(P)84(.)-506(Bjorstad,)-548(W.)-506(Gropp,)]TJ/F18 10.9091 Tf 200.295 0 Td [(Domain)-516(De)51(c)51(omp)51(osition:)-776(Par)51(al)-51(lel)-516(Multilevel)]TJ -177.871 -13.549 Td [(Metho)51(ds)-432(for)-432(El)-51(liptic)-433(Partial)-432(Di\013er)51(ential)-432(Equations)]TJ/F15 10.9091 Tf 244.309 0 Td [(,)-434(Cam)27(bridge)-414(Univ)28(ersit)28(y)-415(P)1(re)-1(ss,)]TJ -244.309 -13.549 Td [(1996.)]TJ +1 0 0 1 -103.3695 -397.4862 cm +BT +/F15 10.9091 Tf 108.824 397.4862 Td[(B.)-506(S)1(mith,)-548(P)84(.)-505(B)-1(j)1(orstad,)-548(W.)-505(Gr)1(opp,)]TJ/F20 10.9091 Tf 177.8706 0 Td[(Domain)-516(De)51(c)51(omp)51(osi)1(t)-1(i)1(on:)-777(Par)51(al)-51(l)1(el)-516(M)1(ultil)1(evel)]TJ -177.8706 -13.5492 Td[(Metho)51(ds)-432(for)-432(El)-51(l)1(iptic)-432(P)-1(ar)1(t)-1(i)1(al)-432(Di\013er)51(ential)-432(Equations)]TJ/F15 10.9091 Tf 244.3085 0 Td[(,)-434(C)-1(am)28(br)1(idge)-414(Univ)28(ersit)28(y)-414(Pr)1(e)-1(ss)-1(,)]TJ -244.3085 -13.5492 Td[(1996.)]TJ +ET +1 0 0 1 86.3998 347.8722 cm 0 g 0 G - -22.424 -22.516 Td [([21])]TJ +1 0 0 1 -86.3998 -347.8722 cm +BT +/F15 10.9091 Tf 86.3998 347.8722 Td[([21])]TJ +ET +1 0 0 1 103.3695 347.8722 cm 0 g 0 G - [-500(M.)-317(Snir,)-321(S.)-317(Otto,)-321(S.)-317(Huss-Lederman,)-321(D.)-317(W)83(alk)28(er,)-321(J.)-317(Dongarra,)]TJ/F18 10.9091 Tf 317.503 0 Td [(MPI:)-343(The)-343(Complete)]TJ -295.079 -13.549 Td [(R)51(efer)51(enc)51(e.)-357(V)76(olume)-357(1)-358(-)-358(The)-358(MPI)-357(Cor)51(e)]TJ/F15 10.9091 Tf 179.356 0 Td [(,)-333(second)-334(edition,)-333(MIT)-333(Press,)-334(1998.)]TJ +1 0 0 1 -103.3695 -347.8722 cm +BT +/F15 10.9091 Tf 108.824 347.8722 Td[(M.)-317(S)1(nir)1(,)-321(S)1(.)-318(O)1(tto,)-321(S)1(.)-317(Huss)-1(-Le)-1(d)1(e)-1(r)1(m)-1(an)1(,)-321(D.)-317(W)84(alk)28(e)-1(r)1(,)-321(J)1(.)-318(Don)1(garra,)]TJ/F20 10.9091 Tf 295.0793 0 Td[(MPI:)-342(The)-343(Compl)1(et)-1(e)]TJ -295.0793 -13.5492 Td[(R)51(efer)51(enc)51(e.)-357(V)76(ol)1(ume)-358(1)-357(-)-358(The)-357(MPI)-358(C)1(or)51(e)]TJ/F15 10.9091 Tf 179.3563 0 Td[(,)-333(s)-1(econd)-333(editi)1(on,)-333(MIT)-333(Press)-1(,)-333(1998.)]TJ +ET +1 0 0 1 86.3998 311.8074 cm 0 g 0 G - -201.78 -22.516 Td [([22])]TJ +1 0 0 1 -86.3998 -311.8074 cm +BT +/F15 10.9091 Tf 86.3998 311.8074 Td[([22])]TJ +ET +1 0 0 1 103.3695 311.8074 cm 0 g 0 G - [-500(K.)-547(S)1(t)-28()528(ub)-28(en,)]TJ/F18 10.9091 Tf 83.114 0 Td [(A)25(l)1(gebr)51(aic)-554(Multigrid)-554(\050AMG\051:)-554(an)-554(Intr)51(o)51(duction)-554(with)-554(Applic)51(ations)]TJ/F15 10.9091 Tf 310.671 0 Td [(,)-600(in)]TJ -371.361 -13.549 Td [(A.)-493(Sc)27(h)-27()527(uller,)-533(U.)-493(T)83(rotten)28(b)-28(erg,)-534(C.)-493(Oosterlee,)-534(editors,)-533(Multigrid,)-533(Academic)-494(Press,)]TJ 0 -13.549 Td [(2000.)]TJ +1 0 0 1 -103.3695 -311.8074 cm +BT +/F15 10.9091 Tf 108.824 311.8074 Td[(K.)-546(St)-27()527(u)1(b)-28(en,)]TJ/F20 10.9091 Tf 60.6904 0 Td[(A)25(l)1(gebr)51(aic)-554(M)1(ulti)1(grid)-554(\050AMG)1(\051:)-554(an)-554(Intr)51(o)51(ducti)1(o)-1(n)-554(with)-554(A)-1(ppl)1(ic)51(ations)]TJ/F15 10.9091 Tf 310.6701 0 Td[(,)-600(in)]TJ -371.3605 -13.5492 Td[(A.)-493(Sc)28(h)-28()528(ul)1(le)-1(r)1(,)-534(U.)-493(T)83(r)1(otte)-1(n)29(b)-28(erg,)-533(C.)-493(Oos)-1(terlee,)-534(edi)1(tors,)-534(M)1(ulti)1(grid)1(,)-534(Academic)-494(Pr)1(e)-1(ss)-1(,)]TJ 0 -13.5492 Td[(2000.)]TJ +ET +1 0 0 1 86.3998 262.1935 cm 0 g 0 G - -22.424 -22.515 Td [([23])]TJ +1 0 0 1 -86.3998 -262.1935 cm +BT +/F15 10.9091 Tf 86.3998 262.1935 Td[([23])]TJ +ET +1 0 0 1 103.3695 262.1935 cm 0 g 0 G - [-500(R.)-408(S.)-408(T)83(uminaro,)-427(C.)-408(T)84(ong,)]TJ/F18 10.9091 Tf 152.548 0 Td [(Par)51(al)-51(lel)-426(Smo)51(othe)51(d)-427(A)51(ggr)51(e)51(gati)1(on)-427(Multigrid:)-597(A)51(ggr)51(e)51(gation)]TJ -130.124 -13.55 Td [(Str)51(ate)51(gies)-369(on)-370(Massively)-369(Par)51(al)-51(lel)-370(Machines)]TJ/F15 10.9091 Tf 200.325 0 Td [(,)-349(in)-346(J.)-347(Donn)1(e)-1(l)1(le)-1(y)84(,)-349(e)-1(d)1(itor,)-350(Pro)-27(c)-1(eedin)1(gs)-347(of)]TJ -200.325 -13.549 Td [(Sup)-28(erComputing)-333(2000,)-333(Dallas,)-334(2000.)]TJ +1 0 0 1 -103.3695 -262.1935 cm +BT +/F15 10.9091 Tf 108.824 262.1935 Td[(R.)-408(S.)-407(T)83(uminar)1(o,)-427(C.)-408(T)83(on)1(g,)]TJ/F20 10.9091 Tf 130.1241 0 Td[(Par)51(al)-51(l)1(el)-426(S)-1(m)1(o)51(o)-1(the)51(d)-426(A)50(ggr)52(e)51(gation)-427(Mu)1(ltigr)1(id:)-597(A)50(ggr)52(e)51(gation)]TJ -130.1241 -13.5492 Td[(Str)51(ate)51(gies)-369(on)-370(Massi)1(vely)-369(Pa)-1(r)52(al)-51(l)1(el)-370(M)1(achines)]TJ/F15 10.9091 Tf 200.3253 0 Td[(,)-349(in)-346(J.)-345(Donn)1(e)-1(ll)1(e)-1(y)84(,)-349(e)-1(d)1(itor,)-349(P)1(ro)-28(ce)-1(edin)1(gs)-347(of)]TJ -200.3253 -13.5492 Td[(Su)1(p)-27(e)-1(rCompu)1(tin)1(g)-334(2000,)-333(Dall)1(as)-1(,)-333(2000.)]TJ +ET +1 0 0 1 86.3998 212.5795 cm 0 g 0 G - -22.424 -22.515 Td [([24])]TJ +1 0 0 1 -86.3998 -212.5795 cm +BT +/F15 10.9091 Tf 86.3998 212.5795 Td[([24])]TJ +ET +1 0 0 1 103.3695 212.5795 cm 0 g 0 G - [-500(P)83(.)-287(V)83(an)28(\024)472(ek,)-297(J)1(.)-288(Mandel)-288(and)-287(M.)-288(Brezina,)]TJ/F18 10.9091 Tf 200.525 0 Td [(A)26(lgebr)51(aic)-316(Multigrid)-315(by)-316(Smo)51(othe)51(d)-316(A)51(gg)1(r)51(e)51(gation)]TJ -178.101 -13.55 Td [(for)-358(Se)51(c)51(ond)-357(and)-358(F)77(ourth)-358(Or)51(der)-358(El)-51(liptic)-357(P)-1(r)52(oblems)]TJ/F15 10.9091 Tf 223.344 0 Td [(,)-333(Computing,)-334(56,)-333(1996,)-333(179-196.)]TJ +1 0 0 1 -103.3695 -212.5795 cm +BT +/F15 10.9091 Tf 108.824 212.5795 Td[(P)84(.)-288(V)84(an)28(\024)472(ek,)-297(J)1(.)-288(M)1(andel)-287(and)-287(M.)-287(B)-1(r)1(e)-1(zin)1(a,)]TJ/F20 10.9091 Tf 178.101 0 Td[(A)25(l)1(gebr)51(aic)-315(Mul)1(tigri)1(d)-316(by)-315(S)-1(m)1(o)51(o)-1(the)51(d)-316(A)51(ggr)52(e)51(gat)-1(i)1(on)]TJ -178.101 -13.5492 Td[(for)-357(Se)51(c)51(on)-1(d)-357(a)-1(nd)-358(F)77(ou)1(rth)-358(Or)52(d)-1(er)-357(El)-51(li)1(pt)-1(i)1(c)-358(Pr)51(oblem)1(s)]TJ/F15 10.9091 Tf 223.3438 0 Td[(,)-333(Com)-1(p)1(uti)1(ng,)-333(56,)-333(1996,)-333(179-)-1(196.)]TJ +ET +1 0 0 1 86.3998 91.633 cm 0 g 0 G +1 0 0 1 412.4511 0 cm 0 g 0 G -ET endstream endobj -482 0 obj << +518 0 obj << /Type /Page -/Contents 483 0 R -/Resources 481 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 472 0 R +/Contents 519 0 R +/Resources 517 0 R +/MediaBox [0 0 595.2756 841.8898] +/Parent 508 0 R >> endobj -484 0 obj << -/D [482 0 R /XYZ 86.4 740.002 null] +520 0 obj << +/D [518 0 R /XYZ 86.3998 740.0018 null] >> endobj -293 0 obj << -/D [482 0 R /XYZ 86.4 715.095 null] +323 0 obj << +/D [518 0 R /XYZ 86.3998 715.0952 null] >> endobj -182 0 obj << -/D [482 0 R /XYZ 86.4 683.983 null] +200 0 obj << +/D [518 0 R /XYZ 86.3998 683.9827 null] >> endobj -181 0 obj << -/D [482 0 R /XYZ 86.4 634.066 null] +199 0 obj << +/D [518 0 R /XYZ 86.3998 634.0657 null] >> endobj -216 0 obj << -/D [482 0 R /XYZ 86.4 584.755 null] +236 0 obj << +/D [518 0 R /XYZ 86.3998 584.7548 null] >> endobj -215 0 obj << -/D [482 0 R /XYZ 86.4 535.141 null] +235 0 obj << +/D [518 0 R /XYZ 86.3998 535.1408 null] >> endobj -228 0 obj << -/D [482 0 R /XYZ 86.4 485.527 null] +248 0 obj << +/D [518 0 R /XYZ 86.3998 485.5269 null] >> endobj -284 0 obj << -/D [482 0 R /XYZ 86.4 435.913 null] +312 0 obj << +/D [518 0 R /XYZ 86.3998 435.9129 null] >> endobj -178 0 obj << -/D [482 0 R /XYZ 86.4 412.791 null] +196 0 obj << +/D [518 0 R /XYZ 86.3998 412.7913 null] >> endobj -183 0 obj << -/D [482 0 R /XYZ 86.4 365.905 null] +201 0 obj << +/D [518 0 R /XYZ 86.3998 365.9046 null] >> endobj -279 0 obj << -/D [482 0 R /XYZ 86.4 327.719 null] +307 0 obj << +/D [518 0 R /XYZ 86.3998 327.7186 null] >> endobj -280 0 obj << -/D [482 0 R /XYZ 86.4 280.226 null] +308 0 obj << +/D [518 0 R /XYZ 86.3998 280.2258 null] >> endobj -180 0 obj << -/D [482 0 R /XYZ 86.4 228.491 null] +198 0 obj << +/D [518 0 R /XYZ 86.3998 228.4907 null] >> endobj -481 0 obj << -/Font << /F15 123 0 R /F41 124 0 R /F18 173 0 R /F44 200 0 R >> +517 0 obj << +/Font << /F15 131 0 R /F43 134 0 R /F20 181 0 R /F46 219 0 R >> /ProcSet [ /PDF /Text ] >> endobj -485 0 obj -[892.9] -endobj -486 0 obj -[674.8 778.2 674.6 1074.4 936.9 671.5 778.4 462.3 462.3 462.3 1138.9 1138.9 478.2 619.7 502.4 510.5 594.7 542 557.1 557.3 668.8 404.2 472.7 607.3 361.3 1013.7 706.2 563.9 588.9 523.6 530.4 539.2 431.6 675.4 571.4] -endobj -487 0 obj -[877 323.4 384.9 323.4 569.5 569.5 569.5] -endobj -488 0 obj -[458.3 458.3 416.7 416.7 472.2 472.2 472.2 472.2 583.3 583.3 472.2 472.2 333.3 555.6 577.8 577.8 597.2 597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 791.7 791.7 583.3 583.3 638.9 638.9 638.9 638.9 805.6 805.6 805.6 805.6 1277.8 1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000] -endobj -489 0 obj -[566.2 523.3 571.8 644 590.3 466.4 725.7 736.1 750 621.5 571.8 726.7 639 716.5 582.1 689.8 742.1 767.4 819.4 779.9 586.7 750.7 1021.9 639 487.8 811.6 1222.2 1222.2 1222.2 1222.2 379.6 379.6 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 379.6 379.6 963 638.9 963 638.9 658.7 924.1 926.6 883.7 998.3 899.8 775 952.9 999.5 547.7 681.6 1025.7 846.3 1161.6 967.1 934.1 780 966.5 922.1 756.7 731.1 838.1 729.6 1150.9 1001.4 726.4 837.7 509.3 509.3 509.3 1222.2 1222.2 518.5 674.9 547.7 559.1 642.5 589 600.7 607.7 725.7 445.6] -endobj -490 0 obj -[531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 295.1 826.4] -endobj -491 0 obj -[826.4 295.1 826.4] -endobj -492 0 obj -[470.1 429.5 467 533.2 495.7 376.2 612.3 619.8 639.2 522.3 467 610.1 544.1 607.2 471.5 576.4 631.6 659.7 694.5 660.7 490.6 632.1 882.1 544.1 388.9 692.4 1062.5 1062.5 1062.5 1062.5 295.1 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 826.4 531.3 826.4 531.3 559.7 795.8 801.4 757.3 871.7 778.7 672.4 827.9 872.8 460.7 580.4 896 722.6 1020.4 843.3 806.2 673.6 835.7 800.2 646.2 618.6 718.8 618.8 1002.4 873.9 615.8 720 413.2 413.2 413.2 1062.5 1062.5 434 564.4 454.5 460.2 546.7 492.9 510.4 505.6 612.3 361.7 429.7 553.2 317.1 939.8 644.7 513.5 534.8 474.4 479.5 491.3] -endobj -493 0 obj -[525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525] -endobj -494 0 obj -[777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 500 500 611.1 500] -endobj -495 0 obj -[444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 570 517 571.4 437.2 540.3 595.8 625.7 651.4 622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 298.4 878 600.2 484.7 503.1 446.4 451.2 468.7 361.1 572.5 484.7 715.9 571.5 490.3 465] -endobj -496 0 obj -[613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 460 664.4 463.9 485.6 408.9] -endobj -497 0 obj -[638.9 638.9 958.3 958.3 319.4 351.4 575 575 575 575 575 869.4 511.1 597.2 830.6 894.4 575 1041.7 1169.4 894.4 319.4 350 602.8 958.3 575 958.3 894.4 319.4 447.2 447.2 575 894.4 319.4 383.3 319.4 575 575 575 575 575 575 575 575 575 575 575 319.4 319.4 350 894.4 543.1 543.1 894.4 869.4 818.1 830.6 881.9 755.5 723.6 904.2 900 436.1 594.4 901.4 691.7 1091.7 900 863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4 702.8 319.4 602.8 319.4 575 319.4 319.4 559 638.9 511.1 638.9 527.1 351.4 575 638.9 319.4 351.4 606.9 319.4 958.3 638.9 575 638.9 606.9 473.6 453.6 447.2 638.9 606.9 830.6] -endobj -498 0 obj -[319.4 436.1 436.1 552.8 844.4 319.4 377.8 319.4 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 319.4 319.4 844.4 844.4 844.4 523.6 844.4 813.9 770.8 786.1 829.2 741.7 712.5 851.4 813.9 405.6 566.7 843 683.3 988.9 813.9 844.4 741.7 844.4 800 611.1 786.1 813.9 813.9 1105.5 813.9 813.9 669.4 319.4 552.8 319.4 552.8 319.4 319.4 613.3 580 591.1 624.4 557.8 535.6 641.1 613.3 302.2 424.4 635.6 513.3 746.7 613.3 635.6 557.8 635.6 602.2 457.8 591.1 613.3 613.3 835.6 613.3 613.3] -endobj -499 0 obj -[583.3 555.6 555.6 833.3 833.3 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 277.8 277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 500 500] -endobj -500 0 obj -[489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8] -endobj -501 0 obj -[350 300 500 500 500 500 500 500 500 500 500 500 500 300 300 300 750 500 500 750 726.9 688.4 700 738.4 663.4 638.4 756.7 726.9 376.9 513.4 751.9 613.4 876.9 726.9 750 663.4 750 713.4 550 700 726.9 726.9 976.9 726.9 726.9 600 300 500 300 500 300 300 500 450 450 500 450 300 450 500 300 300 450 250 800 550 500 500 450 412.5 400 325 525 450] -endobj -502 0 obj -[625 625 937.5 937.5 312.5 343.7 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 812.5 875 562.5 1018.5 1143.5 875 312.5 342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.7 562.5 625 312.5 343.7 593.7 312.5 937.5 625 562.5 625 593.7 459.5 443.8 437.5 625 593.7 812.5 593.7 593.7 500] -endobj -503 0 obj << -/Length1 1468 -/Length2 9742 -/Length3 0 -/Length 11210 +347 0 obj << +/Length1 745 +/Length2 581 +/Length3 532 +/Length 1858 >> stream -%!PS-AdobeFont-1.1: CMBX10 1.00B -%%CreationDate: 1992 Feb 19 19:54:06 +%!PS-AdobeFont-1.1: CMSY7 1.0 +%%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.00B) readonly def +/version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMBX10) readonly def +/FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def -/ItalicAngle 0 def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def /isFixedPitch false def end readonly def -/FontName /RAJEKX+CMBX10 def +/FontName /LGTQPA+CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put -dup 73 /I put -dup 75 /K put -dup 76 /L put -dup 77 /M put -dup 79 /O put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 85 /U put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put -dup 101 /e put -dup 102 /f put -dup 12 /fi put -dup 53 /five put -dup 52 /four put -dup 103 /g put -dup 45 /hyphen put -dup 105 /i put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 57 /nine put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 46 /period put -dup 114 /r put -dup 115 /s put -dup 55 /seven put -dup 54 /six put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 48 /zero put +dup 0 /minus put readonly def -/FontBBox{-301 -250 1164 946}readonly def +/FontBBox{-15 -951 1252 782}readonly def currentdict end currentfile eexec -oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou_cst ?}ߴ7-95†笟M/Z+FCxw\#㺴DɫN^?0^~o&fZ9-(*ϟVV9 -|J7@s.$DFYMi+M즒DSW['1qy4qZ;]6y@F< -V&N3n]Db a[sK kԃ9$[F=e,&Ȩ)uv1DVIjaIç# -5k~QaMjFJL3.0lVem; YnⱪyRyh$&'gYx Qi- o 7kacg92X3]*#5sJ^fXגbA>!đkLa\wi\p d³JKWpt+2~-OC=<ߨ7H'4FDS٤d4isCD3M`=eO7mfz~6H36&UԍPց(5ۍX.:|[H"ɂ7SyZ?actS[lDA\t966an,2A?":6ߙ7xH/5e=v es% .,?RIGM< ,9M&^;mN`0\@'tM@/f+d)9*CSeE-&bqPQxVyï^>Ye['@O&IӁ7_yջ19qxavʶD\BhI.fN2iRC 05H-Ga/qB_7Ue>h];[MgaJ>?-.}6 - P^$0 ->B}|CR;0̦Fh2ie(I:CxVtgoqǙL6n zrWV_2;L6쥉\ؗ~=ViswķWEd21gxC<%JeG@>O@DYW:SL≖d}/F⋙j$˚ ԗ8SQ -Idl -FU"-EI\]T;/nǕ!b#i`XcqlOl!켷M!Mc98ub@ ;Fc"Y_HkhA˧A( 0Uة}d+IoQwe`",*ڕ%oi",G#pyVT@"]Kփ0Myuhv㞻|e 0 ixy./;/c$~qGME(_k-12tY|B Ztsss=n^ܘS -u]ߓn @&xwŃL8ֆe;o9S:P.dBz_UT*|ǼU:*3HP`)՟^PebTV)>6%rG֔{{3c )6[e)^\d7zm8Ue's$eT0ْKɩrQ!Jjٔs9AN t_fፗ4@߷$abLS+H`0 - Evv̽Vh><`nD4g^óxw«| ' =;h T6qu:6P0j.6efׇɊyir7[srHexY@7܃֚)H]0&&[ `~@#(펡r+HO;"u]lIEhg$a$vϕyjDo!%uO1L$~_[!W|w;\sM^}&tz5LOy߽=#)FhuƄY?Ӏ%f.=){jX^jc37C1osN޹Ø};i:ix"kiEOIa7fzE yd,ߎfD\4Q+eW_3<$ eoE pk^`oVT}ӹؐ&@s乧 / G2٠`Y g繅 $2L( {IR:/IlKDNtNJ=> ۙbPR+SzڛU57|׿-}elvs]౯f%Kvր9 !f07=>RPYčYţ۟#d`3#dE]4`xe%U[9U=uTHG`q45[X4Izx,[qzfz̑[j g6*Ы5>3m_ǿ,12 y8F̠;L *A Yd҂7w2PbvSV,;Ƙ5_R dS)'$M p(ɭ<\ AM}zT:YoL!S6["R4N=&ǹҨ S~E? IcECנ臯yH0"j&kN?RG%%3YŌh~Roܿ)̀X --݀_`5§(0xegQ5w)V-.)HsI8(@ `C2Վsᴢǎ‰^Y鉨 ;?E̓jFqvuų 9(!yl<FUd9I,#tvRXoʬ -?3 afSԪѨ;_рvo99Th7} ۲B]GJaa[}""qJsӁ|dC,Aa:Owau+™ Vc ]^W =J?!Bu1;C}n9-֟ӴCr##Bf/]\ &ƚ,Y!~@9P\0܇Y0,gX5;WmD kF3 *Lx _ =AQ N[wUu|:+]VDI`5k8"3pt1hgŰ첺Im'Z;|S)o,OSZIQ0HDDPhKqYa#ZUyL{.ro}ʿnuW?gMie.\Ml')/HXqȫ55^紥d}b%!0\6k e,Dδ}nvA^ѽuA/~ -'Mjr.jU0}M4>d8\Ƣp@ʨ+=MxLSD= oaFtrln+GJMi>F >X}GLMr5K=%ZIl YEn(FP۠:{P/қ>{YfMW_Fڄ_=}d)AfFpD^;s wt9ߥ2H\o~czT;8NX,^b\aN195Ndo|N͔J%0,A\Jw8˹N'r@#dLeMrk[k`xX4r~P}nU:X$8RZg7}!$ipN!^GM`ao wdD~ \$|SŠX (` MԷRͯE6y@+.ĜxV /ӄѸ/DF/2nz= i &}҄ڈ*cUbBͰ8Acymg'MDywHhvY2+h8jgePz\4+Ug<;"%B2$}nޤcs0X`NV-BGkZHHT%`86JqX2oΙr.۴q -G| #FCJ*fwm鋁qi:i@(Ѹ5.d\K=ˤ1l܉v X%nþdP rZM`Avb>Wݳ5/K`5Wv0.L3YWO@cv -m`4XIq&yaVR;twrgϪ` LW&99/GA똍ףnӬL, ` oߊk:ZlÔl@Pڀ -]|X0|WsT#^:=v~53G؝OՀJeʄ'&O'^ƫt('JR -LEr"n\)8Q$JDǢeҸڳ=1+װC:x*j.N۰Rh,p*ܘ1]Ic낙ΏmTZo}Ǩ?YXfвct/Zrs(1q$VIpzY -'o%{5^Z<^8(}n1gdnJ0#z{Q d>Njeyt0܊V+l8Ox$S$!X'P#QSqiucz["7]/u!vUZYqa{!VmS/%%腏^|:L(v/w0/4 ,%?r\Gsr"_yLMF3-RopngTa ý:&yt>F])460^W^4OJ-5('hS@mz! 9oFde?XҴQ1 4/SPQ G=_[*Dsk]z%6ؑ $ziޠSJ]Lc5B V@vk% J.:fL*5PYƗb%Bd:k0._lG:hN-Cڃ^0[@zHFѮ C+Ho|-Oњxn׌>1n\M-Z9l6s鵔K͵,\{Õ3j  -&q բl;EaBm @)*93Cu_M-|ެt@B)`l:RV!`N -ޞ%咯lo{PEqv_U6WRAX|4jd 2)I96&b#,[nҵe9;ES Tp4b{Ĥm02@no)ZtJBkҭ†c!58z[G K -¶aw*P0{g\שl:lq*G}!âqΏ|q[؇9Hix=dVd vֽY%({f" ςګ/0CzFo5Zث^f=gkwP-ss=V~GEm58:a +YA?DȂ!iHa)ݿw$=a[ ^?$nf5.l$߉[ 8[5a!q~LGԑ;K3"Qh/YtO[ -rճ1 L.LXiti)\;rs.!:Uš]]={!AB$nZe`+ ZҪՙM]q!8KJ8V['n@Bdw4.,ܑp$`@ޤN Gms 5[E|q8JXt[xoNT.< -))o --;9ǂM :\`Uvz5AVsP2%]p?wj 8;'be2[k?/Z~̥n>Lk)> C)eg_`AE-Q5TssŞ7ch3DKhJ*ȾL> a Js`wv2)a+47St4bS(i$"Z1!XǞF4mG&K'/hv${?tI]DI?-ρ.z_T$oVN71G_>wLDsY-v1&[1"s>ћ6f+TQ@e#RPHL᠛zIN[H#*>Aʒ3_9(7EQ.(\}6}S|ckqFomL*6 ' i\ Tסԕii1t8\%ĭ®U:m2iDZ[zl +oc;j~EЪ/ ȭX~id}S5Q!gtⵎkJc;rN^X5.Sy +'IqV:r㚉#,# dBZ *R*"7٨yQIeύrZp(IJ8#+P.ղNC; +[i-{')/Pph QC +AȜ;k5,4Cof^^ "XWeBL'>@{.'b[>PP.DW,={ #VX6nzT`qN&=`~+GH c%=TF{v/҄fwsj j-${fwkxze4G$JB%p"&g4BW[x-n)ǡ~('?CE-QeSO9sY=`lz%i$/neu*TVyBܡ mM/|8ySx{+˄sߨ39Ӟ:QXE':c *ȝ?/vwC'kH0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -504 0 obj << -/Type /FontDescriptor -/FontName /RAJEKX+CMBX10 -/Flags 4 -/FontBBox [-301 -250 1164 946] -/Ascent 694 -/CapHeight 686 +348 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 521 0 R +/FirstChar 0 +/LastChar 0 +/Widths 522 0 R +/BaseFont /LGTQPA+CMSY7 +/FontDescriptor 346 0 R +>> endobj +346 0 obj << +/Ascent 750 +/CapHeight 683 /Descent -194 -/ItalicAngle 0 -/StemV 114 -/XHeight 444 -/CharSet (/A/B/C/D/E/F/G/H/I/K/L/M/O/P/R/S/U/a/b/c/d/e/f/fi/five/four/g/hyphen/i/k/l/m/n/nine/o/one/p/period/r/s/seven/six/t/three/two/u/v/w/zero) -/FontFile 503 0 R +/FontName /LGTQPA+CMSY7 +/ItalicAngle -14.035 +/StemV 93 +/XHeight 431 +/FontBBox [-15 -951 1252 782] +/Flags 4 +/CharSet (/minus) +/FontFile 347 0 R >> endobj -505 0 obj << -/Length1 1513 -/Length2 8660 -/Length3 0 -/Length 10173 +522 0 obj +[893 ] +endobj +521 0 obj << +/Type /Encoding +/Differences [ 0 /minus 1/.notdef] +>> endobj +344 0 obj << +/Length1 803 +/Length2 1857 +/Length3 532 +/Length 3192 >> stream -%!PS-AdobeFont-1.1: CMBX12 1.0 -%%CreationDate: 1991 Aug 20 16:34:54 +%!PS-AdobeFont-1.1: CMMI7 1.100 +%%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.0) readonly def +/version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMBX12) readonly def +/FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def -/ItalicAngle 0 def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /VZSPNB+CMBX12 def +/FontName /GIHYLR+CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put -dup 73 /I put -dup 76 /L put -dup 77 /M put -dup 79 /O put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 85 /U put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put +dup 84 /T put dup 101 /e put -dup 102 /f put -dup 12 /fi put -dup 53 /five put -dup 52 /four put -dup 103 /g put -dup 104 /h put -dup 45 /hyphen put -dup 105 /i put -dup 107 /k put dup 108 /l put -dup 109 /m put dup 110 /n put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 46 /period put -dup 113 /q put -dup 39 /quoteright put -dup 114 /r put -dup 115 /s put -dup 55 /seven put -dup 54 /six put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put readonly def -/FontBBox{-53 -251 1139 750}readonly def +/FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec -oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou_dV`Ky Z]uMYb[1[l',t\pڮԞZO4GJ7 i!U&Ϸݢh`ZṆhKGz; #1&()$J3KُօEsjFf"P$-I޵˕B -6=hqDV<` EkENrraƌJG ~L{6IE6U'y 0gK>&)o>2\U]$XW-1f@'B 1mW=L%5t.O-]N CT4>&wvNXŅCf עr1fׁVCȖ~q0 Xf^^$ӷ%G7dȱ\lFc0]g<銷_&W{>}N|ӷ 054H4ܞlG>T_cќ6Y1 nUr-u$zq1k.s+6'F2炁.rq5#3|u)pվc Nr3 p<~s?aG:m+-뢅^dҭG)qQE;%鬎F02y'9N#`=gh7+eC:é&3ˎMYn;96WLN(^r⼛nY#sdB1_èx/u!gcY';(/5t@aYkYeLYREz1o/bXK06P,)^^"!Hߪ7A3vćNB"Pij.:QV8yJ *Tۀ$F"yLX;5:E Gɢ|| UݢuɂSύRǷR B, fV6 ><=bPÊO6˸t9|bs6ݳ<CRC|C #(2nOr&ĝ=F)x־'c0$UnKޣl?ZP-} -0`3w='·~轙"IvAnVoK$դY*꬀QWͱzv/6䱢tkf R-+vV6A< -dWl`.b'v-= LJdٝd5qMc %s2pʚ?'OfKo('xm1`1{X?k>p:8mz}W,nfҲt5xmPٱ2YoAۓ1BK@fe>*\V FhsW rYSԁ_Hw-\% ¯5qBxLY^_)T1"b" 0rLizge8,ˮ6fP~曹 c6KOhj9l90 7E\8J0N( Z~e=+ʢiN],!#G5tHXS/ρM {Xr8 CYY^`J! /:xēQ9`f{tmFQܡ<Vh]PV%:G%H^z@Gww=Z .%9U^+_$J*\b]J2Q.‘؉Xd;R\&r {$}L[s6THr _%ߪHGيFHmBGN38][ S6<|kTu@Eh|tݳԱG4t3 $W2)d"*BN#\-LBb>p9j]UIĂ֎R-CET|Ac,[uϘe%BC[ (Zo(-pnӹJC0A;cHK.eire7&T]C--mK:wb SsߒF[6oq{{݂IvܯT֘Kjj})|s}WDfM#U;/ϴN'ھAOT@B_3˄̊jFnF?W0WI]Ke9TjE!#0Xdfųgp=|svhSpr5#rnAFNg}9XfczjNd -!A&RMQfg 8s]5c˾իWd!{;9+U:{x$SYR5A\7e~i:y236SK5U_JS+{.2{j-EQz|\fNO$z>M"g1|l3e# $^˥087'ĕDcۦхRo8ɿl>qIbB B̀_1@ݝT/]o[*FME"f*\*e6^cުvfǕѭkGF'Ni![r%bϋBԫPd~c#Y7jF;R'bg_?㒺[50bFm}W*TZ ep_Y~!dpLDbՔR"^9*Jw@{PV {&!N ^=j'#1VxǽږFPHYH̜BF^m -ٸDa[v`qyPYQ;{,._¿U\d0ly&(aʼnar -0gozМ7oˌ4C=rz4lsr>`K709"w[JURC*:'ҎBt76PKyj!{ٷ H%}9=K Y. ݂!]E%_bK-;>h II:͞P؀+?0Zھ+7 `c^T {rOr- b(P`YАV al9VKῒ UkOog z#gPőĭX`lZZ_ͣDoٝy(ICy bqO(\s5q|kj(> VE b$Cw-ٴ${ -ŹYre*~ڬ E -j'LzƐyèߛ/DPN-lQ"Iw,_owX)Axw'i S-jzЯ*xA@*;_#Ե%KSOFɴD7B_l~bGd5n/ ~$3XRm6;hc;!A@E}|-G @&5:+: }j7-=/2 :I<,SFh"ΒtY[k, -p®aI zEzќB['4}Aw.ѷ.oK3CJ߷TMAHAOXuigAD- -S=s|x2HՉM6{Z$*v`?|jq)/&\{g8yLJI8SR'He'AyI>-v6a~37rz$/m"=di={g0sYwl}xyֱyh8hNOA06jGg6nj{\!b#/g>k>`}Cfld84(ǩVi]}zWf\M.*;; - -Ÿ"s^]R9rkIXA"ט>SrWǮ54X|BhFኳ&7%Wtc$y V;)Jc6A\W * Aoyg" ckzl[OiZpZG2{/SMXdR\ob͹ĥ9hS*E&F8x57,EaR702+':p+,C%x0iO7U9Z*+i!+|cZ*Z*B \Aߑgi1wџNJ'揈/u f!(Nl%xFoBׯ~jdIēpUG?ӷIFn{[eͶQP+V:JtfbP|):S*yb4F# pʾVt^}2D%r8.>9S|8Nϳ eea$_4ZPWJD`!l~^fP_t CINrMeQ><8=4oΆU -}t|hO=N{FtNqăxŀQHi"7K\Nÿt_O\'4f/&5QgǶKøB G` -U`K {@H8xA&X'}:WJ - itHe,&}Fw92 55gY=lV@  hCwxBkȒ[; -,6Cխine6z'Jtv@g3SNS~cvꑌt -yY0X(prޜ-AYW&ZP j#mR̛uo=;mXՇ6rqA 4\{SkjnYl݉fh"py8.[Lcdjh>ym{''uSK珘kKg&ɉ6+ߩr`5P;e ωge8*R>O -:iC_a&N3 gPV7u*jldbKYMl%G|W6C}zq\7ӒQ8vЃK<_ը@+pE?LsAyz>JtVAbjq -;T|amQ2P#vwL@8cjڳ@oY ZEsv .F^4!_#> n=;${|Z6I`[8s9_u2_,B.ʲ98xAJz7r&̗q-/ )=GB $x`_&Шn f{q\cK-2M]z)vdQqźfe_ue4/+9ab`RjT7}?I7 RpGS/h |"IB+)NyJ7yq - +Oӽ:GvfVM7}0҄]R褼Y5-<0 -}aclܿ? AOK:7.mוAqZI!-uLE~MۨaH 6KA9Y*=OTF7 hGr=nFS~1])#כ5r -O;T Gu))yY\ z0;^'D !Lf{΀s6Sgy.~0T<; $Wc/nwov[8`ez>xϟ-g)J~Bjh%jzGm >NjS])7uևUQh4)-×p#z{8YаGP9 )"Pƣ3ГzYYZgp_PC߬CܔDC'<|(Rl/IxXMYzntԟlAv)|*iQP3|TxL" ʃ?Aw·pҋ:r)6,N{?JoA剳Js(0T9$ն''0j%&4LwQcKHpY Bֶ6$bZXZmX>B#9xҥ6IUJeG#݆>@P1o(ߋUcCо"[D.)>;@Ly͗`50/+R1&e7H?6y@Vx!+ԁ Sk,M8ڱkp/ h(!:ԟH'5II,LIl9#oz)bz&2epDQ/TU^ riFQd'@8NL5`NCAm3IQAJqla_Y&PmjNaz!v4%.\֖b`+#`\ܠḄFr=Z +L2-q; ]Ƽnl,Lt4-`_My檭 +RBٝ1jGO._=] Vi氚l@%f齅YB1q4Mk$_N>B0}\SZh?sȀOwJXmQ68XN3A?(Y}ND$R{տ& \\z޺m块*P k-죰BF *♹8clmotgJ(Olj^~^&Y0TI\1'6ؓBcx3|']PxTi\[`߻,}y*1PA@H1}c >I|N_Dkغ^~+($65)qAahJҾU(qs3FjékX[;8v;;$=NYn \X=(iv/Qg_,\-]C 3ӈG;V-|yn^4@dx]*~.|8D?,㋽5`a0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -506 0 obj << -/Type /FontDescriptor -/FontName /VZSPNB+CMBX12 -/Flags 4 -/FontBBox [-53 -251 1139 750] +345 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 523 0 R +/FirstChar 84 +/LastChar 118 +/Widths 524 0 R +/BaseFont /GIHYLR+CMMI7 +/FontDescriptor 343 0 R +>> endobj +343 0 obj << /Ascent 694 -/CapHeight 686 +/CapHeight 683 /Descent -194 -/ItalicAngle 0 -/StemV 109 -/XHeight 444 -/CharSet (/A/B/C/D/E/F/G/H/I/L/M/O/P/R/S/U/a/b/c/d/e/f/fi/five/four/g/h/hyphen/i/k/l/m/n/o/one/p/period/q/quoteright/r/s/seven/six/t/three/two/u/v/w/x/y/z) -/FontFile 505 0 R +/FontName /GIHYLR+CMMI7 +/ItalicAngle -14.04 +/StemV 81 +/XHeight 431 +/FontBBox [0 -250 1171 750] +/Flags 4 +/CharSet (/T/e/l/n/v) +/FontFile 344 0 R >> endobj -507 0 obj << -/Length1 1432 -/Length2 8170 -/Length3 0 -/Length 9602 +524 0 obj +[675 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 542 0 0 0 0 0 0 361 0 706 0 0 0 0 0 0 0 571 ] +endobj +523 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 84/T 85/.notdef 101/e 102/.notdef 108/l 109/.notdef 110/n 111/.notdef 118/v 119/.notdef] +>> endobj +341 0 obj << +/Length1 752 +/Length2 1167 +/Length3 532 +/Length 2451 >> stream -%!PS-AdobeFont-1.1: CMCSC10 1.0 -%%CreationDate: 1991 Aug 18 17:46:49 +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMCSC10) readonly def +/FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /WARYBH+CMCSC10 def +/FontName /YAHUKT+CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 71 /G put -dup 73 /I put -dup 76 /L put -dup 77 /M put -dup 79 /O put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 85 /U put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put -dup 101 /e put -dup 102 /f put -dup 53 /five put -dup 52 /four put -dup 103 /g put -dup 104 /h put -dup 45 /hyphen put -dup 105 /i put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put +dup 43 /plus put dup 49 /one put -dup 112 /p put -dup 40 /parenleft put -dup 39 /quoteright put -dup 114 /r put -dup 115 /s put -dup 55 /seven put -dup 54 /six put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 121 /y put readonly def -/FontBBox{14 -250 1077 750}readonly def +/FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec -oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# -]LeVߐGoo٥\k 9Mՙ= 0)xf -0v7ϱ9 àE(O&k{ǛHFſꇼw -R^q&AԛhF8N&{oi(^[ol W%'5,.V!0&u%ˎKxZ4pX:;[4+ @c -ߌ -}s$)PͶ'/CզxBCxSƫE\ 'MXpͰԁ C q6 2T1e|jԲH*} t.-"k5,h:J.X 4Z@0v)FEʫ@"jKNJrYDdcm!G~,f\HAӮhcc>SK}pkkRX>LfU8dWNb䊌b ?g~8o|R<)C쩔fxgm.sAQjEbp]ly''͔Ϟ[tVt{`z -D$V{ EV|4-<G"퓾.?ךe\^/fWn8Yzs=p2΀.1pTxK(ۤc ]?ٷcP'eOz?.ǴB5ҙoScfaK1k;G/{b28m u- VG?DpB4HvG}hUƜonɎz Ϟɵfv.Y83 w._n=m8ջ̒J2-oјx w.%(7䔛ųZXT4 Vr|1_ &B(E:'N@uuݰ_̱+DƅhYD{֮1D`'hyzE;W -zx))?IwuϻRG924ďk|^qeE_idwt䀓w{ - D17h""JŐ" !Ӣ`>J^UEpX gU)S&%]fsJ]筷bŇ;_/ɡ@2詟LtK=Wi(D/cv+m) l_8 - - ҢaYu1ĸQȔ25ޛDzLSEMr0$[/zTȈ Ib {og;n":")[hHwvGWxBxBѷ&+ ƻPdaUc:q=q)Ү^:CnuEg1\Dce` C| oV`w'chPՀڈܔ+~8$9XDcV衙WpF{[یR۠rܑw0ԠϒxcuQm#twjd, (LvɏTzGXt csWZOi}po?x{g#|!]wpݛd 1NHK}ԨaT}{zd\n2D Wx>(C\vLG:ΐ^ zt8,f)s,zvqRy)㏿}]?Tmܾ- OOWsЂ*]lL}7C -8SWHA{Κ\S% ~~xL4^"2çq>9+\݈ .)VjZ耕 3ృΟ0թxD*{= ZmHQuA#eReu~X%bf*K'c$:*}. &)wG8aP+-(C|]" c+[ H`eI ṁ$Lxlc17-PY #{0J\"6 -κ=ӈй2VZc}d<8,e u|ˁ(ǟO5>NIۺ1 cb"4f 7'ɳE=T96ܮl:lt&9q5j*O 춇IG#n.=elT_cQFCYK^=OF"Y!yM'}T:P j)N]xhu"-b7 -7d4WmIh;eU"ٝsGɘ -͜bb@ -kZ6Z3l-BV6~_c( ώ1l+r*NzX!mW邏L-}:3xa攎? (dy2U!L-:NW [c|HcC`q& qԅì9=w6 -0%j g/Q%]4e4p?s' 6@pņHto+rݗY  -~h qRa ,:}Az=kYB>—DXV@qlK2Kτ%wlzZ :X,y'Xşa.'mDTq{/0P}t0>V[5\l"3"eOO 9qj:y!l]Aݗ!Qa"d[|Kƍ'``dW2/ՈAqs*"4w ҁUS e&(ʀEۥ~kZU!k`d -۷la, %hn Arla_\1' h<_fjߔ}u N{Gg ٕtvk( ?ŧcfOF :Ww8doNVhkC9?ݠtԡd7ʎL!!dbP=Wl! +5&/(қxR:y,x=uyxI{LJ0 ٦1-9372 -֡wyuޗxc_<%+p/f ɭU3Zقe ]b -}p Ne2 AluѺ.wE EJVĭaǑh~-Y|. 5 XbXt{woVEf!OWO}ێwagg2@p譸@7&=ήK4]7܋>ؗשI  ٵԭN^(>E52}n(Xy-kD2 gjݟgO[Ls8ksZT>c#=Ws`;9P˾r3NjĿ&wS` fҴ FBupb:'8oUH'i vz .[2GSNN?K8"@9tV -JZŭ>q0ը1,A;A -gHѱ6ƂQr)UFN+VȗbvMm2*xbB( xOTƟvhmkV;o -((lDh.Lx8)e҂W\GJkr{੡Ȳrg=B%aث]LɃzLAg0-͠R0Į罼pRX>3X%FlP\^DScqzUٟbˋsXQYAn PH?/RpI>V&lU `[McaA{LQ課6XJ(r"#(OU%tqX ](5,8ns1MC@ &WTY_UdnؼTn9Umq,&|B0]M\pQY w*2}ę0X2DhaCmA؁߸? +:{n51`KZ -\k=@ROC5nfcPn`EZZGD&/n`ۥs+4YӸU@sP.bPNcJ>~h爼͚YI9#oY ,&T^yl.WP0E#TݼEsT"K04-wbJ9d~>vZ>OI奓Wn,zU!j%͚XkiI%>dCu(dʛߏe wJ^gH|X wsj.3[uMVtn6=`{zlt9 OOwE~RrA/(X @w[?ZC,Z(Aw(LP0ȻNliVR\Z{#[x%՜)$* Gu3Iv+L 2ЙU 0-P+ -'j-Cs$SW`ʹ'"l0g w'Ȟ8Eݏ1J6!-xY?u!mab/<@-9)nq^4U!r*-!#O5yd}pv[z*eK՗FA!+ zo}P:jz<6Cʹ?%WKLJ]fTe]*"bCDp~PQi\ևv=y6s - -'ZE מYfDB/oHx~Dz%)wUq;ynKs3tfe2*"Sgz=$5İ,Xcˤʁ SL{g}K|Wg6iOD1 Tᕿn@&Z>4{%ɶጾtE:@ȇ,NP!y5bq4.} -'!4JL`$",l2n6>d{N5&tURT=O=hb0C.`P(e$^c} Jo3ePݾA}M]g#l?8/G "qD2п&N`͎NѼrji='"+jO],VK8VOw)f<۟>?'މkm'uhpC]ݳ -:X0$hVb ҅r4C|Ovn.-nw і -a}}ǍIfNC -ϳ6}m +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\ʻl24`}IRB s\pzEGAۋa4_p0uAEG)Q|8B*dGWj'0Vix#(=@'qIT5i +(Ѵt` ?E)4E^yҴF+$8&G"Yl?eYjt+TI2! nXKt`˱~h]{>Qaiσ\mFU#Gvh2un8W;R4Ej1B4b ;b9y[lV:P񕈇9g`\J~ O>%V0 ݬ;cJԺjYrt6yql4Qo٫~o_=6xqw,",kϷo +#vI7_ fz!y(3)5*кYb#aM?3G%wG*L4}. f0Fp)@C,W' ']87Go}y-Iނ% ;dݻy%I+-t7ˬ'$ ;9WJ].IuZ8Cp-$X ӽTֶc+DߍEA1_oKC5@{ !^qRB֭dp=̝?E OS97k,+āI^+͆S# +ias1 +'_m 'd,]X{&41Y9HY_\*2|$g}/M#9]rZRa^3cs!7烬yD6$1/nh0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -508 0 obj << -/Type /FontDescriptor -/FontName /WARYBH+CMCSC10 -/Flags 4 -/FontBBox [14 -250 1077 750] -/Ascent 514 +342 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 525 0 R +/FirstChar 43 +/LastChar 49 +/Widths 526 0 R +/BaseFont /YAHUKT+CMR7 +/FontDescriptor 340 0 R +>> endobj +340 0 obj << +/Ascent 694 /CapHeight 683 -/Descent 0 +/Descent -194 +/FontName /YAHUKT+CMR7 /ItalicAngle 0 -/StemV 72 +/StemV 79 /XHeight 431 -/CharSet (/A/B/C/D/E/G/I/L/M/O/P/R/S/U/a/b/c/d/e/f/five/four/g/h/hyphen/i/k/l/m/n/o/one/p/parenleft/quoteright/r/s/seven/six/t/three/two/u/v/w/y) -/FontFile 507 0 R +/FontBBox [-27 -250 1122 750] +/Flags 4 +/CharSet (/plus/one) +/FontFile 341 0 R >> endobj -509 0 obj << +526 0 obj +[877 0 0 0 0 0 569 ] +endobj +525 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 43/plus 44/.notdef 49/one 50/.notdef] +>> endobj +301 0 obj << /Length1 935 /Length2 2339 -/Length3 0 -/Length 3274 +/Length3 532 +/Length 3806 >> stream %!PS-AdobeFont-1.1: CMEX10 1.00 @@ -5560,20 +8866,20 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /QZSJAN+CMEX10 def +/FontName /ZVMNAU+CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 110 /braceleftBig put -dup 26 /braceleftbigg put -dup 111 /bracerightBig put dup 0 /parenleftbig put dup 1 /parenrightbig put -dup 112 /radicalbig put -dup 88 /summationdisplay put +dup 26 /braceleftbigg put dup 80 /summationtext put +dup 88 /summationdisplay put +dup 110 /braceleftBig put +dup 111 /bracerightBig put +dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end @@ -5589,149 +8895,52 @@ A _gPsB1uU 4N%p.h7MHSF`Yv9>m.(dFn o 53MT g CAkmS:d_Q=]MxY5pQwu)rW)-n[$qtR;¯~M܇V ZƗkSuM(+<0Z7_U>_ulq$U(³h(2:S2;Go~9՚}uV-^%P vUXKb|%4& a_0Tw}GLPR3=Vgy K'CECݽHV xEv}=soÇ\{ھ"c>QF@( Y:e&l`Z+Ilr^˖NG ЗDas51ӣɠ?D}|^ME>BRȒq `4I"ho=y`]W1`э{tr tv -zF9)[?h|)bg3.&Bj: X3;Gk(B,v +zF9)[?h|)bg3.&Bj: X3;Gk(B,v0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -510 0 obj << -/Type /FontDescriptor -/FontName /QZSJAN+CMEX10 -/Flags 4 -/FontBBox [-24 -2960 1454 772] +302 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 527 0 R +/FirstChar 0 +/LastChar 112 +/Widths 528 0 R +/BaseFont /ZVMNAU+CMEX10 +/FontDescriptor 300 0 R +>> endobj +300 0 obj << /Ascent 40 /CapHeight 0 /Descent -600 +/FontName /ZVMNAU+CMEX10 /ItalicAngle 0 /StemV 47 /XHeight 431 -/CharSet (/braceleftBig/braceleftbigg/bracerightBig/parenleftbig/parenrightbig/radicalbig/summationdisplay/summationtext) -/FontFile 509 0 R +/FontBBox [-24 -2960 1454 772] +/Flags 4 +/CharSet (/parenleftbig/parenrightbig/braceleftbigg/summationtext/summationdisplay/braceleftBig/bracerightBig/radicalbig) +/FontFile 301 0 R >> endobj -511 0 obj << -/Length1 1315 -/Length2 8350 -/Length3 0 -/Length 9665 ->> -stream -%!PS-AdobeFont-1.1: CMMI10 1.100 -%%CreationDate: 1996 Jul 23 07:53:57 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.100) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMMI10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -end readonly def -/FontName /SQUASS+CMMI10 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 68 /D put -dup 69 /E put -dup 71 /G put -dup 73 /I put -dup 77 /M put -dup 78 /N put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 86 /V put -dup 87 /W put -dup 97 /a put -dup 98 /b put -dup 59 /comma put -dup 14 /delta put -dup 101 /e put -dup 62 /greater put -dup 105 /i put -dup 106 /j put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 33 /omega put -dup 112 /p put -dup 58 /period put -dup 114 /r put -dup 26 /rho put -dup 115 /s put -dup 61 /slash put -dup 116 /t put -dup 18 /theta put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put -readonly def -/FontBBox{-32 -250 1048 750}readonly def -currentdict end -currentfile eexec -oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# -]LeVߐGoo٥\k 9Mՙ= 0)xf -1kX9JS:6V =!X>KM)9! I}HWIUcl=GeZm>nQk2=1p%R`%$]c{!W+8?v(+)0ӈ!YahtA?H @m?|M X9Հ֨#2 -:m,MZ+ǒ\Ex9Yn<Ŀ2^FC[`T+ȬD]ǸFF$oB!>;A\T hxh|5:6;ϖUǷ6~k.T*{8K`y8'dT|-QkKmy9 91|Afr (K*)%_ʬtP`.rY?nrn{v2O_5;\g>R{4_ -: 9pEz~Gu E[n窙i9ヽu#=X&>~J~ПUt0t1Cqs-b5 4AG˧OE1"?@~ -R Oԁ>XO8' IVTnP #ԫ3L3zٛoH9@uD Jsf*+5x/Jl dc!=2~S،%Wq ˒¯p sFc]@{F,̖:0 -Z^E Y;Fp'*_*C]q+1^mtv`#ԽDצ=., `CWt UbxkF㴠2VauO"-FU/IJpKZW`cpCݪ``Nm\G -pVUXYm?q jL}+:R':\Lz -ŊeY_g #g|: I {6C*}VqG()ѧ12 fF\Xn(V<˜grIpK9216Y )vXmK3p*{oav&6 .<}mi oxR,z`J!D=es\%Qu֩L߫AP[9JZ܃7 pTIEj%[?ӕ6A&Pt-#,o<8|g&"HO sɰE(\AD.%]d1>‚c@J%K_ Ts51H<Ԧ,~d((Ko9;4? 3GgF$TdE Ӻ}#mm-/\?uGd:"ђH+Tf#Tq ZL$?3-}nN} mP8sL/Pk,>Vb9 -} Hs` -kE -YYoQHvF6+^@6ޓ|h`crMQWcj?~`oMwXߓz5 -i|DQGz*6, dq(2^ux{ ؅j:<|0G݈(ιx,ZB\14+! -DÅF60Nۿc)!BæK m'b xY֞5WܹUz&̫5*fY'POĐUuky{sXDs};רsl(̤θ~oEn& Ds( Y֧Ѣwgє ay|aI -_?_2ūU}lfcya\~P2]eS-陶 9 v`XS)g*ij6VeaBV 0|^DVNYּA;uoO xyHo3÷Z 9(3S\,[BgöÍ0xGjQ(sLQApQ^@(B8Ge2'0Tjxm: ]HTfE=%_^6ҿ9TKIV(/©*i8N,|Ӧ n?nj#uJS77TTZlnf&[rzM:oA, -k"WUD.B=E -#Qzm"2v';Wu-Pml,"&LyԲ8>rOokSDamgυ_YGt"+.AkB22MtE3pɶ4J -\m'ț^6zq3U-/na:LFxr?t8H%hotW:gFq{T(.QkcQWO8(psAv%?0"4X%W,MٺA]6C42BT(w+,ʶ`b7 -̉WRa $1'Uk;+>`T؅#xG*ʈ˨9Ⱦw4nC-5ic*t"<.j9h)/o^*?8zG7⛪ȃjIr1_CoghOΛ"C HDx%: -K˞7=Y2kt > fD\`v.#`5LZ44w| m -)4URI%a1՞[-ue|iߌt'ђnL35gUE?ag-4+Lnkf -U"`HEΩ Jq~!ٜ{i upЧ?6&Ro±h6".Eм֜,fBy޾RungZc "p;sy*n ~Ay)TsjB?EfxcF knPݎkG 3>R -hhkF244[OrGM疠&'eo$#n qaF T@9}Ɣ)2Ae9VO}3T 2R9cDBU~29 w@232YWR`t\ݜY4"ŧ-6g/WoQ5el]_Ivu0 KuïsרLKgޒ AmIYI}#ʸ;EiGsZ™OV(H -+7~P}J~3 j 7K|/$)zt }a^!Jte!:/&k~<93K*udIbR^Ӡ:հМeb]$-Z;,@(هo$/!]i3X Q|t{ -9%9P0@~ -Re'ig:@?})MqBL5.=~ T[2ɡgn//oD4.(1ZoWP87l-f& 7 U/fwKF>Ƚs,ڦV)F-,^L'٬'(OGf{фr_`UNu._M)}&LEwi/ox D*/Xn5_ Zgfw*ZG",8o2wHe:yx~.yL%8T.3mQ{b]Ik5guTZYLz?=(*-xq+ iaxnm5Z6L%7lV/Knp?Hamgw]|w~PvkI5 -0k,kP6M iDj9]$H[wt>k>}]5Eʶbukd~}ƟEC œ -Nk*~T䁚Z?f9R7}#Ѱ҉I"FVJ7#|٩lJ73I+ ;Leڄx.Z IJ4FAxIM6l"!KY3е?,@P:+!.vve삝;@zə󆠽*bȡKOԱm7DH{' L#lb]VKB"WFmr`l0IMS -zrrjp ă-(by5{;҈(|z!1uw^+Ri4OƬ5P2`V -$یd.&ģs(b66;p) M謎UlZXyzO;# -@220'n3d /YyhRZ#@ޥX=USAe/~A5|K}eYMf_KDӺd*֣j.cq<,\Y?2,P(I$\'4\㟋`L yG +/'XznxTÈ_ďnWCE: u)ߎNSޝP<9* ڌgXYζ2N5VOp3BcPiq,3oIogqsW8<Ş`+w (D(\AJ7:=6h#@ŪP%.Khk f>?-/VzrFeӕP`ŧgz:YU xrp?Eit \&U>SqcuGUx2*hV9ò*ZTPy~P5ǭ8 -C=jz.pSrAUPbEMwvYc$s;}MGO,RɍfKk.ZͲ] GzR%=ތy.LH6ǁ>6Ubj>Ql_qd63 -}HЃ KrR,higQ-x!|+XZyB.8r^hڡ)}ň*UcW[Y}ab7cb ߈$qrbD6$'8+x}j3k7194Ͻ=}|BQr4fjpsXMMq[>T`T<;gug1KQjOւBW];رQ+Zz;>~S'3305X@ΖT~A݁޹l;Sx6-TY>xCS,J&v ehX-W{)&v~JZY%b^P)aZ')z&Ύ쑰&J:yǗ Q}ɵ'_b'DDb+1˜tPXzNrhC(‹5l˯9^>m^o(ǨI-*9BCL}Ov]MGI/o < /P3!o@3]`̡%Qɦģ#_RYu_&jĜρឩ K)5v[)67Riu8*3H js2ZBue!M<ި۱J%a솁@-N^!!KIJ7^|VT &OUXQ{ 8'YA3]~φ9SPy~tK^$dkXu7b+u?7>l<  C:gup*UATe-yt,ɢ{Lt[: ; DټW/J|B|==L ǡ@>r/Wc2_ZrsY :K0쎓 ǝxC2|Lu<4\gdhQ`T.HgyѤk=_sh!ߥ-o'5ZCVcAD˫bpzmg7ܺ\~E,waDK?]r]ˀ1"_EMԉW);D(5Lbc5!LV7jj/OR\~f/W*}Vƚ;uJ*]t0ޠaӦ^kث=7DroA=<`^0TA@,$ '9428;d,DuMIXC֣–i~o&'ݕig 0L()C4BD~N ` &fv$kѣCx(],?G)kI$=X40Wϋ9Xñq9٦T]Gگ"#rVl6rF& õawa]K8Fe^qqUv> "xByuzR29 M@,ăS\~oI 7ڽvS1&813M#EL œIq[Lsmw_RoxR)#w3PN*.3@k?M'~=Sz6Q -endstream +528 0 obj +[458 458 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1056 0 0 0 0 0 0 0 1444 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 667 1000 ] endobj -512 0 obj << -/Type /FontDescriptor -/FontName /SQUASS+CMMI10 -/Flags 4 -/FontBBox [-32 -250 1048 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 72 -/XHeight 431 -/CharSet (/A/D/E/G/I/M/N/P/R/S/V/W/a/b/comma/delta/e/greater/i/j/l/m/n/o/omega/p/period/r/rho/s/slash/t/theta/v/w/x/y/z) -/FontFile 511 0 R +527 0 obj << +/Type /Encoding +/Differences [ 0 /parenleftbig/parenrightbig 2/.notdef 26/braceleftbigg 27/.notdef 80/summationtext 81/.notdef 88/summationdisplay 89/.notdef 110/braceleftBig/bracerightBig/radicalbig 113/.notdef] >> endobj -513 0 obj << +298 0 obj << /Length1 777 /Length2 1473 -/Length3 0 -/Length 2250 +/Length3 532 +/Length 2782 >> stream %!PS-AdobeFont-1.1: CMMI6 1.100 @@ -5747,14 +8956,14 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /OFGSEC+CMMI6 def +/FontName /XYXRBB+CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 67 /C put dup 14 /delta put +dup 67 /C put dup 105 /i put readonly def /FontBBox{11 -250 1241 750}readonly def @@ -5767,83 +8976,207 @@ currentfile eexec 9IZCD\y~4.vɏ_ilqQϻaRa}8UZ ySrq't5\~; (ϐ?^AKޔf:*mVo2)A]foLӘt\7g3&5#e5qe]unwE9,}#WD=^'ߛ]Jq],Tm |>=VDZ*Z4D%6V6>" ӡ[%Rq2t5h]QS2TyIA@ҩc' |31Od~ ZT_h]Ꮣŵ -^׵GS761z'CUH gG(?W f%[*&T&":|6A $< UDԐ5 > +^׵GS761z'CUH gG(?W f%[*&T&":|6A $< UDԐ5 >0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -514 0 obj << -/Type /FontDescriptor -/FontName /OFGSEC+CMMI6 -/Flags 4 -/FontBBox [11 -250 1241 750] +299 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 529 0 R +/FirstChar 14 +/LastChar 105 +/Widths 530 0 R +/BaseFont /XYXRBB+CMMI6 +/FontDescriptor 297 0 R +>> endobj +297 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/ItalicAngle -14 +/FontName /XYXRBB+CMMI6 +/ItalicAngle -14.04 /StemV 85 /XHeight 431 -/CharSet (/C/delta/i) -/FontFile 513 0 R +/FontBBox [11 -250 1241 750] +/Flags 4 +/CharSet (/delta/C/i) +/FontFile 298 0 R >> endobj -515 0 obj << -/Length1 803 -/Length2 1857 -/Length3 0 -/Length 2660 +530 0 obj +[566 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 884 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 446 ] +endobj +529 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 14/delta 15/.notdef 67/C 68/.notdef 105/i 106/.notdef] +>> endobj +295 0 obj << +/Length1 786 +/Length2 1479 +/Length3 532 +/Length 2797 >> stream -%!PS-AdobeFont-1.1: CMMI7 1.100 -%%CreationDate: 1996 Jul 23 07:53:53 +%!PS-AdobeFont-1.1: CMR8 1.0 +%%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.100) readonly def +/version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMMI7) readonly def +/FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def -/ItalicAngle -14.04 def +/ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /CFAIUE+CMMI7 def +/FontName /JVLCLM+CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 84 /T put -dup 101 /e put -dup 108 /l put -dup 110 /n put -dup 118 /v put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 61 /equal put readonly def -/FontBBox{0 -250 1171 750}readonly def +/FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec -oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# -]LeVߐGoo٥\k 9Mv92#:iQ?.n>%jzGm >NjS])7uևUQh4)-×p#z{8YаGP9 )"Pƣ3ГzYYZgp_PC߬CܔDC'<|(Rl/IxXMYzntԟlAv)|*iQP3|TxL" ʃ?Aw·pҋ:r)6,N{?JoA剳Js(0T9$ն''0j%&4LwQcKHpY Bֶ6$bZXZmX>B#9xҥ6IUJeG#݆>@P1o(ߋUcCо"[D.)>;@Ly͗`50/+R1&e7H?6y@Vx!+ԁ Sk,M8ڱkp/ h(!:ԟH'5II,LIl9#oz)bz&2epDQ/TU^ riFQd'@8NL5`NCAm3IQAJqla_Y&PmjNaz!v4%.\֖b`+#`\ܠḄFr=Z -L2-q; ]Ƽnl,Lt4-`_My檭 -RBٝ1jGO._=] Vi氚l@%f齅YB1q4Mk$_N>B0}\SZh?sȀOwJXmQ68XN3A?(Y}ND$R{տ& \\z޺m块*P k-죰BF *♹8clmotgJ(Olj^~^&Y0TI\1'6ؓBcx3|']PxTi\[`߻,}y*1PA@H1}c >I|N_Dkغ^~+($65)qAahJҾU(qs3FjékX[;8v;;$=NYn \X=(iv/Qg_,\-]C 3ӈG;V-|yn^4@dx]*~.|8D?,㋽5`a +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\@[6]nhmlhaH+4/?3&n=a6E#|~.ԅˡw,"rg[eHi>u +Wת>~ӖѿJmdvA +[4|ܾ.Vz_1. Ff |X9^Rw] +ۊ31S\DKZW` P^3 eێ 8`2?l;Ȋ!eXxh +Df@=$*IBXԏ!Wx-b1 C; p}hQi=HXbgbmǣR,>_Q! +Z؞Ar]< Qjt8?B,mN3v լǵ+K6 t{AJcQ%r?v60RmXsŤ+pǸi:Us)kPW\~; 7T.N }.&:D~zp0C_HOzCByAOve1k`G|f28'j0&®uk6sw, I5&{oP}p2d +CA!8Z⓪٦ǎaBLeblsLK1Bf/H[UD&V{FB16hX"lLMT.?pSZϞ@+/kb/t9{Q 2l6TH[.*!9 wm4k%glqQOc[l~b'D_^b`& O[cNDObkfrɉHˡlY]z&Q=P~lMrO9yh7OonXli'w h.us-4{ +9cO `+m.f)KZҜ/ȫMf?PG,|Ϲq-Zy#nbly@Jnz2GE]=̤+&@<~h'u &B3+*/h:,uv޽GCb-ĈizzeԠ=˻iK_xjx%ZUL1(Se]/^ǝ ama[ ‘a`TQ)|FNj+mC[P+> endobj +294 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/ItalicAngle -14 -/StemV 81 +/FontName /JVLCLM+CMR8 +/ItalicAngle 0 +/StemV 76 /XHeight 431 -/CharSet (/T/e/l/n/v) -/FontFile 515 0 R +/FontBBox [-36 -250 1070 750] +/Flags 4 +/CharSet (/zero/one/two/equal) +/FontFile 295 0 R >> endobj -517 0 obj << +532 0 obj +[531 531 531 0 0 0 0 0 0 0 0 0 0 826 ] +endobj +531 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 48/zero/one/two 51/.notdef 61/equal 62/.notdef] +>> endobj +292 0 obj << +/Length1 765 +/Length2 745 +/Length3 532 +/Length 2042 +>> +stream +%!PS-AdobeFont-1.1: CMSY8 1.0 +%%CreationDate: 1991 Aug 15 07:22:10 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY8) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /BIOIUU+CMSY8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +dup 2 /multiply put +readonly def +/FontBBox{-30 -955 1185 779}readonly def +currentdict end +currentfile eexec +oc;j~EЪ/ ȭX~id}S5Q!gtⵎkJc;rN^X5.Sy +'IqV:r㚉#,# dBZ *R*"7٨y! [R߻*|]~[C֨a[#ԙ jY!4J"3&ejc\J$2626wIaUIrnFB/Г(Hp%#O.,snݸt%\b9?_\ <+n6rBPYԥ Tlp4űI=+rp% !<'y1# 0wyr(X|X> endobj +291 0 obj << +/Ascent 750 +/CapHeight 683 +/Descent -194 +/FontName /BIOIUU+CMSY8 +/ItalicAngle -14.035 +/StemV 89 +/XHeight 431 +/FontBBox [-30 -955 1185 779] +/Flags 4 +/CharSet (/minus/multiply) +/FontFile 292 0 R +>> endobj +534 0 obj +[826 0 826 ] +endobj +533 0 obj << +/Type /Encoding +/Differences [ 0 /minus 1/.notdef 2/multiply 3/.notdef] +>> endobj +289 0 obj << /Length1 994 /Length2 4891 -/Length3 0 -/Length 5885 +/Length3 532 +/Length 6417 >> stream %!PS-AdobeFont-1.1: CMMI8 1.100 @@ -5859,12 +9192,13 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /VCFHMD+CMMI8 def +/FontName /NQUZUX+CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for +dup 14 /delta put dup 65 /A put dup 67 /C put dup 69 /E put @@ -5875,7 +9209,6 @@ dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put -dup 14 /delta put dup 105 /i put dup 106 /j put dup 108 /l put @@ -5899,49 +9232,99 @@ currentfile eexec di).[V;'c1:{6@]PZ,Vci6](f9qڙ,o BJex@˩#Gr kP8Lg/Ó!<]"bX_ <u7߇\l.&D/uGN,(EzR9Z>}ԃqbWɟ"ϟ@0y-γ#3j?$j>Y:6atsNroh8H`2s~)Ӄyoo2>>YQWu>;-ٜ<,E3r/g.#R/ff1|zMT!Dz/x*);bkZkҎ1kLQ\ 5ݒ/XлWb~E.C6cWS|Lߦ "c,/T2ɺSz=~̞g+f)9AX(3יFY9['vӒÄ7k5z>-Gh=UEQ#ǸLΞ<9c@<޴mdkFtTT iwX-4^;qKL}IBR& Hx1Nw v̸H>i,N~IG-PCD +,'N]d.KiYVpi Ԏa8".8y 7yݟ݉sMBbHI_g,ۄ9ЬΌ~MX~Ɯ2t8bCP3=(˜[ *]V5OD2pϡ2~4{؄?_Hf;\%7WiGèǩ-IWj>Y:6atsNroh8H`2s~)Ӄyoo2>>YQWu>;-ٜ<,E3r/g.#R/ff1|zMT!Dz/x*);bkZkҎ1kLQ\ 5ݒ/XлWb~E.C6cWS|Lߦ "c,/T2ɺSz=~̞g+f)9AX(3יFY9['vӒÄ7k5z>-Gh=UEQ#ǸLΞ<9c@<޴mdkFtTT iwX-4^;qKL}IBR& Hx1Nw v̸H>i,N~IG-PCD0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -518 0 obj << -/Type /FontDescriptor -/FontName /VCFHMD+CMMI8 -/Flags 4 -/FontBBox [-24 -250 1110 750] +290 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 535 0 R +/FirstChar 14 +/LastChar 115 +/Widths 536 0 R +/BaseFont /NQUZUX+CMMI8 +/FontDescriptor 288 0 R +>> endobj +288 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/ItalicAngle -14 +/FontName /NQUZUX+CMMI8 +/ItalicAngle -14.04 /StemV 78 /XHeight 431 -/CharSet (/A/C/E/H/L/O/P/R/S/T/delta/i/j/l/m/n/r/s) -/FontFile 517 0 R +/FontBBox [-24 -250 1110 750] +/Flags 4 +/CharSet (/delta/A/C/E/H/L/O/P/R/S/T/i/j/l/m/n/r/s) +/FontFile 289 0 R >> endobj -519 0 obj << -/Length1 2138 -/Length2 15267 -/Length3 0 -/Length 17405 +536 0 obj +[470 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 796 0 757 0 779 0 0 873 0 0 0 723 0 0 806 674 0 800 646 619 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 362 430 0 317 940 645 0 0 0 479 491 ] +endobj +535 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 14/delta 15/.notdef 65/A 66/.notdef 67/C 68/.notdef 69/E 70/.notdef 72/H 73/.notdef 76/L 77/.notdef 79/O/P 81/.notdef 82/R/S/T 85/.notdef 105/i/j 107/.notdef 108/l/m/n 111/.notdef 114/r/s 116/.notdef] +>> endobj +218 0 obj << +/Length1 2088 +/Length2 13404 +/Length3 532 +/Length 16024 >> stream -%!PS-AdobeFont-1.1: CMR10 1.00B -%%CreationDate: 1992 Feb 19 19:54:52 +%!PS-AdobeFont-1.1: CMTT10 1.00B +%%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMR10) readonly def +/FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def -/isFixedPitch false def +/isFixedPitch true def end readonly def -/FontName /KZBLKD+CMR10 def +/FontName /DVVBUR+CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for +dup 33 /exclam put +dup 34 /quotedbl put +dup 36 /dollar put +dup 39 /quoteright put +dup 40 /parenleft put +dup 41 /parenright put +dup 42 /asterisk put +dup 43 /plus put +dup 44 /comma put +dup 45 /hyphen put +dup 46 /period put +dup 47 /slash put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +dup 56 /eight put +dup 57 /nine put +dup 58 /colon put +dup 59 /semicolon put +dup 60 /less put +dup 61 /equal put +dup 62 /greater put +dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put @@ -5958,6 +9341,7 @@ dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put +dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put @@ -5966,378 +9350,133 @@ dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put -dup 97 /a put -dup 98 /b put dup 91 /bracketleft put +dup 92 /backslash put dup 93 /bracketright put +dup 95 /underscore put +dup 96 /quoteleft put +dup 97 /a put +dup 98 /b put dup 99 /c put -dup 20 /caron put -dup 58 /colon put -dup 44 /comma put dup 100 /d put -dup 127 /dieresis put dup 101 /e put -dup 56 /eight put -dup 124 /emdash put -dup 123 /endash put -dup 61 /equal put -dup 33 /exclam put dup 102 /f put -dup 11 /ff put -dup 14 /ffi put -dup 12 /fi put -dup 53 /five put -dup 13 /fl put -dup 52 /four put dup 103 /g put dup 104 /h put -dup 45 /hyphen put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put -dup 57 /nine put dup 111 /o put -dup 49 /one put dup 112 /p put -dup 40 /parenleft put -dup 41 /parenright put -dup 46 /period put -dup 43 /plus put dup 113 /q put -dup 92 /quotedblleft put -dup 34 /quotedblright put -dup 96 /quoteleft put -dup 39 /quoteright put dup 114 /r put dup 115 /s put -dup 59 /semicolon put -dup 55 /seven put -dup 54 /six put -dup 47 /slash put dup 116 /t put -dup 51 /three put -dup 126 /tilde put -dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put -dup 48 /zero put +dup 126 /asciitilde put readonly def -/FontBBox{-251 -250 1009 969}readonly def +/FontBBox{-4 -235 731 800}readonly def currentdict end currentfile eexec -oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\c3R*R?쨤ȯ@ gSr RIzE_EMv,X!%6]ަ_3+_hJإ0o'z 9K$|tV\)Z! j#ZŚz1UA~ -"p?{u@]A}s -ijB)~Ob {z;O9mT[Ğ^dUl$Wh: ?Ƃ(r6;Bt6cFCr$/;!,KqLeWuG h7IQ[u20uZ8*#qP|̖I̓pe}#YۇW{ -Hs(}CE c;[e/SmV& -i2ǡmc\0kC'sp)X0@$2jOGG9%fLJD@m2b5\cdy!iz+lxa+2S@uIY5F>qgROEowK*;/sDGǡx=>J ujLDfdžk4ؐ. -vî|1wm% QiwXDN}}x|E.gK{ T >k&յ2Ҡ^Sg,m1"7CS-ƶkDD K-syRb1ȧ!j h OVk!JEJcуvӘDI6%;>fA/j2C?)hל':QS¿j"D9JI9cA<)3k!̰#pZx7cT6]tN7[T렍(W $a8|Gsaw%e;'s]6|Ǔ7!ib_,{d)>Cow<]=(d<%! %zP圯ٝ ~ELFM]#9yzFpU9n6Pn&([,ne$Ɂ<l&&9?1{3OQC3/Ly&$O/By_\)GK\bi1!|Ԁ9`)'grKU9Ӛ8 #1[ߨ DP%<6֠)#K @"H>}Xbg* ft uac@f QgQADW* -T q^A]JFr49{)C bY/*8 :ywXR[]lWU s? R1GrNs 5W#oXʎZm3.@& |48XKP~02]]1Zaz !zWzFFѼji_Zg֙(弭TSh({׸'&Œ҈$k5w4PvR.',:d4> }5[Uc1gZVw0 80O -jV-0#'lYMYo#{N -8k>;w}(x>EW,(HH=+RbaHʧE'F{!괐kI2Ľ@Z:l%&#։cf5mqbfzITб'FV#鶡!((x\&7h>EPd5#S*䰋IBhCDBC6eb/x;J(M vIdv0_$ c"U9KE!S~:N$Y=e5kΜUhƢW`6#"aT8=a4El62"Aw>TO2hH(1Ӟ(4kO!њ]rhۆ`\@SMJ'Nl - o֗|%mvߘ];tŶwTbb HtLIᅸ G\v`yrvW$J Zj%--<0:x,Q\"Oc+gwpwO#~ˆ:> Q99Aުۊd #te/Mru܂0g6t?d2WOp[) z}- C*EBFaf](h$ ɰH%U1X^QmKQ(6j^RĿɭV$a5\3MpX!WݜEk,1}wJՠl$J4#ua8'sheN@@#lmaqE0<-|NxE#YAoNp[_)g3"g=rNЄ >2D RǴv' hslF./5YLoF+=7uI< ZuV&hi\fqa^84Y3ݍ'F&L2S={ ._~f4s~35⺩s8F) 4$ tf@*R"K ~i;Tq|oWm -owmsfn0\RU͒* ~{x*o0z9KA5sF`X+0g3_entMbuA3 -TŴ /3㕻>*Fa5"˭(t/Nhj5٣}EaѐEOuv:Ͷg`LK@m3-%#n Hmp,vRM?  Z|9 Ԫ6 -恜u\dE4Bl:6A$ބM{>JHҒ6J4LT*GylM1zWWqhG#1NB!wA  @ՑW2GK,?AŖkę+EPXxpL^b @3 f*)u&|:1ClŜ4"Ttݴa{ܘx3$[ -6  9odWng>Igz# B,*JJ] b-xwvqD~F ->QMq>րMOiiN}O?s2J+(p*$T 0\cb0=;Ϙq; '$.JS('O--^j - $3g?}8ᆘ[\^)~VcH4s7bU{MۗXЇus1=WEw ?/Rp?|l~]D=V[KZp&N݂b"l=TT˼`|Q#mU8zѱM"? -_Y?ʤ19 6+?]G(Uhp&.4!H̞$Q'>rhDPgs',UF0T;Z^!+"]WɖP2JoIr,?!2h#04ˌ >(ͅe&vzesQ#Z ]ͻ8 Vƿ.:`paisf/cj_(T[NMir}Obe,OɥҜoh經F;3 bƾ/զm$RЭ,K=} #[SDFKStl#j#6,~:V kU> B](r@qeB\ZY\`הUNx*rczlC^r]Gƛ=[Mް)gd-$XT jdH0:1| si6ЧXxѶ5~0n1Bzmہo`[b: *6CIԕnz$:]SEJ?HsO1HV>6=M5Bҽ4'k|30zOfN]SrBZKPvcc+%[P9Ԕ0Ӽ LV`U*zH0OâH/|?Am\n<5Aоw -%g8IX%__ -:fdhߑ*RNpw+dJd[)KZ%2U3FA~♼vQ{9}*dTΔ=rv8.G4" 6/AĨ93,2|>a$s9Ս j[&lZ Q൑ 4*h$˓醜~=|dsuφs]M?pm<5aK)EOːT6c+O='{4Ы`c6Ƅ(f2eV(/n>,B-DjWB@ -z'RqZAz!WP%R쾐'{RVP9X6c]CؘМ|chz(0wvvدYyЪp#:<ފvO% @hߍi܍wI,*bx\I PjFo{㼐{lĥDK> ZtR:\Sم(d1*,= pWM vkr QNIas-/a'kLU=s{+L4Qy"Ν;!D[ x˨Z=B#(>sCs3NQܧ%aRLc -7~򩏇\45浃Lt Oh$.arY7ۣnC[/ִbd$C֨LB&hӞXo+`p<⢚M'{KHP}[ϷΡX2f^סE:B0~7.YExgi=d8.H -r8yɃ< j,Hvm.< -<=k-bSEDT9jb?l^ڏ8⋶cgEx:MPO;z6M -lJt TYu۽LBCJ&) tJ6L:s`(HDH;*5/B_h7AP Jw=iy=c,rKc@6 -Jܺrݺ.<7*ܳWi<:m1FGbC{*e0R_;2N08?eUZdЧ;sl-%L,3Jв.qRէ<~T8>1rK4aCtN gP-ZU7|N\BAEz!U9v RjD8Ž@6'g4Oʶnjq?ga>**ˆbm"`DtS'c] -<SA cxG]Zik4PX̦ۍ? - -cq5Ac]5IvCRD\J>8 ^qrw4:3q*+37<^+K55?^W¯2ēWTkZY 2X3RIbl˟QB+8^ɽʓ8[e?ӡsrj87|#GcGx' 9\]h -Jvy g+5i'L&D2A|brJ{b6?Md#҂@t[f>K䇛d;&0Lȥ&oe`#@5'9 -{ ޕ5o>ܲ/Kw)1NIN'8Ԅ"VDbO&`HE|429v$\E_>@r#-~Ml2qbZf`1u!LSplR{SlyȬhP)ew誏άCGkضmAt8gC͌=TQ&tF1lc Y=k<2F'RĀb1*{ -VuI=cVtC~JLG&o_R6jct( o@!jWO@>6u{:@(6.|b0G1Ϗ+=dYӖ^tj&׊ؒ]˸ꆆ‹;uxJd'o2~] c,'ݙdlQرqogP) -ҋˎeF1C GRL.ON23e:4O@]'13i(.(RT`Ŧ;8mќg2΢ @pRt}1[ڮ(':uZi,OZtngP̉+_DEj륅𢦱y׹c w;ɗ籽"S7jxq|3%ٮRaүtǮqYBXpʙL-{lq!}}m_ۗ/@|Y[е47 K $r__z`4ѺN)#l2>$U|SEkd@t7Y+1%N f)əvS2H淵 -Uw|dU̓hXRp)[7F[}~71k;n?J$,y-]1qɶ?qh9xp;H}t԰IIo'lFN/d^Ƽd)NE<}Zҧ[࠳0U^d]; cG/!/7 C!RdN`F[35 :|m\C# LtgىTimK*h[reBd,Iכ N7&Na -Υ2ۀZ -,CQד}H;{&l^v}̏YMJzEg*]Jز X}<^H.8=rr.V]w;W1Cs`'w䡀>[sI z&CYF=EǀeXWna.#pͤ %8`ıOUc7EFkϿk2C-st>cSW?QՆj؆ fbl6!~GfL:-^IKV rB0z"8 i*3Äg* W7#e0O&}r[$#Hhc(GpeƓ^67ST}Tɕ#c I?8w9SA{!\V%+OI)܏T3Sz bd/8ͤ|m̚ҝL 3K(I>U2ӝj21M %V`F=́`tV +K^ޅ)P7B=R@WϽx}Y1sBh ^朂nl%δCs]Qj̎ ٺuơ]EuF yݮ3z6](Iafx':׫d@ -)`uAks2j"S[wg#A@РGunb.=`Yn֎΀vλ t/R=,niaO(Ě+Cx`hߺobn2iqbD?"x}iV/.oYn#1؆[^!> _ ^FƉg],ƽMMqWzfIM3>Zum̑)isv -&ѰvP<+ e6<ژѪ=I%Xp`)\B0 ch- Ȋ|VDP(A OX&iԗ?SEr&4Ph1Kh ѬgЉXVoB#ŵpTO0k,g])3z6tȈnj&!Y\*R9*)},ZuqKz0죢A!{g.ڈBJIlmenY1&;yj1mФެYڌ5%lz,i`^ -!4\.:OgC)N&fZLevZmsL vW_2!RS@te}d>ְxw4qc*#)ݦ 8 v^'>L2hx`~S0?<(dv hj$sĝ3dERׁmZ6z.}w7p 0XڭtDqLU"3 -=:.;eP!g6wn A;)Q%::-FEW<:=il J$SVN#˄4Ħ6X˲RQU E$b)e#Z - -DR B2y6_<~ n‰/3cOl ?xJ,-Ԩ6'KVO-l~$/NĔNcF&]Z2iGzv 3kM诩 jD\Pݨ P@UxwD *Q,2ҌҠfLȒHx,T {Ę}c[n˄%;+TXzOpQϖ'BʘɫĠ5d8ų}:@*7"ݑ3 ,E,yC:क़ZlI+*0G#R?H S@,ošdD*(7T?KyA7&K^ <.H·v%kM@4aM?)wc^u -*cȌv({W@iUY-JbCݕvhh֨>)z Kdxg>%]2`#;IRQ\Tte v-nV掟Pw!@Wp$& L~yṭh-$p/GObRGZG/MC<%b=3 *nHؾN_Ԓtdp#ityOG^*E,umDs|RyR!>! k2a E\(4h9&x{XHTjvG?П*Z fɎř3%ZWH h~',UM[lsZunB;t -xnH}Abk)5$ݘ>WzrÛX@yB1ZI{mBS(cDq# _w!'k%+ف׻r|k^< B5:(b^!{9'yauGW\ -pY3xD-Pd)^5Z/ok':CU+*Ӟ֐*ٯsEMs>e2ңrrx,ވE0E8ƎP75mʜ#)ruGMMUXդ#o*-Yc1&";h'JkA$ RG6FM3G(`Az|=\Vʪhm0-eG3.=lcli>}T&LQ ,gnp ^mdF6 ; /ĹlT+M/OG% JcG -y"7Gop;wndmjR>y^4o8z\1R<uz.0[ H4/ A'Uk>ذ K"oQ_dB')0*71N?Bᜍ&݉45VæK { (X K7[ ]S}ļ?ea|9x&T1Zpn,ٞBo ԓqZ?HZĨQѱ[jL3q2`'q/[E@(2-@^}wZj'5avګ @zu3YW>wkRXo"l2%:12p=E$ߒ"-ڛ#`D["=MS0"K3w>@kjaiTV^|])nms -[wFPwQ WnĬy G4GgHDN:Ax?y -_RPc f:_WLH|MDouͤЬeQ˶9Cmո7d{C#WS<Ǩ]ʤ!lٕn .jo?LbO}-n$9ӍjaЌPaOΉ}Vux8 woC -endstream -endobj -520 0 obj << -/Type /FontDescriptor -/FontName /KZBLKD+CMR10 -/Flags 4 -/FontBBox [-251 -250 1009 969] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle 0 -/StemV 69 -/XHeight 431 -/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/R/S/T/U/V/W/X/Y/a/b/bracketleft/bracketright/c/caron/colon/comma/d/dieresis/e/eight/emdash/endash/equal/exclam/f/ff/ffi/fi/five/fl/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/plus/q/quotedblleft/quotedblright/quoteleft/quoteright/r/s/semicolon/seven/six/slash/t/three/tilde/two/u/v/w/x/y/z/zero) -/FontFile 519 0 R ->> endobj -521 0 obj << -/Length1 1353 -/Length2 7074 -/Length3 0 -/Length 8427 ->> -stream -%!PS-AdobeFont-1.1: CMR12 1.0 -%%CreationDate: 1991 Aug 20 16:38:05 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMR12) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -end readonly def -/FontName /SHLUJC+CMR12 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 67 /C put -dup 73 /I put -dup 74 /J put -dup 78 /N put -dup 82 /R put -dup 83 /S put -dup 84 /T put -dup 85 /U put -dup 86 /V put -dup 97 /a put -dup 99 /c put -dup 58 /colon put -dup 44 /comma put -dup 100 /d put -dup 101 /e put -dup 56 /eight put -dup 102 /f put -dup 52 /four put -dup 103 /g put -dup 45 /hyphen put -dup 105 /i put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 46 /period put -dup 92 /quotedblleft put -dup 34 /quotedblright put -dup 114 /r put -dup 115 /s put -dup 116 /t put -dup 50 /two put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 121 /y put -dup 48 /zero put -readonly def -/FontBBox{-34 -251 988 750}readonly def -currentdict end -currentfile eexec -oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\@[6]nhmlhaH+4/?3&n=a6E#|~.ԅˠLw2.槝sNY ڻ.,VnNX3|裠k(QIOs m;fߖC1}_a Io#0wݙ\P,f *bG3Z2کP8L3r[vnc_Eh~g9|M) }YaѕH|1m![AzXpPNCU7Uֲ7ΖTgx_hyW^]W}s_Zfs@dYr ȟsy&vJx)ݱ~Kq -45hL#q:4pP?g |GJSn^i26M Ęz0. v31껰xCj 7}0a `~iEfÎ}O>&*gϿ60CL͘sc·^X0IF +3yP.wP=vH?tx??jKvcJ ފO(WfnYc+ՈuMWkSMpy2La }gH,HA ngVU4NN7z3=ʿM1(2iznl7 J[7һDH]WUMi)hiwuPJv+]/XNkn|´?4ҫf kE{'ǺW1 os!w#v. -RGgkx0S"MB$0kSlk6C)R`+&gljᑢ_5s$ U$;|Q|nÜ2 @%ړqP c Tݓz#rr%sV 5jXmcxco!e<꯿!j_&a招Dʕ񮄏]_ZbJm*:/gO!**$_ !YEBě `Ek14#!"AGgJt+1u!*(*}U\#6g1.*u =>Jx7bdژپ|8K8u+0aYq/2S8|ea7lt+qo[YD5v_W <Zw[}7{<p s'}up/Pl Ēde.+R/rHu /&T V]jSXDT ]v2OG90g}M;ρ}Ҙ#LdWVoft&<"C8&rŔyTqd.2*Em9u.m}pk&QUZr t2A -5'Vh*He"z8<`jCZnpZ.C^L̮uÑ9LTr>Ғʩ]]H)eܨ<1BDvT h8#JPϸQ>#<8&6Cc`mE}w56_z#h}ʅDFM"ֶ+\@esx~1lP:S/ \H)l_᤺ѼYrvε[ɹHP:xb_ S6٩,^b~q, ;FKkgB*.6څy!rhN㉳^K0Z\dRoþIh /A]&.t i> -N)`~L CɬS -374TldǧA?*2|iwtYɪA5R%t/Pd -?Ty&$銥f+J y l?cڵ*W𲌲BNE n>PL^x|Gq?"#o",eGb3*|g]BhKxs,9M+d XB1:: ?5gGP, 626y|Bn\AD ū|-_C;s+|/Lmj=f*( wRڮ]e~:XOOnXp6%dLQx %"!租`NƩd_ 2a?Gj}>+={yIb̍e= ZcZLĴ[)2 gqbՖa|؇ DH -ހ `b^U|? R*wC쌆96 GrFwߊt>^hnIlT>RXJagM6#ő j~cG,9#P_# -Lq -< (,] 'LL^ufU[8$IL袋qiIC¹űnC8]ܖ>(/^4G 6oq `^=\xHnN~j;];KmCG$L*Ya*`wL~$_4rL2Z)F$LkL A%Rx5^"aFܒ}zq;:>C`L% -Nx&$Tn3^ 7mʫ28Hr"k~80OXi)ΟL3L<9Ҙ~ro6S tDR] /H/+)♹ 8I͊ >r(,'H@pǦC2=G ".)GgD;x:ڜ}? 0S-Bk2LQnߍjXyRFp4=Kv6`a( 7_vTLxsxV{!v{GGݫ *4Uꮵ$@+s'A͚'{` 95"b@̎juTE[Ii} x9nM(yʑA[^`08|EtUsyޛk*Kw/ze48RnO%zghHK3HU2,?8{ŋ8 @N)x`4OD ҍ] P%PcyM=4E)ccYš~PDi<!ϴ۠r0p_\_^i?! 6:0\ !( - aOYly^\J8AH.4,zVU'U W'"؊Go Z΃Q ~W^N>^U+X*-7H! '%_1U&L˕~)5"jx2$?q9Cz%v6kܱ޾yWdC Л~QF:=#"`eؐe9|>]tp"m:O|m:.~/z&;%KeŻz7ajEA2 |a!OMb4>WkfgXl -Pѿ5wJWß8p0ƌ\}RRkF_z7b;h8 ЖI-[V'8u Ř9ISUu'm4;gi}8q+P .F3q/^?]؎̢[soD&ęjn*0QBE=Ws I, Q =KP~Y^V #( }$ΐpg,9X夲G{q؋O 絬:oz09ܞ+xqs y5';w"6(Y}[L 4i(yo3S*Fw\2j*U%K)fr["7SV2T""&'_}O-qpO'%4[^Ro51~9tp6B'*רILleAxŝm|_j6LJh\Erd k p>B- Rʓq^I.lEvXā0XЄ$Wun#6x07/0u^<6uu@r42Vm2iںte[e|m(!>J9lY椀ꏺ"r6fϔ+'^*hbK}'Cdi㴂F!>[1 |kt -6  +\\8>XnJs^2VKU{Xn:8uQpݎ4^ -{KEķ%YUBF^hp֩Z9k*`pKN%%R<:ڒWR#_\q$ΔP<G7=<5fb*.#_/[QzVT~"E}Ռo5}6nzqĆIi٥g=)"-=_Vx P|f.e j(fO03i^dt%V"Q"yE%]k?!5A啇n1E3B[/Z:G{UuǫJh6 b@ڄ XL8Bfr7b; Ni!k= &z\JثL5_D]<K -?]1!Ԛ.*txO T!ٞOV ->қHJ;\0?Y1jZ<؟~f1 xP>HlL;l#%VRܐNBL(s3wm)m Ep]?g]΅]~]<@ݍ^|Id> #*Z`iɫmG2{c-EVbj; KS"LV+Z+ѼHO*f2`Nƻdo/GB@f=ձLy H҈!@ys$ǝyTRƳ)[Syi:e.Ho*ثT7w&Ivi](>˔iGHs{G}<+W+uAm=|YZo;{Ya8Q2+i`776d PE:_pC`WYq4xfcnK +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou_c2Bطj=-8\Dg݌] /%bԺnٻڿSy b*L(9sWF R:EMksH02E?Oe+Z'zK΃оif <,EDNZ|J#BW3ϗMp(%5%~(5Bk}Aj c'S-8*!iy$G.w g J0nr +;଍ Kr^ox7p4= CyO#y[49'n*xx/J}o֯p6Oޏe}hà1W6Ϋ%(i]Ii +텴""b3=5sJzbJ>[Wе H 2"ێ0Oy9.t:=$EǪ ]to`% +'EKKfrRK^y`vO^v~ZwR iNMW3HSp+T,q!s0(ع;U+3"J8q3dJ`77+IuؿhH<=!'T́2.r% +v rd c[[ Hu,>d*,R`8'ξD 4} SYe8X|v{ }"--GdvImDRM&OT`MaXc:rNS؆'GSk,ې >a cֵpeW1Jm=6dgaeR#l/`Nj5NEN~QJSYm#M$_#8٘w 8HȞ2'{G [a%ºQE%1l$ks@+ʢ@U4x R3O迚#0GL + G(ŕ!8Bcz^48G`xѰNE@PC@a9g.7Q$hWJ\U`z < )QKtXcs[)&:S[]+39n\qx҆3Jy>Dg"^ݘX4d{ hsKA_&F05nȗ=:#7GJp\S=j48ĿIgi'9)2+$ޥ\ĚҮ'Ȱ;Ó cEzMhi#1P]+>N\r&fBbfI) h[&]/4ZYk0&gvr&tAgD=Q:t`{0a]U$qpHsS@%%+tv Eu $Ǐ`i 3SV,Vw-a?vg)K}koz|nB 7mik 8[ ya6o!:z~4]:1!jl0Rl*aA-d~ԇ %~ôn: qKVs=-0чg#}$;AKhjP#U^݊8ufiҞ6=]L|\' ՋOΓYW}@<~c3zEc!NjH 7gj~ՅN}8`L4_R㩃`pJ[ +6>bE@GG( &6GqL\#ǿ{'2: ˦5)!#W:tĝ)1%@goviWv0B%fmLgP$ԾTGh +w|=ϊʼh`@e㕒D˖ar&|[J ߀ O j'Fڙ3uЧ;L/7)]4Ab r3,̖IM.Iv6y,mzɏ ~ˎMT1Ȍfŋϐa:/̼Ȝ 's. +)G XJytCK]n TMew%a{zs:o ;L@uM0&:J#n5ё}&z]Pʡ5#cܭMEVIڄd$tRIQt,D%<:|(%IT 71 JLg3inF&[Q^rV_Wv4T= ưx\@RUu'*R.4p'8G{)ů ) /On.yQ+9i`羷9ܤ*ݖvWȥ"մ;Q$ڥWm2$o_Yy\ ;S34z2=QK+GOYB _qX|.p|Jjm҄ɥ ʴ.7w!J4a]o +BQ2^m*(p'P3Z8ScJ*T2dPd 5la*/ S:Sؾa| 6_f,ȗz%3| U zV5Q jq2# T_x$[ii4jJ>c֕:"?u[yF)͕cO;uQ;{ţr(好mv/cFxsGDXm~Զ9,UnĮCݒf>="#BӉ2%dh ޺VH-Q)?<ɿj氊03",'?Emw1uHtu}|QBWdQf,[ư#d|muVc +F%xKƕ:8|s,&DQe;?ƒɯ` ^ (4m/ ?pq6vۣ}%=iL[]J/2vJ8FB'o\QJj.lGt$*iT2n$]KtrX!V}riܺ5D;s_>Nb8YopUNU'>VT qB1goquh~3tO3i4=B]g8D6L|W~K?L\F?i<;JSLS;.ax +-eSlSV"57Q:]-Io-pUWb;v$]FB3󰁃!~GS )+CP&Dq݇rEU9?kr$F+)U){xgc'*5ŋ>vc6l%d=ƍN(2Gz0Gc>cXGR*/̸Nk @kvmddzj. ;+K33'I15D%hw"R'ܿ{y2uwtus[M͵3E:!ޱw'G #{-{\qrQQ7iټygert@ +?⿪_az-L7GBDRlAxCO0bz AQY6>QRhCV$ʽO#U[!*R_jowYWdvժž;:nL4Bl3MjSCL+a۲bu,] cpTɉ!'₲"){OK'yz0'o|.X0qΑ끒b jB/h3B9tCO`ɥMiThboRsŤ +q;TxOƲXCp:$ Bn +m#+V+J>7kس[Q_cg.N#' H򥿱]K8?>b`[z/3 䮀o'*I ,ƀh8Zn.cį׺י#lKg. +4#d K€X+jν FO鉎VmߛxSWTƜ56wʮaztAܑ;}?+.\䃻c-JuG0xHٍ9MG"?M | 5h󀺽*{soq[=ՊF{W  j%f_i fUބscp<֥TTX +jN8hac]n}O}ndO +5nO^xQTwnj/twLQ_ra#95TӁ} g7qtء\y}O|Ddpc\Aod#2~d"yɒEe\BnqZ0JT[=CT/K +W0GτGeјJWYK\›WB*jƞ$XBkz8'VQn`e8O K?n'z\M|CK nI ‘.2&r:o0%h^T=F583|H1JuR8c' C]$WHħq-#T;l%{dfjLio7/ z) PF=W(@- +_z7Q4E׋:hHY@5HSxd0c"ڃ㞿~}/N(R{µDHI"^>49NW6>PRtG !GCnI#E!? F5ac,E)~};nj 8x؏/HaFf3Z6΄΍YgfhrV@wj򞞹^2 a6ŕbphқ%nuWB.M6p 2bYoz׋.ai)lXuqL6b%;34jDdFGKʚ%)Vq̌c&:Du9BgAȳi&ݾk1uQBs(} ؞H%X¡ qBh>]3#GCet ЈWoP7L0ӦkE8o /2}6rJ;+X1ݾ7sE +?|4&$,دP wtbCMj6')5p$AHQLA_ʥB3F9"l:HqTuf5^1vĒZ\)?ae՝#B\OA[d} Jc(rR[8c|ם>0U)ԗ=Ð\ 9ֻVht ڂَ!z UH,#"CS +faC;}d-KQ)9OTrp40W`"B֚ŰO0ߵ0 ?%\ h.؇İqĞ) +6 yEUPDP:VVZ̒<"5hǑ[n?t5ƪ@mlpЖA!XP;:ŤŽEp`p`Zc<ޠU!ҥ '(ͳ=ח>8ҢD?'`lȱq%q7Plhue Ӆ# Oi+j1䦚;;l0ER|hag@g= ;dm+):h(tfcql{}7BTޤKi7t{D2a;7' ` Nj`OV$FxT.bpCՇ7gm\zb3ix<ٯGfB3(Gy2!bʬDسPI?a*BYsli^uMP Awj/iwh-αP3(yW>7{ò:R﭅[SYj!zf `2,$&Dy7m^I` tz!qK`TMɭ7>xt(\}qp%^ [*cEt`뀾9KMS(^/,(Hz $Kr py3|!D]@T< +#TnpmρL%2*_dyפ2 dv슲-Z|& ru\1fV-dA{N0ޡ&Y}yas=`tȡa\>flhΈ,‹Y4^*X}9׆׈&q]ʑ#鮥ij7=&tf5/fz:U [m>A-T +dv﯎xS S^gg\i +B'8vJ "S۞uNtD ޗijBkt~_(9b`b?#mV\ҔeЙGjůnwa|Ol~z( 7uZwK%VsvOaX7:k%}GF^C0σ~ ӒAusYoIO`)U!'&7eIѿNFCK4#_V)ڛGdǪORå~ +ITtEMXh#8[ȍ~n$僳oc>h6;N f<vT9 3S'QLZ}8z_9*OB+0u8/f R\LVG +UHM/6گf|P(D ZGt;+UC#7 ? 0餥d&^lms +21 ڋ'P5jhs$\ l _ybTl'k) _ 3MQk Q&tzcA_Ί^Mb}gM0 &%b*`<$g)_ZP*(PDŠF㔢zgXo2+hși+AHApD]b\=hOȲZ 9Լ5 >+F9y.>u`]պ?T9cԾX UW_ +2m,;(}#u.Zf偏9%Ez 4e$@B(Ab5-o"Wx3qH> w+pB<˗׸nFNO +"}Fvc +/WYa"^[[&O9y\"\R9oljFOQٞO{9 ~CŋU4oK_B/"d★#5ռ[:[7Wo`8inNt}42Yr3潍 .Ika:R141omLRod V)f!ނPBU-@*?zc[TA-xQgPIK}γ?șBvvNU916MD>pEM搨?"1ZjDNS7VbRVY=Y22*(x@)_1Bebv[V~qB?%KGU_7N2ڟb=}Jë8ɻL"4}'͡ۇE(aJpX5QZTN$dW}I>`h+LZm]IA4)t"f9vDW4VRW|,<Ⱥ%PK(^?cZ\So>TEJ{[*Ku7{ hJQ4S35ޙ3+V [2'rwCu$g3,̪2Ec(^]sM{GԭXaaҿs+ipk^dƙCu~lw\$`^U]$XNp,nq6Qؕ*LY{;́v>\RyemŒ+ͻN*{ޮA U* +$K[!.ݦ~!Ln$ޓ;w[y@HX&g"dtoG.I~5^=ax}fPO* 6Zfxwtx)|oOx]~JPtjɬx0\4xC! +s* gR(=֓ Am muE6V}.ɼ*CeYN +ނsƋ]<5&uwt.W J0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -522 0 obj << -/Type /FontDescriptor -/FontName /SHLUJC+CMR12 -/Flags 4 -/FontBBox [-34 -251 988 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle 0 -/StemV 65 -/XHeight 431 -/CharSet (/A/C/I/J/N/R/S/T/U/V/a/c/colon/comma/d/e/eight/f/four/g/hyphen/i/l/m/n/o/one/p/period/quotedblleft/quotedblright/r/s/t/two/u/v/w/y/zero) -/FontFile 521 0 R +219 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 537 0 R +/FirstChar 33 +/LastChar 126 +/Widths 538 0 R +/BaseFont /DVVBUR+CMTT10 +/FontDescriptor 217 0 R >> endobj -523 0 obj << -/Length1 752 -/Length2 1167 -/Length3 0 -/Length 1919 ->> -stream -%!PS-AdobeFont-1.1: CMR7 1.0 -%%CreationDate: 1991 Aug 20 16:39:21 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMR7) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -end readonly def -/FontName /TQVOAL+CMR7 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 49 /one put -dup 43 /plus put -readonly def -/FontBBox{-27 -250 1122 750}readonly def -currentdict end -currentfile eexec -oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\ʻl24`}IRB s\pzEGAۋa4_p0uAEG)Q|8B*dGWj'0Vix#(=@'qIT5i -(Ѵt` ?E)4E^yҴF+$8&G"Yl?eYjt+TI2! nXKt`˱~h]{>Qaiσ\mFU#Gvh2un8W;R4Ej1B4b ;b9y[lV:P񕈇9g`\J~ O>%V0 ݬ;cJԺjYrt6yql4Qo٫~o_=6xqw,",kϷo -#vI7_ fz!y(3)5*кYb#aM?3G%wG*L4}. f0Fp)@C,W' ']87Go}y-Iނ% ;dݻy%I+-t7ˬ'$ ;9WJ].IuZ8Cp-$X ӽTֶc+DߍEA1_oKC5@{ !^qRB֭dp=̝?E OS97k,+āI^+͆S# -ias1 +'_m 'd,]X{&41Y9HY_\*2|$g}/M#9]rZRa^3cs!7烬yD6$1/nh -endstream -endobj -524 0 obj << -/Type /FontDescriptor -/FontName /TQVOAL+CMR7 -/Flags 4 -/FontBBox [-27 -250 1122 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 +217 0 obj << +/Ascent 611 +/CapHeight 611 +/Descent -222 +/FontName /DVVBUR+CMTT10 /ItalicAngle 0 -/StemV 79 +/StemV 69 /XHeight 431 -/CharSet (/one/plus) -/FontFile 523 0 R +/FontBBox [-4 -235 731 800] +/Flags 4 +/CharSet (/exclam/quotedbl/dollar/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/eight/nine/colon/semicolon/less/equal/greater/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/bracketleft/backslash/bracketright/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/asciitilde) +/FontFile 218 0 R >> endobj -525 0 obj << -/Length1 786 -/Length2 1479 -/Length3 0 -/Length 2265 ->> -stream -%!PS-AdobeFont-1.1: CMR8 1.0 -%%CreationDate: 1991 Aug 20 16:39:40 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMR8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -end readonly def -/FontName /CGCFOU+CMR8 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 61 /equal put -dup 49 /one put -dup 50 /two put -dup 48 /zero put -readonly def -/FontBBox{-36 -250 1070 750}readonly def -currentdict end -currentfile eexec -oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\@[6]nhmlhaH+4/?3&n=a6E#|~.ԅˡw,"rg[eHi>u -Wת>~ӖѿJmdvA -[4|ܾ.Vz_1. Ff |X9^Rw] -ۊ31S\DKZW` P^3 eێ 8`2?l;Ȋ!eXxh -Df@=$*IBXԏ!Wx-b1 C; p}hQi=HXbgbmǣR,>_Q! -Z؞Ar]< Qjt8?B,mN3v լǵ+K6 t{AJcQ%r?v60RmXsŤ+pǸi:Us)kPW\~; 7T.N }.&:D~zp0C_HOzCByAOve1k`G|f28'j0&®uk6sw, I5&{oP}p2d -CA!8Z⓪٦ǎaBLeblsLK1Bf/H[UD&V{FB16hX"lLMT.?pSZϞ@+/kb/t9{Q 2l6TH[.*!9 wm4k%glqQOc[l~b'D_^b`& O[cNDObkfrɉHˡlY]z&Q=P~lMrO9yh7OonXli'w h.us-4{ -9cO `+m.f)KZҜ/ȫMf?PG,|Ϲq-Zy#nbly@Jnz2GE]=̤+&@<~h'u &B3+*/h:,uv޽GCb-ĈizzeԠ=˻iK_xjx%ZUL1(Se]/^ǝ ama[ ‘a`TQ)|FNj+mC[P+> endobj -527 0 obj << +188 0 obj << /Length1 1016 /Length2 2355 -/Length3 0 -/Length 3371 +/Length3 532 +/Length 3903 >> stream %!PS-AdobeFont-1.1: CMSY10 1.0 @@ -6353,25 +9492,25 @@ stream /ItalicAngle -14.035 def /isFixedPitch false def end readonly def -/FontName /WYYAGH+CMSY10 def +/FontName /EPCAIV+CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 60 /Rfractur put -dup 110 /backslash put -dup 106 /bar put -dup 102 /braceleft put -dup 103 /braceright put +dup 0 /minus put dup 15 /bullet put -dup 50 /element put dup 21 /greaterequal put -dup 0 /minus put -dup 54 /negationslash put dup 26 /propersubset put dup 27 /propersuperset put +dup 50 /element put +dup 54 /negationslash put +dup 60 /Rfractur put dup 91 /union put +dup 102 /braceleft put +dup 103 /braceright put +dup 106 /bar put +dup 110 /backslash put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end @@ -6387,294 +9526,1055 @@ x Qk%Α%֋jo&i I"ay\v*[5`mzh1(l -y[ gI𬥦P,EHJz̘ZokO3 D&'5cCWOKf^T/lJA|6 Ĭ`YS@QȿdEH`L$-bH3ԕSMH7Ib=ae}L*"V:-<7?+gmJ - 6ٜ[A#=MdP'V\'C E4 9\d{$eMqvbN6իpE$3cʝpR]Z<t*!'ě4a{K ?JeRraΝ&>6.ɯ*]#O0^N+k]1<ÐŮ*g5]_$9^6oMdGj + 6ٜ[A#=MdP'V\'C E4 9\d{$eMqvbN6իpE$3cʝpR]Z<t*!'ě4a{K ?JeRraΝ&>6.ɯ*]#O0^N+k]1<ÐŮ*g5]_$9^6oMdGj0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -528 0 obj << -/Type /FontDescriptor -/FontName /WYYAGH+CMSY10 -/Flags 4 -/FontBBox [-29 -960 1116 775] -/Ascent 750 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 +189 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 539 0 R +/FirstChar 0 +/LastChar 110 +/Widths 540 0 R +/BaseFont /EPCAIV+CMSY10 +/FontDescriptor 187 0 R +>> endobj +187 0 obj << +/Ascent 750 +/CapHeight 683 +/Descent -194 +/FontName /EPCAIV+CMSY10 +/ItalicAngle -14.035 /StemV 85 /XHeight 431 -/CharSet (/Rfractur/backslash/bar/braceleft/braceright/bullet/element/greaterequal/minus/negationslash/propersubset/propersuperset/union) -/FontFile 527 0 R +/FontBBox [-29 -960 1116 775] +/Flags 4 +/CharSet (/minus/bullet/greaterequal/propersubset/propersuperset/element/negationslash/Rfractur/union/braceleft/braceright/bar/backslash) +/FontFile 188 0 R >> endobj -529 0 obj << -/Length1 745 -/Length2 581 -/Length3 0 -/Length 1326 +540 0 obj +[778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 0 0 0 0 0 778 0 0 0 0 778 778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 0 0 0 0 0 0 0 0 0 722 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 0 0 0 0 0 0 0 0 0 0 500 500 0 0 278 0 0 0 500 ] +endobj +539 0 obj << +/Type /Encoding +/Differences [ 0 /minus 1/.notdef 15/bullet 16/.notdef 21/greaterequal 22/.notdef 26/propersubset/propersuperset 28/.notdef 50/element 51/.notdef 54/negationslash 55/.notdef 60/Rfractur 61/.notdef 91/union 92/.notdef 102/braceleft/braceright 104/.notdef 106/bar 107/.notdef 110/backslash 111/.notdef] +>> endobj +185 0 obj << +/Length1 1315 +/Length2 8350 +/Length3 532 +/Length 10197 >> stream -%!PS-AdobeFont-1.1: CMSY7 1.0 -%%CreationDate: 1991 Aug 15 07:21:52 +%!PS-AdobeFont-1.1: CMMI10 1.100 +%%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.0) readonly def +/version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMSY7) readonly def +/FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def -/ItalicAngle -14.035 def +/ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /PXBGHL+CMSY7 def +/FontName /VZKOJU+CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 0 /minus put +dup 14 /delta put +dup 18 /theta put +dup 26 /rho put +dup 33 /omega put +dup 58 /period put +dup 59 /comma put +dup 61 /slash put +dup 62 /greater put +dup 65 /A put +dup 68 /D put +dup 69 /E put +dup 71 /G put +dup 73 /I put +dup 77 /M put +dup 78 /N put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 86 /V put +dup 87 /W put +dup 97 /a put +dup 98 /b put +dup 101 /e put +dup 105 /i put +dup 106 /j put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 122 /z put +readonly def +/FontBBox{-32 -250 1048 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# +]LeVߐGoo٥\k 9Mՙ= 0)xf +1kX9JS:6V =!X>KM)9! I}HWIUcl=GeZm>nQk2=1p%R`%$]c{!W+8?v(+)0ӈ!YahtA?H @m?|M X9Հ֨#2 +:m,MZ+ǒ\Ex9Yn<Ŀ2^FC[`T+ȬD]ǸFF$oB!>;A\T hxh|5:6;ϖUǷ6~k.T*{8K`y8'dT|-QkKmy9 91|Afr (K*)%_ʬtP`.rY?nrn{v2O_5;\g>R{4_ +: 9pEz~Gu E[n窙i9ヽu#=X&>~J~ПUt0t1Cqs-b5 4AG˧OE1"?@~ +R Oԁ>XO8' IVTnP #ԫ3L3zٛoH9@uD Jsf*+5x/Jl dc!=2~S،%Wq ˒¯p sFc]@{F,̖:0 +Z^E Y;Fp'*_*C]q+1^mtv`#ԽDצ=., `CWt UbxkF㴠2VauO"-FU/IJpKZW`cpCݪ``Nm\G +pVUXYm?q jL}+:R':\Lz +ŊeY_g #g|: I {6C*}VqG()ѧ12 fF\Xn(V<˜grIpK9216Y )vXmK3p*{oav&6 .<}mi oxR,z`J!D=es\%Qu֩L߫AP[9JZ܃7 pTIEj%[?ӕ6A&Pt-#,o<8|g&"HO sɰE(\AD.%]d1>‚c@J%K_ Ts51H<Ԧ,~d((Ko9;4? 3GgF$TdE Ӻ}#mm-/\?uGd:"ђH+Tf#Tq ZL$?3-}nN} mP8sL/Pk,>Vb9 +} Hs` +kE +YYoQHvF6+^@6ޓ|h`crMQWcj?~`oMwXߓz5 +i|DQGz*6, dq(2^ux{ ؅j:<|0G݈(ιx,ZB\14+! +DÅF60Nۿc)!BæK m'b xY֞5WܹUz&̫5*fY'POĐUuky{sXDs};רsl(̤θ~oEn& Ds( Y֧Ѣwgє ay|aI +_?_2ūU}lfcya\~P2]eS-陶 9 v`XS)g*ij6VeaBV 0|^DVNYּA;uoO xyHo3÷Z 9(3S\,[BgöÍ0xGjQ(sLQApQ^@(B8Ge2'0Tjxm: ]HTfE=%_^6ҿ9TKIV(/©*i8N,|Ӧ n?nj#uJS77TTZlnf&[rzM:oA, +k"WUD.B=E +#Qzm"2v';Wu-Pml,"&LyԲ8>rOokSDamgυ_YGt"+.AkB22MtE3pɶ4J +\m'ț^6zq3U-/na:LFxr?t8H%hotW:gFq{T(.QkcQWO8(psAv%?0"4X%W,MٺA]6C42BT(w+,ʶ`b7 +̉WRa $1'Uk;+>`T؅#xG*ʈ˨9Ⱦw4nC-5ic*t"<.j9h)/o^*?8zG7⛪ȃjIr1_CoghOΛ"C HDx%: +K˞7=Y2kt > fD\`v.#`5LZ44w| m +)4URI%a1՞[-ue|iߌt'ђnL35gUE?ag-4+Lnkf +U"`HEΩ Jq~!ٜ{i upЧ?6&Ro±h6".Eм֜,fBy޾RungZc "p;sy*n ~Ay)TsjB?EfxcF knPݎkG 3>R +hhkF244[OrGM疠&'eo$#n qaF T@9}Ɣ)2Ae9VO}3T 2R9cDBU~29 w@232YWR`t\ݜY4"ŧ-6g/WoQ5el]_Ivu0 KuïsרLKgޒ AmIYI}#ʸ;EiGsZ™OV(H ++7~P}J~3 j 7K|/$)zt }a^!Jte!:/&k~<93K*udIbR^Ӡ:հМeb]$-Z;,@(هo$/!]i3X Q|t{ +9%9P0@~ +Re'ig:@?})MqBL5.=~ T[2ɡgn//oD4.(1ZoWP87l-f& 7 U/fwKF>Ƚs,ڦV)F-,^L'٬'(OGf{фr_`UNu._M)}&LEwi/ox D*/Xn5_ Zgfw*ZG",8o2wHe:yx~.yL%8T.3mQ{b]Ik5guTZYLz?=(*-xq+ iaxnm5Z6L%7lV/Knp?Hamgw]|w~PvkI5 +0k,kP6M iDj9]$H[wt>k>}]5Eʶbukd~}ƟEC œ +Nk*~T䁚Z?f9R7}#Ѱ҉I"FVJ7#|٩lJ73I+ ;Leڄx.Z IJ4FAxIM6l"!KY3е?,@P:+!.vve삝;@zə󆠽*bȡKOԱm7DH{' L#lb]VKB"WFmr`l0IMS +zrrjp ă-(by5{;҈(|z!1uw^+Ri4OƬ5P2`V +$یd.&ģs(b66;p) M謎UlZXyzO;# +@220'n3d /YyhRZ#@ޥX=USAe/~A5|K}eYMf_KDӺd*֣j.cq<,\Y?2,P(I$\'4\㟋`L yG +/'XznxTÈ_ďnWCE: u)ߎNSޝP<9* ڌgXYζ2N5VOp3BcPiq,3oIogqsW8<Ş`+w (D(\AJ7:=6h#@ŪP%.Khk f>?-/VzrFeӕP`ŧgz:YU xrp?Eit \&U>SqcuGUx2*hV9ò*ZTPy~P5ǭ8 +C=jz.pSrAUPbEMwvYc$s;}MGO,RɍfKk.ZͲ] GzR%=ތy.LH6ǁ>6Ubj>Ql_qd63 +}HЃ KrR,higQ-x!|+XZyB.8r^hڡ)}ň*UcW[Y}ab7cb ߈$qrbD6$'8+x}j3k7194Ͻ=}|BQr4fjpsXMMq[>T`T<;gug1KQjOւBW];رQ+Zz;>~S'3305X@ΖT~A݁޹l;Sx6-TY>xCS,J&v ehX-W{)&v~JZY%b^P)aZ')z&Ύ쑰&J:yǗ Q}ɵ'_b'DDb+1˜tPXzNrhC(‹5l˯9^>m^o(ǨI-*9BCL}Ov]MGI/o < /P3!o@3]`̡%Qɦģ#_RYu_&jĜρឩ K)5v[)67Riu8*3H js2ZBue!M<ި۱J%a솁@-N^!!KIJ7^|VT &OUXQ{ 8'YA3]~φ9SPy~tK^$dkXu7b+u?7>l<  C:gup*UATe-yt,ɢ{Lt[: ; DټW/J|B|==L ǡ@>r/Wc2_ZrsY :K0쎓 ǝxC2|Lu<4\gdhQ`T.HgyѤk=_sh!ߥ-o'5ZCVcAD˫bpzmg7ܺ\~E,waDK?]r]ˀ1"_EMԉW);D(5Lbc5!LV7jj/OR\~f/W*}Vƚ;uJ*]t0ޠaӦ^kث=7DroA=<`^0TA@,$ '9428;d,DuMIXC֣–i~o&'ݕig 0L()C4BD~N ` &fv$kѣCx(],?G)kI$=X40Wϋ9Xñq9٦T]Gگ"#rVl6rF& õawa]K8Fe^qqUv> "xByuzR29 M@,ăS\~oI 7ڽvS1&813M#EL œIq[Lsmw_RoxR)#w3PN*.3@k?M'~=Sz6Q0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +186 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 541 0 R +/FirstChar 14 +/LastChar 122 +/Widths 542 0 R +/BaseFont /VZKOJU+CMMI10 +/FontDescriptor 184 0 R +>> endobj +184 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /VZKOJU+CMMI10 +/ItalicAngle -14.04 +/StemV 72 +/XHeight 431 +/FontBBox [-32 -250 1048 750] +/Flags 4 +/CharSet (/delta/theta/rho/omega/period/comma/slash/greater/A/D/E/G/I/M/N/P/R/S/V/W/a/b/e/i/j/l/m/n/o/p/r/s/t/v/w/x/y/z) +/FontFile 185 0 R +>> endobj +542 0 obj +[444 0 0 0 469 0 0 0 0 0 0 0 517 0 0 0 0 0 0 622 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 278 278 0 500 778 0 0 750 0 0 828 738 0 786 0 440 0 0 0 970 803 0 642 0 759 613 0 0 583 944 0 0 0 0 0 0 0 0 0 529 429 0 0 466 0 0 0 345 412 0 298 878 600 485 503 0 451 469 361 0 485 716 572 490 465 ] +endobj +541 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 14/delta 15/.notdef 18/theta 19/.notdef 26/rho 27/.notdef 33/omega 34/.notdef 58/period/comma 60/.notdef 61/slash/greater 63/.notdef 65/A 66/.notdef 68/D/E 70/.notdef 71/G 72/.notdef 73/I 74/.notdef 77/M/N 79/.notdef 80/P 81/.notdef 82/R/S 84/.notdef 86/V/W 88/.notdef 97/a/b 99/.notdef 101/e 102/.notdef 105/i/j 107/.notdef 108/l/m/n/o/p 113/.notdef 114/r/s/t 117/.notdef 118/v/w/x/y/z 123/.notdef] +>> endobj +180 0 obj << +/Length1 1707 +/Length2 14054 +/Length3 532 +/Length 16293 +>> +stream +%!PS-AdobeFont-1.1: CMTI10 1.00B +%%CreationDate: 1992 Feb 19 19:56:16 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /VGYYJT+CMTI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 11 /ff put +dup 12 /fi put +dup 39 /quoteright put +dup 40 /parenleft put +dup 41 /parenright put +dup 44 /comma put +dup 45 /hyphen put +dup 46 /period put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +dup 56 /eight put +dup 57 /nine put +dup 58 /colon put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 113 /q put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 122 /z put +readonly def +/FontBBox{-163 -250 1146 969}readonly def +currentdict end +currentfile eexec +oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# +]LeVߐGoo٥\k 9Mՙ= 0)xf +1kX9H!.vPN 7qjj7!6CɫTw.]ʂԬ/J1]0': fqdU24tԡ?@^g+0[ +KTB/UٝFMz7 .U{7K.=UٯI C^$O7Û-tGrz J:"ia~ +T"*^MMчff0EM +z8uwi*?rw5(*5nZ٫ +4*RX&RTdRM3m ѫ& .Pd8;]F |H!%T [-͘ޞ E|pV$MU]n11RP} +d +.{IQ7^N-+C #̲]\M؅1 +pk2 +\t,o)2TTڮw}Ҏvq `;lSgs3c-h}W9;ڤ9Ö`2 ${};;m򉅘^l1'C*~O`XUn0x|cɾ'iD%WNCەU.9R*R?nLWˆs/[趡ۆ8>H@#ٻx wf} ayBR C1|P|'r,߰INJU`DkUQe ]Am\"GmFO )2rIuW\SW,'vdy]eqXH0#~Z9|pŞPOHau`Cb鬅<=?t8!-~C0VY-aht`rxK[3,f @=]wG2C#܎d5BYIWu8]o\ !~}SJZ݀$c̪OJ.k0F)L0Gɴ Mں45Ȟ1l֕(4݃h8?CL7HHǷh+ }$ DO.ZkJ[Gtכ?Tcp{nRƷWHW%8޸d +7Pep_=R(`9p++9+@dW4Å5]ĕB⯞dPkbܕ'm4vLδS*0\-JUr%'Tq~̈́\5O?ƯE6"Abe(eSd87mQX7IR*tGPz%x!vxJ+#}A|?qIHHje6h2[r"l˦1צAfZGn懗{]}%,Ɵ!@cϿi f&瀌] xRs;AZ ;S:|$8H*\Eϕ/j=F~lR!꿸dq4*x(B"ZY4RN f8XW^eńiZN'Y + :1@H9D0kq'Su|#Η<{8t؞#DfQ_4pC&D409oZBԕV4*2t +ӄ/SS뼗%ĝwhtB*mtX>aO Zbc&sYrw^&euL ( 5H$!(xJM Ply/6qc2Poi֬c)mX=^Wʓ(*cKeq^zyZ*:@w0㢇)_]?|vlIyJ;45 71:l.=cS(Cb*Y58%D<:TD$S*o=T5 L۾CӶ7;.tB]j;vUCzPaF>vb5tz7HԇU^g@& +iO{&3oʍ1j6*37A^s^P Ig06Y: ih\fojHNkͣ$ x+ X5Y)n3N +aBx̞?1"^ ȋ!# +ԡ{#U588)[IǠ_7X)n cMt##*) 6iۋۂGb*kԻQ +>+9 ג+H\o;.7`+He 'mg>".V7!=ql7ξһ>Y@P\(I1:9>Is ~ϊWuSŪ|a+₥K? 'jv6;`x(T>Ԛ6aH4 ӈ0K[ (uO\hT3^v-4@W؈qWq)'4}P;?/D-}R~ g}BVhٽǁ%#mO}6%UB#lۘT_p[M9΂MGr +g1@NF!v>LK`0%3Sy)RX0B7BK`3[eƝ{c! /T[,S QlѢ**O[, ^1T2^].[LyP-HYx3:X@>x惼Q`Ӻ~wrĵ:o0X8G9ͬb)$nW L4~T-+A@g~i Q J%|}0'AzUؼDD`I`$~t=rk鍆yl;h?rǬߓgiG)}ߝ+@cdo]  bꄆ_t0ǣ:O"9\I.l^&TB@Ȅ駐^ئ93̒6i"Sa̺1 +k$6@i0f.0=C5pbR n)@G+ooWܳɎeh5/H-|Ҙz /aۗ 9A~?f<'fKH7(@Q 6?6{L(+zDxk=aOc* mS0 +KNykHrxTc[q9%]i'ۢ R 3r#SB}ZQ6H +ћCT*BLνR$?:R*YPmyb&a(58җp1&`D+'$e( {:\.@#\Йs% u;GY% a߁G S/AUr8VRZ?TT*hVr J F0؟mɓgX9w4e+.P +L$͇}cUv?fn@SB$Nc c5$x-3,>h"1u{dxII!ݠ}A ̀ qmpT IS5Z`_H0#̅;JʘHv.TG,}H.*XiPp nM^:}if̤_OhEh>q{LYRz 8/sī9u&=J88Wo,)vL΁ ˄']^U<dk.K^}@d:sFK%+lv_WI]kc{WU%*EَG}.kAH0߾bqF)k6h!C61E3*<Y +yc$lHa>1AP%u'ezHӢOF-4toPZ܋w@L{ ˍ`biK ]z62h k.2åb ؋"!2`Ie(>95[>Ysl~:L*v{ŀxbp(o԰}(0oCasl,يXfCS}N\1~C8AY.Ft(p*5x J51Hv2 c(mAM319;vP6hC>O ⇽;+_%K`03!'#: w$1&iNN1H%~K𡜫/ԵZjj@,!H!ʁr&U0ڎe,7 d / +7!cp9 +gi2 X0c(2&M 5׮++u;6sN$_8P1Jh OJzTd.n E1^k|hvK3x'&8AT]J,x{Cv`׃PcއpȚ3Z=Ը}lUo쵉< ђTƫ$ U){X0), +0=D)7UAhU¤؁V`iT֫D> JS'@&ߨ6 YQ.sFH,(Qo>x>AuHIp7!2aT8.g{}D|qfl>ƁDw_ Z#5GZ~c%7ީZ!~a^gטH/+1}3=^1~(0{;2D6JhETclFwۓrTTWg1YyqE5a#/!Oo}0ԅR5Ʋvt@fF +0x Kq4ePQ0}G͏7!uyIGe(m?%7:ӄ}܄όL91L׊-“;eNYд[N7eׅy;=JTMaX">1WN]mtL0TBKHVbeatmr$vvGnq׫^>ƭzm,<_yk]6[5wRgldXsCCtW So9ѧ>Xo;_V7x {hL,W(R,H`M~I-dKy-BTwIfcރ-ؓulȉEXyՉ+ozP:R,# PO~h8tV~.R习 E?uA >U,0''7S臽a$3 OSlOF +ykB}L1ˏ>ʫGXIn%lCeA.(@YjFb)%,`Rۇ3lj:J@xPQ_ۮϊ5'\iEA<%=R3d߿0qѨ~KmK0!eᄃgq4: ܡ.@u%} _@|e^c|2MVDtΘ QhCk-2뮕{L % lObv>F|ݵ\R3ۇ8" $+z|--2tfunE׳w,e<0:=0(Q*|Lt.2*pS,f+%J[ˑ +d'-+1|cuz`NL EIA|A+&\}&ym<]_a0\#Y4z /k2]?i +}^/2moeuiz\9UgƊ|wmH]5#fW_D.shfۅc\e`0tlŨG.f&7EӖ :Ᏺ&_??, f<fNcDžU1H]]O=m$g0߇ @YTq\14è?}j}ünJ 0 rG fGV,Tܷk}<3Ze`osP}7N X@ge&|  nQB+t' 0 }X8Yd4L#fE9/r‹D+08,_ZQ1]QbxMSuIC/*(T &(/jjNb8U 'ShVnj[ڐ>C5h cX_H;ޠh8'Fm%݊| IÉOeZzڹ Fp=7 ΡooIɑ)-lVw ͨtU 15I+OlJULP >6еAG܈=IyF -A\g[&ѿ> +S6'0gwJͬ m yRby͹RWwx3"RX>$YOfVM}HO;sH_?~lRR'⊓Sr7oWDD_ZdO]he g@brsލYIpΘQjyshxd$')ژ6B7Qh(HAVD}tG8-BWiƖv+py7f-OxGCSU=F7jW-(" H,-mCt\[y*z7uhDGzf λÍg>%Эe5`SHmXfHb!`NjߥU,:&zR%-)⾳b"6ro_p96bN6,3($1Ѓz"dζH (2tyq {If1(}=!t.͓,kQ2]=-PjXF0çuꫀ"xaB+&1,ʚYuܸO;S@U:xާGN_ 2ѐ>l^$U~]g$i8Sțk|[2YY^2T1lԙVnszg 1BIu'g=+xhX ӒUU|ȦvC tKg,̔v+7dYG%ӀXւ΅`)*zDXQ˺^G(f5 N6i{”ÍMB3'l}67, Q9LG^/4?k{N9tBg5)S0Mq}c_yL JU9}ל +YOݙA܀K|Qc@'=ikhڬ HyĞ dE6NYwp"rAn@W(k;फ़8zev64N<#}dGIwhjrsRY4g?N9r18YBzuQa66~ ? F\:'٘^_Č_P簉NL#h#:ŀ`vPfw1xaehp3BkxzE#8s})`֚HECa 0 b8g"| 7Fyb\G*e5_g9%^AWJ]Ѷ<'6&35׵yFsJq3D&zZ%pB{P>”ѼVٙ4"VMLWc]R2БJUWKoKwS.NoGfFH+y&&d81ґm0G#f&n,Ɍ1 F{'hL߾~򯺦A.;UmngB~WH`{gPkkێb+/-)u;M @X:@ BvX=rrZItO͗M~W|28нU8BÝC (')yK@3*: ҶD1fɏdL<u9CbºCMmEJu,%MKOvF4N;1 kWE[.`-GS7/EKU Gr,*3uh|`#ZIK(56oOn\׺ uhYL<*>O]ny+$&m!xܸrN㇡[[|G-.WHD~0z"-E[huư<Œ,CeϓQu敥n`y82OekKߪ2o֙0jŠX +?ߟ7Svke,霱(̂c\BUO,׻?)r͕,a@5X*ˢL {` 7nmu=.RnMzuj!sQ4یm\DA$s\1>-%o_A^@hޕgz3./e2gNX37Zh1§{l]2ĀGXWc~aPtFNFև9 [mzl9]bDgh3^6d6C@n v~ܒ#NMg?}"&;E._/z/XYJur77v_'T-pϵIՋְ) 0nΌG:BXvE|)d_iY+賀pgo=pLbɶ24t v5C8[^C/Z;?q/AE!|\% Rw0{\i(|5SFos55gCżR*܂v|ANrO-;sнrrL[[v.AP\}8\ \|OTGǖ9e7gt9 +d9X^aw.4$-P{[%ff3z)}iL6zc?:|:C-Ju2;%P)ag +qie3,UT_!O$!4jgPB&a=k_k+8xd , j|? %Qi`P : m8cA Mv2O@-iz y'& 7 n +rPu3O>B$@CA$*0+;"vw1nD<ۣ9RZYC{e>uXYQcwϯn'dүLQ_ܠحHk~1?IJ}kx+ۆKLC(K+Bg\e ɽj.9)y7@l֣7T䣉V|p:}\8f:ؾ@;T@QnMS@{;WrN,>"C*]1iӄ|XpE% lA(Ez)Urh=66'l6[4.ctq6vfwGoq +3h6o ns.##{>M%&|Ÿ\8;@P@8$Cr?Fol|+YO%(RV/Qkҁ,* ;e\K=.b&+lt8EnTMQIzXLjGS;I\@W. g4^pw|YKF"N&)G1hq`N(Y}ڀ+wM?Po]{&2qR(5ZIp"yvSDmh{RL.kSꄍWe8z m) 0*Lc-/x4|m'*]"\d#ay2i1h#ugHd^v$HMHx8u/44{Xm:!S噓yOt^oT,mBzi! D[@Ls+-pZt}4ܪL^"MrgH+[E ]yƒ=JdQt >'Gv@=ټKex! 1սkxh + +e%rsp{<&6K羒x$k tA~j3p8" -4eFMӆ*;#?HnpoOq:y Y9,z9A{}V(N;O$ƈl,$Ʉ$ծׂkM%^4VPόĉfm!ty]6H8ܔN Ddv"CO]]dPlWtLPp\rP4҈2vA (ɓ_M{9~3xrR9Fgܙ3q5gvR.zQ6>KVfcKٍB6TIN% /\97[ꄼM8e"|$ѫ6zxL16J2}p_yW9ryr+k@i=׸HQO2'G[S~ΫOn% wTS̗": %GS03(OhӜAO'҅ }Mސu)曜^2=+g":cڎeYnIS v(7(IUBfv`Np+% 5\O < $f +l,ƴA[Ȧj)d6D#]<1O&v'^৅p 0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +181 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 543 0 R +/FirstChar 11 +/LastChar 122 +/Widths 544 0 R +/BaseFont /VGYYJT+CMTI10 +/FontDescriptor 179 0 R +>> endobj +179 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /VGYYJT+CMTI10 +/ItalicAngle -14.04 +/StemV 68 +/XHeight 431 +/FontBBox [-163 -250 1146 969] +/Flags 4 +/CharSet (/ff/fi/quoteright/parenleft/parenright/comma/hyphen/period/one/two/three/four/five/eight/nine/colon/A/B/C/D/E/F/G/H/I/K/L/M/N/O/P/R/S/T/U/V/W/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z) +/FontFile 180 0 R +>> endobj +544 0 obj +[613 562 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 307 409 409 0 0 307 358 307 0 0 511 511 511 511 511 0 0 511 511 307 0 0 0 0 0 0 743 704 716 755 678 653 774 743 386 0 769 627 897 743 767 678 0 729 562 716 743 743 999 0 0 0 0 0 0 0 0 0 511 460 460 511 460 307 460 511 307 307 460 256 818 562 511 511 460 422 409 332 537 460 664 464 486 409 ] +endobj +543 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 11/ff/fi 13/.notdef 39/quoteright/parenleft/parenright 42/.notdef 44/comma/hyphen/period 47/.notdef 49/one/two/three/four/five 54/.notdef 56/eight/nine/colon 59/.notdef 65/A/B/C/D/E/F/G/H/I 74/.notdef 75/K/L/M/N/O/P 81/.notdef 82/R/S/T/U/V/W 88/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 123/.notdef] +>> endobj +146 0 obj << +/Length1 1468 +/Length2 9742 +/Length3 532 +/Length 11742 +>> +stream +%!PS-AdobeFont-1.1: CMBX10 1.00B +%%CreationDate: 1992 Feb 19 19:54:06 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /BNDSDG+CMBX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 12 /fi put +dup 45 /hyphen put +dup 46 /period put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +dup 54 /six put +dup 55 /seven put +dup 57 /nine put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 79 /O put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 85 /U put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 105 /i put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +readonly def +/FontBBox{-301 -250 1164 946}readonly def +currentdict end +currentfile eexec +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou_cst ?}ߴ7-95†笟M/Z+FCxw\#㺴DɫN^?0^~o&fZ9-(*ϟVV9 +|J7@s.$DFYMi+M즒DSW['1qy4qZ;]6y@F< +V&N3n]Db a[sK kԃ9$[F=e,&Ȩ)uv1DVIjaIç# +5k~QaMjFJL3.0lVem; YnⱪyRyh$&'gYx Qi- o 7kacg92X3]*#5sJ^fXגbA>!đkLa\wi\p d³JKWpt+2~-OC=<ߨ7H'4FDS٤d4isCD3M`=eO7mfz~6H36&UԍPց(5ۍX.:|[H"ɂ7SyZ?actS[lDA\t966an,2A?":6ߙ7xH/5e=v es% .,?RIGM< ,9M&^;mN`0\@'tM@/f+d)9*CSeE-&bqPQxVyï^>Ye['@O&IӁ7_yջ19qxavʶD\BhI.fN2iRC 05H-Ga/qB_7Ue>h];[MgaJ>?-.}6 + P^$0 +>B}|CR;0̦Fh2ie(I:CxVtgoqǙL6n zrWV_2;L6쥉\ؗ~=ViswķWEd21gxC<%JeG@>O@DYW:SL≖d}/F⋙j$˚ ԗ8SQ +Idl +FU"-EI\]T;/nǕ!b#i`XcqlOl!켷M!Mc98ub@ ;Fc"Y_HkhA˧A( 0Uة}d+IoQwe`",*ڕ%oi",G#pyVT@"]Kփ0Myuhv㞻|e 0 ixy./;/c$~qGME(_k-12tY|B Ztsss=n^ܘS -u]ߓn @&xwŃL8ֆe;o9S:P.dBz_UT*|ǼU:*3HP`)՟^PebTV)>6%rG֔{{3c )6[e)^\d7zm8Ue's$eT0ْKɩrQ!Jjٔs9AN t_fፗ4@߷$abLS+H`0 + Evv̽Vh><`nD4g^óxw«| ' =;h T6qu:6P0j.6efׇɊyir7[srHexY@7܃֚)H]0&&[ `~@#(펡r+HO;"u]lIEhg$a$vϕyjDo!%uO1L$~_[!W|w;\sM^}&tz5LOy߽=#)FhuƄY?Ӏ%f.=){jX^jc37C1osN޹Ø};i:ix"kiEOIa7fzE yd,ߎfD\4Q+eW_3<$ eoE pk^`oVT}ӹؐ&@s乧 / G2٠`Y g繅 $2L( {IR:/IlKDNtNJ=> ۙbPR+SzڛU57|׿-}elvs]౯f%Kvր9 !f07=>RPYčYţ۟#d`3#dE]4`xe%U[9U=uTHG`q45[X4Izx,[qzfz̑[j g6*Ы5>3m_ǿ,12 y8F̠;L *A Yd҂7w2PbvSV,;Ƙ5_R dS)'$M p(ɭ<\ AM}zT:YoL!S6["R4N=&ǹҨ S~E? IcECנ臯yH0"j&kN?RG%%3YŌh~Roܿ)̀X +-݀_`5§(0xegQ5w)V-.)HsI8(@ `C2Վsᴢǎ‰^Y鉨 ;?E̓jFqvuų 9(!yl<FUd9I,#tvRXoʬ +?3 afSԪѨ;_рvo99Th7} ۲B]GJaa[}""qJsӁ|dC,Aa:Owau+™ Vc ]^W =J?!Bu1;C}n9-֟ӴCr##Bf/]\ &ƚ,Y!~@9P\0܇Y0,gX5;WmD kF3 *Lx _ =AQ N[wUu|:+]VDI`5k8"3pt1hgŰ첺Im'Z;|S)o,OSZIQ0HDDPhKqYa#ZUyL{.ro}ʿnuW?gMie.\Ml')/HXqȫ55^紥d}b%!0\6k e,Dδ}nvA^ѽuA/~ +'Mjr.jU0}M4>d8\Ƣp@ʨ+=MxLSD= oaFtrln+GJMi>F >X}GLMr5K=%ZIl YEn(FP۠:{P/қ>{YfMW_Fڄ_=}d)AfFpD^;s wt9ߥ2H\o~czT;8NX,^b\aN195Ndo|N͔J%0,A\Jw8˹N'r@#dLeMrk[k`xX4r~P}nU:X$8RZg7}!$ipN!^GM`ao wdD~ \$|SŠX (` MԷRͯE6y@+.ĜxV /ӄѸ/DF/2nz= i &}҄ڈ*cUbBͰ8Acymg'MDywHhvY2+h8jgePz\4+Ug<;"%B2$}nޤcs0X`NV-BGkZHHT%`86JqX2oΙr.۴q +G| #FCJ*fwm鋁qi:i@(Ѹ5.d\K=ˤ1l܉v X%nþdP rZM`Avb>Wݳ5/K`5Wv0.L3YWO@cv +m`4XIq&yaVR;twrgϪ` LW&99/GA똍ףnӬL, ` oߊk:ZlÔl@Pڀ +]|X0|WsT#^:=v~53G؝OՀJeʄ'&O'^ƫt('JR +LEr"n\)8Q$JDǢeҸڳ=1+װC:x*j.N۰Rh,p*ܘ1]Ic낙ΏmTZo}Ǩ?YXfвct/Zrs(1q$VIpzY +'o%{5^Z<^8(}n1gdnJ0#z{Q d>Njeyt0܊V+l8Ox$S$!X'P#QSqiucz["7]/u!vUZYqa{!VmS/%%腏^|:L(v/w0/4 ,%?r\Gsr"_yLMF3-RopngTa ý:&yt>F])460^W^4OJ-5('hS@mz! 9oFde?XҴQ1 4/SPQ G=_[*Dsk]z%6ؑ $ziޠSJ]Lc5B V@vk% J.:fL*5PYƗb%Bd:k0._lG:hN-Cڃ^0[@zHFѮ C+Ho|-Oњxn׌>1n\M-Z9l6s鵔K͵,\{Õ3j  +&q բl;EaBm @)*93Cu_M-|ެt@B)`l:RV!`N +ޞ%咯lo{PEqv_U6WRAX|4jd 2)I96&b#,[nҵe9;ES Tp4b{Ĥm02@no)ZtJBkҭ†c!58z[G K +¶aw*P0{g\שl:lq*G}!âqΏ|q[؇9Hix=dVd vֽY%({f" ςګ/0CzFo5Zث^f=gkwP-ss=V~GEm58:a +YA?DȂ!iHa)ݿw$=a[ ^?$nf5.l$߉[ 8[5a!q~LGԑ;K3"Qh/YtO[ -rճ1 L.LXiti)\;rs.!:Uš]]={!AB$nZe`+ ZҪՙM]q!8KJ8V['n@Bdw4.,ܑp$`@ޤN Gms 5[E|q8JXt[xoNT.< +))o +-;9ǂM :\`Uvz5AVsP2%]p?wj 8;'be2[k?/Z~̥n>Lk)> C)eg_`AE-Q5TssŞ7ch3DKhJ*ȾL> a Js`wv2)a+47St4bS(i$"Z1!XǞF4mG&K'/hv${?tI]DI?-ρ.z_T$oVN71G_>wLDsY-v1&[1"s>ћ6f+TQ@e#RPHL᠛zIN[H#*>Aʒ3_9(7EQ.(\}6}S|ckqFomL*6 ' i\ Tסԕii1t8\%ĭ®U:m2iDZ[zl0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +147 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 545 0 R +/FirstChar 12 +/LastChar 119 +/Widths 546 0 R +/BaseFont /BNDSDG+CMBX10 +/FontDescriptor 145 0 R +>> endobj +145 0 obj << +/Ascent 694 +/CapHeight 686 +/Descent -194 +/FontName /BNDSDG+CMBX10 +/ItalicAngle 0 +/StemV 114 +/XHeight 444 +/FontBBox [-301 -250 1164 946] +/Flags 4 +/CharSet (/fi/hyphen/period/zero/one/two/three/four/five/six/seven/nine/A/B/C/D/E/F/G/H/I/K/L/M/O/P/R/S/U/a/b/c/d/e/f/g/i/k/l/m/n/o/p/r/s/t/u/v/w) +/FontFile 146 0 R +>> endobj +546 0 obj +[639 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 383 319 0 575 575 575 575 575 575 575 575 0 575 0 0 0 0 0 0 0 869 818 831 882 756 724 904 900 436 0 901 692 1092 0 864 786 0 862 639 0 885 0 0 0 0 0 0 0 0 0 0 0 559 639 511 639 527 351 575 0 319 0 607 319 958 639 575 639 0 474 454 447 639 607 831 ] +endobj +545 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 12/fi 13/.notdef 45/hyphen/period 47/.notdef 48/zero/one/two/three/four/five/six/seven 56/.notdef 57/nine 58/.notdef 65/A/B/C/D/E/F/G/H/I 74/.notdef 75/K/L/M 78/.notdef 79/O/P 81/.notdef 82/R/S 84/.notdef 85/U 86/.notdef 97/a/b/c/d/e/f/g 104/.notdef 105/i 106/.notdef 107/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w 120/.notdef] +>> endobj +133 0 obj << +/Length1 1432 +/Length2 8170 +/Length3 532 +/Length 10134 +>> +stream +%!PS-AdobeFont-1.1: CMCSC10 1.0 +%%CreationDate: 1991 Aug 18 17:46:49 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMCSC10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /JDNYRG+CMCSC10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 39 /quoteright put +dup 40 /parenleft put +dup 45 /hyphen put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +dup 54 /six put +dup 55 /seven put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 71 /G put +dup 73 /I put +dup 76 /L put +dup 77 /M put +dup 79 /O put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 85 /U put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 121 /y put +readonly def +/FontBBox{14 -250 1077 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# +]LeVߐGoo٥\k 9Mՙ= 0)xf +0v7ϱ9 àE(O&k{ǛHFſꇼw +R^q&AԛhF8N&{oi(^[ol W%'5,.V!0&u%ˎKxZ4pX:;[4+ @c +ߌ +}s$)PͶ'/CզxBCxSƫE\ 'MXpͰԁ C q6 2T1e|jԲH*} t.-"k5,h:J.X 4Z@0v)FEʫ@"jKNJrYDdcm!G~,f\HAӮhcc>SK}pkkRX>LfU8dWNb䊌b ?g~8o|R<)C쩔fxgm.sAQjEbp]ly''͔Ϟ[tVt{`z +D$V{ EV|4-<G"퓾.?ךe\^/fWn8Yzs=p2΀.1pTxK(ۤc ]?ٷcP'eOz?.ǴB5ҙoScfaK1k;G/{b28m u- VG?DpB4HvG}hUƜonɎz Ϟɵfv.Y83 w._n=m8ջ̒J2-oјx w.%(7䔛ųZXT4 Vr|1_ &B(E:'N@uuݰ_̱+DƅhYD{֮1D`'hyzE;W +zx))?IwuϻRG924ďk|^qeE_idwt䀓w{ + D17h""JŐ" !Ӣ`>J^UEpX gU)S&%]fsJ]筷bŇ;_/ɡ@2詟LtK=Wi(D/cv+m) l_8 + + ҢaYu1ĸQȔ25ޛDzLSEMr0$[/zTȈ Ib {og;n":")[hHwvGWxBxBѷ&+ ƻPdaUc:q=q)Ү^:CnuEg1\Dce` C| oV`w'chPՀڈܔ+~8$9XDcV衙WpF{[یR۠rܑw0ԠϒxcuQm#twjd, (LvɏTzGXt csWZOi}po?x{g#|!]wpݛd 1NHK}ԨaT}{zd\n2D Wx>(C\vLG:ΐ^ zt8,f)s,zvqRy)㏿}]?Tmܾ- OOWsЂ*]lL}7C +8SWHA{Κ\S% ~~xL4^"2çq>9+\݈ .)VjZ耕 3ృΟ0թxD*{= ZmHQuA#eReu~X%bf*K'c$:*}. &)wG8aP+-(C|]" c+[ H`eI ṁ$Lxlc17-PY #{0J\"6 +κ=ӈй2VZc}d<8,e u|ˁ(ǟO5>NIۺ1 cb"4f 7'ɳE=T96ܮl:lt&9q5j*O 춇IG#n.=elT_cQFCYK^=OF"Y!yM'}T:P j)N]xhu"-b7 +7d4WmIh;eU"ٝsGɘ +͜bb@ +kZ6Z3l-BV6~_c( ώ1l+r*NzX!mW邏L-}:3xa攎? (dy2U!L-:NW [c|HcC`q& qԅì9=w6 +0%j g/Q%]4e4p?s' 6@pņHto+rݗY  +~h qRa ,:}Az=kYB>—DXV@qlK2Kτ%wlzZ :X,y'Xşa.'mDTq{/0P}t0>V[5\l"3"eOO 9qj:y!l]Aݗ!Qa"d[|Kƍ'``dW2/ՈAqs*"4w ҁUS e&(ʀEۥ~kZU!k`d +۷la, %hn Arla_\1' h<_fjߔ}u N{Gg ٕtvk( ?ŧcfOF :Ww8doNVhkC9?ݠtԡd7ʎL!!dbP=Wl! +5&/(қxR:y,x=uyxI{LJ0 ٦1-9372 +֡wyuޗxc_<%+p/f ɭU3Zقe ]b +}p Ne2 AluѺ.wE EJVĭaǑh~-Y|. 5 XbXt{woVEf!OWO}ێwagg2@p譸@7&=ήK4]7܋>ؗשI  ٵԭN^(>E52}n(Xy-kD2 gjݟgO[Ls8ksZT>c#=Ws`;9P˾r3NjĿ&wS` fҴ FBupb:'8oUH'i vz .[2GSNN?K8"@9tV +JZŭ>q0ը1,A;A +gHѱ6ƂQr)UFN+VȗbvMm2*xbB( xOTƟvhmkV;o +((lDh.Lx8)e҂W\GJkr{੡Ȳrg=B%aث]LɃzLAg0-͠R0Į罼pRX>3X%FlP\^DScqzUٟbˋsXQYAn PH?/RpI>V&lU `[McaA{LQ課6XJ(r"#(OU%tqX ](5,8ns1MC@ &WTY_UdnؼTn9Umq,&|B0]M\pQY w*2}ę0X2DhaCmA؁߸? +:{n51`KZ +\k=@ROC5nfcPn`EZZGD&/n`ۥs+4YӸU@sP.bPNcJ>~h爼͚YI9#oY ,&T^yl.WP0E#TݼEsT"K04-wbJ9d~>vZ>OI奓Wn,zU!j%͚XkiI%>dCu(dʛߏe wJ^gH|X wsj.3[uMVtn6=`{zlt9 OOwE~RrA/(X @w[?ZC,Z(Aw(LP0ȻNliVR\Z{#[x%՜)$* Gu3Iv+L 2ЙU 0-P+ +'j-Cs$SW`ʹ'"l0g w'Ȟ8Eݏ1J6!-xY?u!mab/<@-9)nq^4U!r*-!#O5yd}pv[z*eK՗FA!+ zo}P:jz<6Cʹ?%WKLJ]fTe]*"bCDp~PQi\ևv=y6s + +'ZE מYfDB/oHx~Dz%)wUq;ynKs3tfe2*"Sgz=$5İ,Xcˤʁ SL{g}K|Wg6iOD1 Tᕿn@&Z>4{%ɶጾtE:@ȇ,NP!y5bq4.} +'!4JL`$",l2n6>d{N5&tURT=O=hb0C.`P(e$^c} Jo3ePݾA}M]g#l?8/G "qD2п&N`͎NѼrji='"+jO],VK8VOw)f<۟>?'މkm'uhpC]ݳ +:X0$hVb ҅r4C|Ovn.-nw і +a}}ǍIfNC +ϳ6}m0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +134 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 547 0 R +/FirstChar 39 +/LastChar 121 +/Widths 548 0 R +/BaseFont /JDNYRG+CMCSC10 +/FontDescriptor 132 0 R +>> endobj +132 0 obj << +/Ascent 514 +/CapHeight 683 +/Descent 0 +/FontName /JDNYRG+CMCSC10 +/ItalicAngle 0 +/StemV 72 +/XHeight 431 +/FontBBox [14 -250 1077 750] +/Flags 4 +/CharSet (/quoteright/parenleft/hyphen/one/two/three/four/five/six/seven/A/B/C/D/E/G/I/L/M/O/P/R/S/U/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/r/s/t/u/v/w/y) +/FontFile 133 0 R +>> endobj +548 0 obj +[319 436 0 0 0 0 378 0 0 0 553 553 553 553 553 553 553 0 0 0 0 0 0 0 0 0 814 771 786 829 742 0 851 0 406 0 0 683 989 0 844 742 0 800 611 0 814 0 0 0 0 0 0 0 0 0 0 0 613 580 591 624 558 536 641 613 302 0 636 513 747 613 636 558 0 602 458 591 613 613 836 0 613 ] +endobj +547 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 39/quoteright/parenleft 41/.notdef 45/hyphen 46/.notdef 49/one/two/three/four/five/six/seven 56/.notdef 65/A/B/C/D/E 70/.notdef 71/G 72/.notdef 73/I 74/.notdef 76/L/M 78/.notdef 79/O/P 81/.notdef 82/R/S 84/.notdef 85/U 86/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 107/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w 120/.notdef 121/y 122/.notdef] +>> endobj +130 0 obj << +/Length1 2138 +/Length2 15267 +/Length3 532 +/Length 17937 +>> +stream +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /SWEJWD+CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 11 /ff put +dup 12 /fi put +dup 13 /fl put +dup 14 /ffi put +dup 20 /caron put +dup 33 /exclam put +dup 34 /quotedblright put +dup 39 /quoteright put +dup 40 /parenleft put +dup 41 /parenright put +dup 43 /plus put +dup 44 /comma put +dup 45 /hyphen put +dup 46 /period put +dup 47 /slash put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +dup 54 /six put +dup 55 /seven put +dup 56 /eight put +dup 57 /nine put +dup 58 /colon put +dup 59 /semicolon put +dup 61 /equal put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 88 /X put +dup 89 /Y put +dup 91 /bracketleft put +dup 92 /quotedblleft put +dup 93 /bracketright put +dup 96 /quoteleft put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 113 /q put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 122 /z put +dup 123 /endash put +dup 124 /emdash put +dup 126 /tilde put +dup 127 /dieresis put readonly def -/FontBBox{-15 -951 1252 782}readonly def +/FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec -oc;j~EЪ/ ȭX~id}S5Q!gtⵎkJc;rN^X5.Sy +'IqV:r㚉#,# dBZ *R*"7٨yQIeύrZp(IJ8#+P.ղNC; +[i-{')/Pph QC -AȜ;k5,4Cof^^ "XWeBL'>@{.'b[>PP.DW,={ #VX6nzT`qN&=`~+GH c%=TF{v/҄fwsj j-${fwkxze4G$JB%p"&g4BW[x-n)ǡ~('?CE-QeSO9sY=`lz%i$/neu*TVyBܡ mM/|8ySx{+˄sߨ39Ӟ:QXE':c *ȝ?/vwC'kH +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\c3R*R?쨤ȯ@ gSr RIzE_EMv,X!%6]ަ_3+_hJإ0o'z 9K$|tV\)Z! j#ZŚz1UA~ +"p?{u@]A}s +ijB)~Ob {z;O9mT[Ğ^dUl$Wh: ?Ƃ(r6;Bt6cFCr$/;!,KqLeWuG h7IQ[u20uZ8*#qP|̖I̓pe}#YۇW{ +Hs(}CE c;[e/SmV& +i2ǡmc\0kC'sp)X0@$2jOGG9%fLJD@m2b5\cdy!iz+lxa+2S@uIY5F>qgROEowK*;/sDGǡx=>J ujLDfdžk4ؐ. +vî|1wm% QiwXDN}}x|E.gK{ T >k&յ2Ҡ^Sg,m1"7CS-ƶkDD K-syRb1ȧ!j h OVk!JEJcуvӘDI6%;>fA/j2C?)hל':QS¿j"D9JI9cA<)3k!̰#pZx7cT6]tN7[T렍(W $a8|Gsaw%e;'s]6|Ǔ7!ib_,{d)>Cow<]=(d<%! %zP圯ٝ ~ELFM]#9yzFpU9n6Pn&([,ne$Ɂ<l&&9?1{3OQC3/Ly&$O/By_\)GK\bi1!|Ԁ9`)'grKU9Ӛ8 #1[ߨ DP%<6֠)#K @"H>}Xbg* ft uac@f QgQADW* +T q^A]JFr49{)C bY/*8 :ywXR[]lWU s? R1GrNs 5W#oXʎZm3.@& |48XKP~02]]1Zaz !zWzFFѼji_Zg֙(弭TSh({׸'&Œ҈$k5w4PvR.',:d4> }5[Uc1gZVw0 80O +jV-0#'lYMYo#{N +8k>;w}(x>EW,(HH=+RbaHʧE'F{!괐kI2Ľ@Z:l%&#։cf5mqbfzITб'FV#鶡!((x\&7h>EPd5#S*䰋IBhCDBC6eb/x;J(M vIdv0_$ c"U9KE!S~:N$Y=e5kΜUhƢW`6#"aT8=a4El62"Aw>TO2hH(1Ӟ(4kO!њ]rhۆ`\@SMJ'Nl + o֗|%mvߘ];tŶwTbb HtLIᅸ G\v`yrvW$J Zj%--<0:x,Q\"Oc+gwpwO#~ˆ:> Q99Aުۊd #te/Mru܂0g6t?d2WOp[) z}- C*EBFaf](h$ ɰH%U1X^QmKQ(6j^RĿɭV$a5\3MpX!WݜEk,1}wJՠl$J4#ua8'sheN@@#lmaqE0<-|NxE#YAoNp[_)g3"g=rNЄ >2D RǴv' hslF./5YLoF+=7uI< ZuV&hi\fqa^84Y3ݍ'F&L2S={ ._~f4s~35⺩s8F) 4$ tf@*R"K ~i;Tq|oWm +owmsfn0\RU͒* ~{x*o0z9KA5sF`X+0g3_entMbuA3 +TŴ /3㕻>*Fa5"˭(t/Nhj5٣}EaѐEOuv:Ͷg`LK@m3-%#n Hmp,vRM?  Z|9 Ԫ6 +恜u\dE4Bl:6A$ބM{>JHҒ6J4LT*GylM1zWWqhG#1NB!wA  @ՑW2GK,?AŖkę+EPXxpL^b @3 f*)u&|:1ClŜ4"Ttݴa{ܘx3$[ +6  9odWng>Igz# B,*JJ] b-xwvqD~F +>QMq>րMOiiN}O?s2J+(p*$T 0\cb0=;Ϙq; '$.JS('O--^j + $3g?}8ᆘ[\^)~VcH4s7bU{MۗXЇus1=WEw ?/Rp?|l~]D=V[KZp&N݂b"l=TT˼`|Q#mU8zѱM"? +_Y?ʤ19 6+?]G(Uhp&.4!H̞$Q'>rhDPgs',UF0T;Z^!+"]WɖP2JoIr,?!2h#04ˌ >(ͅe&vzesQ#Z ]ͻ8 Vƿ.:`paisf/cj_(T[NMir}Obe,OɥҜoh經F;3 bƾ/զm$RЭ,K=} #[SDFKStl#j#6,~:V kU> B](r@qeB\ZY\`הUNx*rczlC^r]Gƛ=[Mް)gd-$XT jdH0:1| si6ЧXxѶ5~0n1Bzmہo`[b: *6CIԕnz$:]SEJ?HsO1HV>6=M5Bҽ4'k|30zOfN]SrBZKPvcc+%[P9Ԕ0Ӽ LV`U*zH0OâH/|?Am\n<5Aоw +%g8IX%__ +:fdhߑ*RNpw+dJd[)KZ%2U3FA~♼vQ{9}*dTΔ=rv8.G4" 6/AĨ93,2|>a$s9Ս j[&lZ Q൑ 4*h$˓醜~=|dsuφs]M?pm<5aK)EOːT6c+O='{4Ы`c6Ƅ(f2eV(/n>,B-DjWB@ +z'RqZAz!WP%R쾐'{RVP9X6c]CؘМ|chz(0wvvدYyЪp#:<ފvO% @hߍi܍wI,*bx\I PjFo{㼐{lĥDK> ZtR:\Sم(d1*,= pWM vkr QNIas-/a'kLU=s{+L4Qy"Ν;!D[ x˨Z=B#(>sCs3NQܧ%aRLc +7~򩏇\45浃Lt Oh$.arY7ۣnC[/ִbd$C֨LB&hӞXo+`p<⢚M'{KHP}[ϷΡX2f^סE:B0~7.YExgi=d8.H +r8yɃ< j,Hvm.< +<=k-bSEDT9jb?l^ڏ8⋶cgEx:MPO;z6M +lJt TYu۽LBCJ&) tJ6L:s`(HDH;*5/B_h7AP Jw=iy=c,rKc@6 +Jܺrݺ.<7*ܳWi<:m1FGbC{*e0R_;2N08?eUZdЧ;sl-%L,3Jв.qRէ<~T8>1rK4aCtN gP-ZU7|N\BAEz!U9v RjD8Ž@6'g4Oʶnjq?ga>**ˆbm"`DtS'c] +<SA cxG]Zik4PX̦ۍ? + +cq5Ac]5IvCRD\J>8 ^qrw4:3q*+37<^+K55?^W¯2ēWTkZY 2X3RIbl˟QB+8^ɽʓ8[e?ӡsrj87|#GcGx' 9\]h +Jvy g+5i'L&D2A|brJ{b6?Md#҂@t[f>K䇛d;&0Lȥ&oe`#@5'9 +{ ޕ5o>ܲ/Kw)1NIN'8Ԅ"VDbO&`HE|429v$\E_>@r#-~Ml2qbZf`1u!LSplR{SlyȬhP)ew誏άCGkضmAt8gC͌=TQ&tF1lc Y=k<2F'RĀb1*{ +VuI=cVtC~JLG&o_R6jct( o@!jWO@>6u{:@(6.|b0G1Ϗ+=dYӖ^tj&׊ؒ]˸ꆆ‹;uxJd'o2~] c,'ݙdlQرqogP) +ҋˎeF1C GRL.ON23e:4O@]'13i(.(RT`Ŧ;8mќg2΢ @pRt}1[ڮ(':uZi,OZtngP̉+_DEj륅𢦱y׹c w;ɗ籽"S7jxq|3%ٮRaүtǮqYBXpʙL-{lq!}}m_ۗ/@|Y[е47 K $r__z`4ѺN)#l2>$U|SEkd@t7Y+1%N f)əvS2H淵 +Uw|dU̓hXRp)[7F[}~71k;n?J$,y-]1qɶ?qh9xp;H}t԰IIo'lFN/d^Ƽd)NE<}Zҧ[࠳0U^d]; cG/!/7 C!RdN`F[35 :|m\C# LtgىTimK*h[reBd,Iכ N7&Na +Υ2ۀZ +,CQד}H;{&l^v}̏YMJzEg*]Jز X}<^H.8=rr.V]w;W1Cs`'w䡀>[sI z&CYF=EǀeXWna.#pͤ %8`ıOUc7EFkϿk2C-st>cSW?QՆj؆ fbl6!~GfL:-^IKV rB0z"8 i*3Äg* W7#e0O&}r[$#Hhc(GpeƓ^67ST}Tɕ#c I?8w9SA{!\V%+OI)܏T3Sz bd/8ͤ|m̚ҝL 3K(I>U2ӝj21M %V`F=́`tV +K^ޅ)P7B=R@WϽx}Y1sBh ^朂nl%δCs]Qj̎ ٺuơ]EuF yݮ3z6](Iafx':׫d@ +)`uAks2j"S[wg#A@РGunb.=`Yn֎΀vλ t/R=,niaO(Ě+Cx`hߺobn2iqbD?"x}iV/.oYn#1؆[^!> _ ^FƉg],ƽMMqWzfIM3>Zum̑)isv +&ѰvP<+ e6<ژѪ=I%Xp`)\B0 ch- Ȋ|VDP(A OX&iԗ?SEr&4Ph1Kh ѬgЉXVoB#ŵpTO0k,g])3z6tȈnj&!Y\*R9*)},ZuqKz0죢A!{g.ڈBJIlmenY1&;yj1mФެYڌ5%lz,i`^ +!4\.:OgC)N&fZLevZmsL vW_2!RS@te}d>ְxw4qc*#)ݦ 8 v^'>L2hx`~S0?<(dv hj$sĝ3dERׁmZ6z.}w7p 0XڭtDqLU"3 +=:.;eP!g6wn A;)Q%::-FEW<:=il J$SVN#˄4Ħ6X˲RQU E$b)e#Z + +DR B2y6_<~ n‰/3cOl ?xJ,-Ԩ6'KVO-l~$/NĔNcF&]Z2iGzv 3kM诩 jD\Pݨ P@UxwD *Q,2ҌҠfLȒHx,T {Ę}c[n˄%;+TXzOpQϖ'BʘɫĠ5d8ų}:@*7"ݑ3 ,E,yC:क़ZlI+*0G#R?H S@,ošdD*(7T?KyA7&K^ <.H·v%kM@4aM?)wc^u +*cȌv({W@iUY-JbCݕvhh֨>)z Kdxg>%]2`#;IRQ\Tte v-nV掟Pw!@Wp$& L~yṭh-$p/GObRGZG/MC<%b=3 *nHؾN_Ԓtdp#ityOG^*E,umDs|RyR!>! k2a E\(4h9&x{XHTjvG?П*Z fɎř3%ZWH h~',UM[lsZunB;t +xnH}Abk)5$ݘ>WzrÛX@yB1ZI{mBS(cDq# _w!'k%+ف׻r|k^< B5:(b^!{9'yauGW\ +pY3xD-Pd)^5Z/ok':CU+*Ӟ֐*ٯsEMs>e2ңrrx,ވE0E8ƎP75mʜ#)ruGMMUXդ#o*-Yc1&";h'JkA$ RG6FM3G(`Az|=\Vʪhm0-eG3.=lcli>}T&LQ ,gnp ^mdF6 ; /ĹlT+M/OG% JcG +y"7Gop;wndmjR>y^4o8z\1R<uz.0[ H4/ A'Uk>ذ K"oQ_dB')0*71N?Bᜍ&݉45VæK { (X K7[ ]S}ļ?ea|9x&T1Zpn,ٞBo ԓqZ?HZĨQѱ[jL3q2`'q/[E@(2-@^}wZj'5avګ @zu3YW>wkRXo"l2%:12p=E$ߒ"-ڛ#`D["=MS0"K3w>@kjaiTV^|])nms +[wFPwQ WnĬy G4GgHDN:Ax?y +_RPc f:_WLH|MDouͤЬeQ˶9Cmո7d{C#WS<Ǩ]ʤ!lٕn .jo?LbO}-n$9ӍjaЌPaOΉ}Vux8 woC0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -530 0 obj << -/Type /FontDescriptor -/FontName /PXBGHL+CMSY7 -/Flags 4 -/FontBBox [-15 -951 1252 782] -/Ascent 750 +131 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 549 0 R +/FirstChar 11 +/LastChar 127 +/Widths 550 0 R +/BaseFont /SWEJWD+CMR10 +/FontDescriptor 129 0 R +>> endobj +129 0 obj << +/Ascent 694 /CapHeight 683 /Descent -194 -/ItalicAngle -14 -/StemV 93 +/FontName /SWEJWD+CMR10 +/ItalicAngle 0 +/StemV 69 /XHeight 431 -/CharSet (/minus) -/FontFile 529 0 R +/FontBBox [-251 -250 1009 969] +/Flags 4 +/CharSet (/ff/fi/fl/ffi/caron/exclam/quotedblright/quoteright/parenleft/parenright/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/equal/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/R/S/T/U/V/W/X/Y/bracketleft/quotedblleft/bracketright/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/tilde/dieresis) +/FontFile 130 0 R >> endobj -531 0 obj << -/Length1 765 -/Length2 745 -/Length3 0 -/Length 1510 ->> -stream -%!PS-AdobeFont-1.1: CMSY8 1.0 -%%CreationDate: 1991 Aug 15 07:22:10 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMSY8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.035 def -/isFixedPitch false def -end readonly def -/FontName /VOEFGO+CMSY8 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 0 /minus put -dup 2 /multiply put -readonly def -/FontBBox{-30 -955 1185 779}readonly def -currentdict end -currentfile eexec -oc;j~EЪ/ ȭX~id}S5Q!gtⵎkJc;rN^X5.Sy +'IqV:r㚉#,# dBZ *R*"7٨y! [R߻*|]~[C֨a[#ԙ jY!4J"3&ejc\J$2626wIaUIrnFB/Г(Hp%#O.,snݸt%\b9?_\ <+n6rBPYԥ Tlp4űI=+rp% !<'y1# 0wyr(X|X> endobj -533 0 obj << -/Length1 1707 -/Length2 14054 -/Length3 0 -/Length 15761 +118 0 obj << +/Length1 1353 +/Length2 7074 +/Length3 532 +/Length 8959 >> stream -%!PS-AdobeFont-1.1: CMTI10 1.00B -%%CreationDate: 1992 Feb 19 19:56:16 +%!PS-AdobeFont-1.1: CMR12 1.0 +%%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.00B) readonly def +/version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMTI10) readonly def +/FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def -/ItalicAngle -14.04 def +/ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /CXHZKE+CMTI10 def +/FontName /IAZJRA+CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for +dup 34 /quotedblright put +dup 44 /comma put +dup 45 /hyphen put +dup 46 /period put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 52 /four put +dup 56 /eight put +dup 58 /colon put dup 65 /A put -dup 66 /B put dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put dup 73 /I put -dup 75 /K put -dup 76 /L put -dup 77 /M put +dup 74 /J put dup 78 /N put -dup 79 /O put -dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put -dup 87 /W put +dup 92 /quotedblleft put dup 97 /a put -dup 98 /b put dup 99 /c put -dup 58 /colon put -dup 44 /comma put dup 100 /d put dup 101 /e put -dup 56 /eight put dup 102 /f put -dup 11 /ff put -dup 12 /fi put -dup 53 /five put -dup 52 /four put dup 103 /g put -dup 104 /h put -dup 45 /hyphen put dup 105 /i put -dup 106 /j put -dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put -dup 57 /nine put dup 111 /o put -dup 49 /one put dup 112 /p put -dup 40 /parenleft put -dup 41 /parenright put -dup 46 /period put -dup 113 /q put -dup 39 /quoteright put dup 114 /r put dup 115 /s put dup 116 /t put -dup 51 /three put -dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put -dup 120 /x put dup 121 /y put -dup 122 /z put readonly def -/FontBBox{-163 -250 1146 969}readonly def +/FontBBox{-34 -251 988 750}readonly def currentdict end currentfile eexec -oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# -]LeVߐGoo٥\k 9Mՙ= 0)xf -1kX9H!.vPN 7qjj7!6CɫTw.]ʂԬ/J1]0': fqdU24tԡ?@^g+0[ -KTB/UٝFMz7 .U{7K.=UٯI C^$O7Û-tGrz J:"ia~ -T"*^MMчff0EM -z8uwi*?rw5(*5nZ٫ -4*RX&RTdRM3m ѫ& .Pd8;]F |H!%T [-͘ޞ E|pV$MU]n11RP} -d -.{IQ7^N-+C #̲]\M؅1 -pk2 -\t,o)2TTڮw}Ҏvq `;lSgs3c-h}W9;ڤ9Ö`2 ${};;m򉅘^l1'C*~O`XUn0x|cɾ'iD%WNCەU.9R*R?nLWˆs/[趡ۆ8>H@#ٻx wf} ayBR C1|P|'r,߰INJU`DkUQe ]Am\"GmFO )2rIuW\SW,'vdy]eqXH0#~Z9|pŞPOHau`Cb鬅<=?t8!-~C0VY-aht`rxK[3,f @=]wG2C#܎d5BYIWu8]o\ !~}SJZ݀$c̪OJ.k0F)L0Gɴ Mں45Ȟ1l֕(4݃h8?CL7HHǷh+ }$ DO.ZkJ[Gtכ?Tcp{nRƷWHW%8޸d -7Pep_=R(`9p++9+@dW4Å5]ĕB⯞dPkbܕ'm4vLδS*0\-JUr%'Tq~̈́\5O?ƯE6"Abe(eSd87mQX7IR*tGPz%x!vxJ+#}A|?qIHHje6h2[r"l˦1צAfZGn懗{]}%,Ɵ!@cϿi f&瀌] xRs;AZ ;S:|$8H*\Eϕ/j=F~lR!꿸dq4*x(B"ZY4RN f8XW^eńiZN'Y - :1@H9D0kq'Su|#Η<{8t؞#DfQ_4pC&D409oZBԕV4*2t -ӄ/SS뼗%ĝwhtB*mtX>aO Zbc&sYrw^&euL ( 5H$!(xJM Ply/6qc2Poi֬c)mX=^Wʓ(*cKeq^zyZ*:@w0㢇)_]?|vlIyJ;45 71:l.=cS(Cb*Y58%D<:TD$S*o=T5 L۾CӶ7;.tB]j;vUCzPaF>vb5tz7HԇU^g@& -iO{&3oʍ1j6*37A^s^P Ig06Y: ih\fojHNkͣ$ x+ X5Y)n3N -aBx̞?1"^ ȋ!# -ԡ{#U588)[IǠ_7X)n cMt##*) 6iۋۂGb*kԻQ ->+9 ג+H\o;.7`+He 'mg>".V7!=ql7ξһ>Y@P\(I1:9>Is ~ϊWuSŪ|a+₥K? 'jv6;`x(T>Ԛ6aH4 ӈ0K[ (uO\hT3^v-4@W؈qWq)'4}P;?/D-}R~ g}BVhٽǁ%#mO}6%UB#lۘT_p[M9΂MGr -g1@NF!v>LK`0%3Sy)RX0B7BK`3[eƝ{c! /T[,S QlѢ**O[, ^1T2^].[LyP-HYx3:X@>x惼Q`Ӻ~wrĵ:o0X8G9ͬb)$nW L4~T-+A@g~i Q J%|}0'AzUؼDD`I`$~t=rk鍆yl;h?rǬߓgiG)}ߝ+@cdo]  bꄆ_t0ǣ:O"9\I.l^&TB@Ȅ駐^ئ93̒6i"Sa̺1 -k$6@i0f.0=C5pbR n)@G+ooWܳɎeh5/H-|Ҙz /aۗ 9A~?f<'fKH7(@Q 6?6{L(+zDxk=aOc* mS0 -KNykHrxTc[q9%]i'ۢ R 3r#SB}ZQ6H -ћCT*BLνR$?:R*YPmyb&a(58җp1&`D+'$e( {:\.@#\Йs% u;GY% a߁G S/AUr8VRZ?TT*hVr J F0؟mɓgX9w4e+.P -L$͇}cUv?fn@SB$Nc c5$x-3,>h"1u{dxII!ݠ}A ̀ qmpT IS5Z`_H0#̅;JʘHv.TG,}H.*XiPp nM^:}if̤_OhEh>q{LYRz 8/sī9u&=J88Wo,)vL΁ ˄']^U<dk.K^}@d:sFK%+lv_WI]kc{WU%*EَG}.kAH0߾bqF)k6h!C61E3*<Y -yc$lHa>1AP%u'ezHӢOF-4toPZ܋w@L{ ˍ`biK ]z62h k.2åb ؋"!2`Ie(>95[>Ysl~:L*v{ŀxbp(o԰}(0oCasl,يXfCS}N\1~C8AY.Ft(p*5x J51Hv2 c(mAM319;vP6hC>O ⇽;+_%K`03!'#: w$1&iNN1H%~K𡜫/ԵZjj@,!H!ʁr&U0ڎe,7 d / -7!cp9 -gi2 X0c(2&M 5׮++u;6sN$_8P1Jh OJzTd.n E1^k|hvK3x'&8AT]J,x{Cv`׃PcއpȚ3Z=Ը}lUo쵉< ђTƫ$ U){X0), -0=D)7UAhU¤؁V`iT֫D> JS'@&ߨ6 YQ.sFH,(Qo>x>AuHIp7!2aT8.g{}D|qfl>ƁDw_ Z#5GZ~c%7ީZ!~a^gטH/+1}3=^1~(0{;2D6JhETclFwۓrTTWg1YyqE5a#/!Oo}0ԅR5Ʋvt@fF -0x Kq4ePQ0}G͏7!uyIGe(m?%7:ӄ}܄όL91L׊-“;eNYд[N7eׅy;=JTMaX">1WN]mtL0TBKHVbeatmr$vvGnq׫^>ƭzm,<_yk]6[5wRgldXsCCtW So9ѧ>Xo;_V7x {hL,W(R,H`M~I-dKy-BTwIfcރ-ؓulȉEXyՉ+ozP:R,# PO~h8tV~.R习 E?uA >U,0''7S臽a$3 OSlOF -ykB}L1ˏ>ʫGXIn%lCeA.(@YjFb)%,`Rۇ3lj:J@xPQ_ۮϊ5'\iEA<%=R3d߿0qѨ~KmK0!eᄃgq4: ܡ.@u%} _@|e^c|2MVDtΘ QhCk-2뮕{L % lObv>F|ݵ\R3ۇ8" $+z|--2tfunE׳w,e<0:=0(Q*|Lt.2*pS,f+%J[ˑ -d'-+1|cuz`NL EIA|A+&\}&ym<]_a0\#Y4z /k2]?i -}^/2moeuiz\9UgƊ|wmH]5#fW_D.shfۅc\e`0tlŨG.f&7EӖ :Ᏺ&_??, f<fNcDžU1H]]O=m$g0߇ @YTq\14è?}j}ünJ 0 rG fGV,Tܷk}<3Ze`osP}7N X@ge&|  nQB+t' 0 }X8Yd4L#fE9/r‹D+08,_ZQ1]QbxMSuIC/*(T &(/jjNb8U 'ShVnj[ڐ>C5h cX_H;ޠh8'Fm%݊| IÉOeZzڹ Fp=7 ΡooIɑ)-lVw ͨtU 15I+OlJULP >6еAG܈=IyF -A\g[&ѿ> -S6'0gwJͬ m yRby͹RWwx3"RX>$YOfVM}HO;sH_?~lRR'⊓Sr7oWDD_ZdO]he g@brsލYIpΘQjyshxd$')ژ6B7Qh(HAVD}tG8-BWiƖv+py7f-OxGCSU=F7jW-(" H,-mCt\[y*z7uhDGzf λÍg>%Эe5`SHmXfHb!`NjߥU,:&zR%-)⾳b"6ro_p96bN6,3($1Ѓz"dζH (2tyq {If1(}=!t.͓,kQ2]=-PjXF0çuꫀ"xaB+&1,ʚYuܸO;S@U:xާGN_ 2ѐ>l^$U~]g$i8Sțk|[2YY^2T1lԙVnszg 1BIu'g=+xhX ӒUU|ȦvC tKg,̔v+7dYG%ӀXւ΅`)*zDXQ˺^G(f5 N6i{”ÍMB3'l}67, Q9LG^/4?k{N9tBg5)S0Mq}c_yL JU9}ל -YOݙA܀K|Qc@'=ikhڬ HyĞ dE6NYwp"rAn@W(k;फ़8zev64N<#}dGIwhjrsRY4g?N9r18YBzuQa66~ ? F\:'٘^_Č_P簉NL#h#:ŀ`vPfw1xaehp3BkxzE#8s})`֚HECa 0 b8g"| 7Fyb\G*e5_g9%^AWJ]Ѷ<'6&35׵yFsJq3D&zZ%pB{P>”ѼVٙ4"VMLWc]R2БJUWKoKwS.NoGfFH+y&&d81ґm0G#f&n,Ɍ1 F{'hL߾~򯺦A.;UmngB~WH`{gPkkێb+/-)u;M @X:@ BvX=rrZItO͗M~W|28нU8BÝC (')yK@3*: ҶD1fɏdL<u9CbºCMmEJu,%MKOvF4N;1 kWE[.`-GS7/EKU Gr,*3uh|`#ZIK(56oOn\׺ uhYL<*>O]ny+$&m!xܸrN㇡[[|G-.WHD~0z"-E[huư<Œ,CeϓQu敥n`y82OekKߪ2o֙0jŠX -?ߟ7Svke,霱(̂c\BUO,׻?)r͕,a@5X*ˢL {` 7nmu=.RnMzuj!sQ4یm\DA$s\1>-%o_A^@hޕgz3./e2gNX37Zh1§{l]2ĀGXWc~aPtFNFև9 [mzl9]bDgh3^6d6C@n v~ܒ#NMg?}"&;E._/z/XYJur77v_'T-pϵIՋְ) 0nΌG:BXvE|)d_iY+賀pgo=pLbɶ24t v5C8[^C/Z;?q/AE!|\% Rw0{\i(|5SFos55gCżR*܂v|ANrO-;sнrrL[[v.AP\}8\ \|OTGǖ9e7gt9 -d9X^aw.4$-P{[%ff3z)}iL6zc?:|:C-Ju2;%P)ag -qie3,UT_!O$!4jgPB&a=k_k+8xd , j|? %Qi`P : m8cA Mv2O@-iz y'& 7 n -rPu3O>B$@CA$*0+;"vw1nD<ۣ9RZYC{e>uXYQcwϯn'dүLQ_ܠحHk~1?IJ}kx+ۆKLC(K+Bg\e ɽj.9)y7@l֣7T䣉V|p:}\8f:ؾ@;T@QnMS@{;WrN,>"C*]1iӄ|XpE% lA(Ez)Urh=66'l6[4.ctq6vfwGoq -3h6o ns.##{>M%&|Ÿ\8;@P@8$Cr?Fol|+YO%(RV/Qkҁ,* ;e\K=.b&+lt8EnTMQIzXLjGS;I\@W. g4^pw|YKF"N&)G1hq`N(Y}ڀ+wM?Po]{&2qR(5ZIp"yvSDmh{RL.kSꄍWe8z m) 0*Lc-/x4|m'*]"\d#ay2i1h#ugHd^v$HMHx8u/44{Xm:!S噓yOt^oT,mBzi! D[@Ls+-pZt}4ܪL^"MrgH+[E ]yƒ=JdQt >'Gv@=ټKex! 1սkxh - -e%rsp{<&6K羒x$k tA~j3p8" -4eFMӆ*;#?HnpoOq:y Y9,z9A{}V(N;O$ƈl,$Ʉ$ծׂkM%^4VPόĉfm!ty]6H8ܔN Ddv"CO]]dPlWtLPp\rP4҈2vA (ɓ_M{9~3xrR9Fgܙ3q5gvR.zQ6>KVfcKٍB6TIN% /\97[ꄼM8e"|$ѫ6zxL16J2}p_yW9ryr+k@i=׸HQO2'G[S~ΫOn% wTS̗": %GS03(OhӜAO'҅ }Mސu)曜^2=+g":cڎeYnIS v(7(IUBfv`Np+% 5\O < $f -l,ƴA[Ȧj)d6D#]<1O&v'^৅p +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\@[6]nhmlhaH+4/?3&n=a6E#|~.ԅˠLw2.槝sNY ڻ.,VnNX3|裠k(QIOs m;fߖC1}_a Io#0wݙ\P,f *bG3Z2کP8L3r[vnc_Eh~g9|M) }YaѕH|1m![AzXpPNCU7Uֲ7ΖTgx_hyW^]W}s_Zfs@dYr ȟsy&vJx)ݱ~Kq +45hL#q:4pP?g |GJSn^i26M Ęz0. v31껰xCj 7}0a `~iEfÎ}O>&*gϿ60CL͘sc·^X0IF +3yP.wP=vH?tx??jKvcJ ފO(WfnYc+ՈuMWkSMpy2La }gH,HA ngVU4NN7z3=ʿM1(2iznl7 J[7һDH]WUMi)hiwuPJv+]/XNkn|´?4ҫf kE{'ǺW1 os!w#v. +RGgkx0S"MB$0kSlk6C)R`+&gljᑢ_5s$ U$;|Q|nÜ2 @%ړqP c Tݓz#rr%sV 5jXmcxco!e<꯿!j_&a招Dʕ񮄏]_ZbJm*:/gO!**$_ !YEBě `Ek14#!"AGgJt+1u!*(*}U\#6g1.*u =>Jx7bdژپ|8K8u+0aYq/2S8|ea7lt+qo[YD5v_W <Zw[}7{<p s'}up/Pl Ēde.+R/rHu /&T V]jSXDT ]v2OG90g}M;ρ}Ҙ#LdWVoft&<"C8&rŔyTqd.2*Em9u.m}pk&QUZr t2A +5'Vh*He"z8<`jCZnpZ.C^L̮uÑ9LTr>Ғʩ]]H)eܨ<1BDvT h8#JPϸQ>#<8&6Cc`mE}w56_z#h}ʅDFM"ֶ+\@esx~1lP:S/ \H)l_᤺ѼYrvε[ɹHP:xb_ S6٩,^b~q, ;FKkgB*.6څy!rhN㉳^K0Z\dRoþIh /A]&.t i> +N)`~L CɬS +374TldǧA?*2|iwtYɪA5R%t/Pd +?Ty&$銥f+J y l?cڵ*W𲌲BNE n>PL^x|Gq?"#o",eGb3*|g]BhKxs,9M+d XB1:: ?5gGP, 626y|Bn\AD ū|-_C;s+|/Lmj=f*( wRڮ]e~:XOOnXp6%dLQx %"!租`NƩd_ 2a?Gj}>+={yIb̍e= ZcZLĴ[)2 gqbՖa|؇ DH +ހ `b^U|? R*wC쌆96 GrFwߊt>^hnIlT>RXJagM6#ő j~cG,9#P_# +Lq +< (,] 'LL^ufU[8$IL袋qiIC¹űnC8]ܖ>(/^4G 6oq `^=\xHnN~j;];KmCG$L*Ya*`wL~$_4rL2Z)F$LkL A%Rx5^"aFܒ}zq;:>C`L% +Nx&$Tn3^ 7mʫ28Hr"k~80OXi)ΟL3L<9Ҙ~ro6S tDR] /H/+)♹ 8I͊ >r(,'H@pǦC2=G ".)GgD;x:ڜ}? 0S-Bk2LQnߍjXyRFp4=Kv6`a( 7_vTLxsxV{!v{GGݫ *4Uꮵ$@+s'A͚'{` 95"b@̎juTE[Ii} x9nM(yʑA[^`08|EtUsyޛk*Kw/ze48RnO%zghHK3HU2,?8{ŋ8 @N)x`4OD ҍ] P%PcyM=4E)ccYš~PDi<!ϴ۠r0p_\_^i?! 6:0\ !( + aOYly^\J8AH.4,zVU'U W'"؊Go Z΃Q ~W^N>^U+X*-7H! '%_1U&L˕~)5"jx2$?q9Cz%v6kܱ޾yWdC Л~QF:=#"`eؐe9|>]tp"m:O|m:.~/z&;%KeŻz7ajEA2 |a!OMb4>WkfgXl +Pѿ5wJWß8p0ƌ\}RRkF_z7b;h8 ЖI-[V'8u Ř9ISUu'm4;gi}8q+P .F3q/^?]؎̢[soD&ęjn*0QBE=Ws I, Q =KP~Y^V #( }$ΐpg,9X夲G{q؋O 絬:oz09ܞ+xqs y5';w"6(Y}[L 4i(yo3S*Fw\2j*U%K)fr["7SV2T""&'_}O-qpO'%4[^Ro51~9tp6B'*רILleAxŝm|_j6LJh\Erd k p>B- Rʓq^I.lEvXā0XЄ$Wun#6x07/0u^<6uu@r42Vm2iںte[e|m(!>J9lY椀ꏺ"r6fϔ+'^*hbK}'Cdi㴂F!>[1 |kt +6  +\\8>XnJs^2VKU{Xn:8uQpݎ4^ +{KEķ%YUBF^hp֩Z9k*`pKN%%R<:ڒWR#_\q$ΔP<G7=<5fb*.#_/[QzVT~"E}Ռo5}6nzqĆIi٥g=)"-=_Vx P|f.e j(fO03i^dt%V"Q"yE%]k?!5A啇n1E3B[/Z:G{UuǫJh6 b@ڄ XL8Bfr7b; Ni!k= &z\JثL5_D]<K +?]1!Ԛ.*txO T!ٞOV +>қHJ;\0?Y1jZ<؟~f1 xP>HlL;l#%VRܐNBL(s3wm)m Ep]?g]΅]~]<@ݍ^|Id> #*Z`iɫmG2{c-EVbj; KS"LV+Z+ѼHO*f2`Nƻdo/GB@f=ձLy H҈!@ys$ǝyTRƳ)[Syi:e.Ho*ثT7w&Ivi](>˔iGHs{G}<+W+uAm=|YZo;{Ya8Q2+i`776d PE:_pC`WYq4xfcnK0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark endstream endobj -534 0 obj << -/Type /FontDescriptor -/FontName /CXHZKE+CMTI10 -/Flags 4 -/FontBBox [-163 -250 1146 969] +119 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 551 0 R +/FirstChar 34 +/LastChar 121 +/Widths 552 0 R +/BaseFont /IAZJRA+CMR12 +/FontDescriptor 117 0 R +>> endobj +117 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/ItalicAngle -14 -/StemV 68 +/FontName /IAZJRA+CMR12 +/ItalicAngle 0 +/StemV 65 /XHeight 431 -/CharSet (/A/B/C/D/E/F/G/H/I/K/L/M/N/O/P/R/S/T/U/V/W/a/b/c/colon/comma/d/e/eight/f/ff/fi/five/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/q/quoteright/r/s/t/three/two/u/v/w/x/y/z) -/FontFile 533 0 R +/FontBBox [-34 -251 988 750] +/Flags 4 +/CharSet (/quotedblright/comma/hyphen/period/zero/one/two/four/eight/colon/A/C/I/J/N/R/S/T/U/V/quotedblleft/a/c/d/e/f/g/i/l/m/n/o/p/r/s/t/u/v/w/y) +/FontFile 118 0 R >> endobj -535 0 obj << +552 0 obj +[490 0 0 0 0 0 0 0 0 0 272 326 272 0 490 490 490 0 490 0 0 0 490 0 272 0 0 0 0 0 0 734 0 707 0 0 0 0 0 353 503 0 0 0 734 0 0 0 721 544 707 734 734 0 0 0 0 0 490 0 0 0 0 490 0 435 544 435 299 490 0 272 0 0 272 816 544 490 544 0 381 386 381 544 517 707 0 517 ] +endobj +551 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 34/quotedblright 35/.notdef 44/comma/hyphen/period 47/.notdef 48/zero/one/two 51/.notdef 52/four 53/.notdef 56/eight 57/.notdef 58/colon 59/.notdef 65/A 66/.notdef 67/C 68/.notdef 73/I/J 75/.notdef 78/N 79/.notdef 82/R/S/T/U/V 87/.notdef 92/quotedblleft 93/.notdef 97/a 98/.notdef 99/c/d/e/f/g 104/.notdef 105/i 106/.notdef 108/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w 120/.notdef 121/y 122/.notdef] +>> endobj +115 0 obj << /Length1 1144 /Length2 6097 -/Length3 0 -/Length 7241 +/Length3 532 +/Length 7773 >> stream %!PS-AdobeFont-1.1: CMTI12 1.0 @@ -6690,12 +10590,13 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /BABWJL+CMTI12 def +/FontName /XQMAPN+CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for +dup 45 /hyphen put dup 65 /A put dup 66 /B put dup 68 /D put @@ -6711,7 +10612,6 @@ dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put -dup 45 /hyphen put dup 105 /i put dup 107 /k put dup 108 /l put @@ -6748,422 +10648,260 @@ Xӷ wsPJ)3*Q=6Z*qlojwjzgs+;Yfr!Q@ $ 2y/ 6Y1zA3{EE v4䲮)8V^ (1*՟3aUO'-oxޝ:Cl н.'Ձ8]ܜ=yǙY 4_*= 5[%atLo*-gehAZԀN~:hǖR{>*_ۛ]ew-#'UNvk9%*\] 'ՈGݙ[*`8HB".J=u&L{xmd[1y h}⒙cl xP7%<4ݫP䬪FAj3" m8Z}!z(MzC]ka,[&*+S~9$@J.9,!uӛ^NuOtlf%2u~#Қ?ã=*3{hgyp#MR,ڿÃ[yz]Sa"1uf^c_Q$GWUI3X}BF1O ܄hmܵ6 aUbf>]k=O`LtRdN>~v-wC':xd -6^js u:(A8vQT0Af(FNC@jU1žP":ZCd޸m$WW޶7+X_K yK5R^X$1V#O2>*絶ph!{W.g~BX0t"!܌IhFKp0\i綀^U&oeG -Y|afeF*}^ -GD+Y|jXGf- ZSRs ū qv[b=ornLRD7o0n*X<rS ^'N`8i$)o/["84Yacqn T2>Nԩ9 ȨەDsc -endstream -endobj -536 0 obj << -/Type /FontDescriptor -/FontName /BABWJL+CMTI12 -/Flags 4 -/FontBBox [-36 -251 1103 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 63 -/XHeight 431 -/CharSet (/A/B/D/L/M/P/S/a/b/c/d/e/f/g/h/hyphen/i/k/l/m/n/o/p/r/s/t/u/v) -/FontFile 535 0 R ->> endobj -537 0 obj << -/Length1 2088 -/Length2 13404 -/Length3 0 -/Length 15492 ->> -stream -%!PS-AdobeFont-1.1: CMTT10 1.00B -%%CreationDate: 1992 Apr 26 10:42:42 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.00B) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMTT10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch true def -end readonly def -/FontName /FRDBIF+CMTT10 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put -dup 73 /I put -dup 74 /J put -dup 75 /K put -dup 76 /L put -dup 77 /M put -dup 78 /N put -dup 79 /O put -dup 80 /P put -dup 81 /Q put -dup 82 /R put -dup 83 /S put -dup 84 /T put -dup 85 /U put -dup 86 /V put -dup 87 /W put -dup 88 /X put -dup 89 /Y put -dup 97 /a put -dup 126 /asciitilde put -dup 42 /asterisk put -dup 64 /at put -dup 98 /b put -dup 92 /backslash put -dup 91 /bracketleft put -dup 93 /bracketright put -dup 99 /c put -dup 58 /colon put -dup 44 /comma put -dup 100 /d put -dup 36 /dollar put -dup 101 /e put -dup 56 /eight put -dup 61 /equal put -dup 33 /exclam put -dup 102 /f put -dup 53 /five put -dup 52 /four put -dup 103 /g put -dup 62 /greater put -dup 104 /h put -dup 45 /hyphen put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 108 /l put -dup 60 /less put -dup 109 /m put -dup 110 /n put -dup 57 /nine put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 40 /parenleft put -dup 41 /parenright put -dup 46 /period put -dup 43 /plus put -dup 113 /q put -dup 34 /quotedbl put -dup 96 /quoteleft put -dup 39 /quoteright put -dup 114 /r put -dup 115 /s put -dup 59 /semicolon put -dup 47 /slash put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 95 /underscore put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put -dup 48 /zero put -readonly def -/FontBBox{-4 -235 731 800}readonly def -currentdict end -currentfile eexec -oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou_c2Bطj=-8\Dg݌] /%bԺnٻڿSy b*L(9sWF R:EMksH02E?Oe+Z'zK΃оif <,EDNZ|J#BW3ϗMp(%5%~(5Bk}Aj c'S-8*!iy$G.w g J0nr -;଍ Kr^ox7p4= CyO#y[49'n*xx/J}o֯p6Oޏe}hà1W6Ϋ%(i]Ii -텴""b3=5sJzbJ>[Wе H 2"ێ0Oy9.t:=$EǪ ]to`% -'EKKfrRK^y`vO^v~ZwR iNMW3HSp+T,q!s0(ع;U+3"J8q3dJ`77+IuؿhH<=!'T́2.r% -v rd c[[ Hu,>d*,R`8'ξD 4} SYe8X|v{ }"--GdvImDRM&OT`MaXc:rNS؆'GSk,ې >a cֵpeW1Jm=6dgaeR#l/`Nj5NEN~QJSYm#M$_#8٘w 8HȞ2'{G [a%ºQE%1l$ks@+ʢ@U4x R3O迚#0GL - G(ŕ!8Bcz^48G`xѰNE@PC@a9g.7Q$hWJ\U`z < )QKtXcs[)&:S[]+39n\qx҆3Jy>Dg"^ݘX4d{ hsKA_&F05nȗ=:#7GJp\S=j48ĿIgi'9)2+$ޥ\ĚҮ'Ȱ;Ó cEzMhi#1P]+>N\r&fBbfI) h[&]/4ZYk0&gvr&tAgD=Q:t`{0a]U$qpHsS@%%+tv Eu $Ǐ`i 3SV,Vw-a?vg)K}koz|nB 7mik 8[ ya6o!:z~4]:1!jl0Rl*aA-d~ԇ %~ôn: qKVs=-0чg#}$;AKhjP#U^݊8ufiҞ6=]L|\' ՋOΓYW}@<~c3zEc!NjH 7gj~ՅN}8`L4_R㩃`pJ[ -6>bE@GG( &6GqL\#ǿ{'2: ˦5)!#W:tĝ)1%@goviWv0B%fmLgP$ԾTGh -w|=ϊʼh`@e㕒D˖ar&|[J ߀ O j'Fڙ3uЧ;L/7)]4Ab r3,̖IM.Iv6y,mzɏ ~ˎMT1Ȍfŋϐa:/̼Ȝ 's. -)G XJytCK]n TMew%a{zs:o ;L@uM0&:J#n5ё}&z]Pʡ5#cܭMEVIڄd$tRIQt,D%<:|(%IT 71 JLg3inF&[Q^rV_Wv4T= ưx\@RUu'*R.4p'8G{)ů ) /On.yQ+9i`羷9ܤ*ݖvWȥ"մ;Q$ڥWm2$o_Yy\ ;S34z2=QK+GOYB _qX|.p|Jjm҄ɥ ʴ.7w!J4a]o -BQ2^m*(p'P3Z8ScJ*T2dPd 5la*/ S:Sؾa| 6_f,ȗz%3| U zV5Q jq2# T_x$[ii4jJ>c֕:"?u[yF)͕cO;uQ;{ţr(好mv/cFxsGDXm~Զ9,UnĮCݒf>="#BӉ2%dh ޺VH-Q)?<ɿj氊03",'?Emw1uHtu}|QBWdQf,[ư#d|muVc -F%xKƕ:8|s,&DQe;?ƒɯ` ^ (4m/ ?pq6vۣ}%=iL[]J/2vJ8FB'o\QJj.lGt$*iT2n$]KtrX!V}riܺ5D;s_>Nb8YopUNU'>VT qB1goquh~3tO3i4=B]g8D6L|W~K?L\F?i<;JSLS;.ax --eSlSV"57Q:]-Io-pUWb;v$]FB3󰁃!~GS )+CP&Dq݇rEU9?kr$F+)U){xgc'*5ŋ>vc6l%d=ƍN(2Gz0Gc>cXGR*/̸Nk @kvmddzj. ;+K33'I15D%hw"R'ܿ{y2uwtus[M͵3E:!ޱw'G #{-{\qrQQ7iټygert@ -?⿪_az-L7GBDRlAxCO0bz AQY6>QRhCV$ʽO#U[!*R_jowYWdvժž;:nL4Bl3MjSCL+a۲bu,] cpTɉ!'₲"){OK'yz0'o|.X0qΑ끒b jB/h3B9tCO`ɥMiThboRsŤ -q;TxOƲXCp:$ Bn -m#+V+J>7kس[Q_cg.N#' H򥿱]K8?>b`[z/3 䮀o'*I ,ƀh8Zn.cį׺י#lKg. -4#d K€X+jν FO鉎VmߛxSWTƜ56wʮaztAܑ;}?+.\䃻c-JuG0xHٍ9MG"?M | 5h󀺽*{soq[=ՊF{W  j%f_i fUބscp<֥TTX -jN8hac]n}O}ndO -5nO^xQTwnj/twLQ_ra#95TӁ} g7qtء\y}O|Ddpc\Aod#2~d"yɒEe\BnqZ0JT[=CT/K -W0GτGeјJWYK\›WB*jƞ$XBkz8'VQn`e8O K?n'z\M|CK nI ‘.2&r:o0%h^T=F583|H1JuR8c' C]$WHħq-#T;l%{dfjLio7/ z) PF=W(@- -_z7Q4E׋:hHY@5HSxd0c"ڃ㞿~}/N(R{µDHI"^>49NW6>PRtG !GCnI#E!? F5ac,E)~};nj 8x؏/HaFf3Z6΄΍YgfhrV@wj򞞹^2 a6ŕbphқ%nuWB.M6p 2bYoz׋.ai)lXuqL6b%;34jDdFGKʚ%)Vq̌c&:Du9BgAȳi&ݾk1uQBs(} ؞H%X¡ qBh>]3#GCet ЈWoP7L0ӦkE8o /2}6rJ;+X1ݾ7sE -?|4&$,دP wtbCMj6')5p$AHQLA_ʥB3F9"l:HqTuf5^1vĒZ\)?ae՝#B\OA[d} Jc(rR[8c|ם>0U)ԗ=Ð\ 9ֻVht ڂَ!z UH,#"CS -faC;}d-KQ)9OTrp40W`"B֚ŰO0ߵ0 ?%\ h.؇İqĞ) -6 yEUPDP:VVZ̒<"5hǑ[n?t5ƪ@mlpЖA!XP;:ŤŽEp`p`Zc<ޠU!ҥ '(ͳ=ח>8ҢD?'`lȱq%q7Plhue Ӆ# Oi+j1䦚;;l0ER|hag@g= ;dm+):h(tfcql{}7BTޤKi7t{D2a;7' ` Nj`OV$FxT.bpCՇ7gm\zb3ix<ٯGfB3(Gy2!bʬDسPI?a*BYsli^uMP Awj/iwh-αP3(yW>7{ò:R﭅[SYj!zf `2,$&Dy7m^I` tz!qK`TMɭ7>xt(\}qp%^ [*cEt`뀾9KMS(^/,(Hz $Kr py3|!D]@T< -#TnpmρL%2*_dyפ2 dv슲-Z|& ru\1fV-dA{N0ޡ&Y}yas=`tȡa\>flhΈ,‹Y4^*X}9׆׈&q]ʑ#鮥ij7=&tf5/fz:U [m>A-T -dv﯎xS S^gg\i -B'8vJ "S۞uNtD ޗijBkt~_(9b`b?#mV\ҔeЙGjůnwa|Ol~z( 7uZwK%VsvOaX7:k%}GF^C0σ~ ӒAusYoIO`)U!'&7eIѿNFCK4#_V)ڛGdǪORå~ -ITtEMXh#8[ȍ~n$僳oc>h6;N f<vT9 3S'QLZ}8z_9*OB+0u8/f R\LVG -UHM/6گf|P(D ZGt;+UC#7 ? 0餥d&^lms -21 ڋ'P5jhs$\ l _ybTl'k) _ 3MQk Q&tzcA_Ί^Mb}gM0 &%b*`<$g)_ZP*(PDŠF㔢zgXo2+hși+AHApD]b\=hOȲZ 9Լ5 >+F9y.>u`]պ?T9cԾX UW_ -2m,;(}#u.Zf偏9%Ez 4e$@B(Ab5-o"Wx3qH> w+pB<˗׸nFNO -"}Fvc -/WYa"^[[&O9y\"\R9oljFOQٞO{9 ~CŋU4oK_B/"d★#5ռ[:[7Wo`8inNt}42Yr3潍 .Ika:R141omLRod V)f!ނPBU-@*?zc[TA-xQgPIK}γ?șBvvNU916MD>pEM搨?"1ZjDNS7VbRVY=Y22*(x@)_1Bebv[V~qB?%KGU_7N2ڟb=}Jë8ɻL"4}'͡ۇE(aJpX5QZTN$dW}I>`h+LZm]IA4)t"f9vDW4VRW|,<Ⱥ%PK(^?cZ\So>TEJ{[*Ku7{ hJQ4S35ޙ3+V [2'rwCu$g3,̪2Ec(^]sM{GԭXaaҿs+ipk^dƙCu~lw\$`^U]$XNp,nq6Qؕ*LY{;́v>\RyemŒ+ͻN*{ޮA U* -$K[!.ݦ~!Ln$ޓ;w[y@HX&g"dtoG.I~5^=ax}fPO* 6Zfxwtx)|oOx]~JPtjɬx0\4xC! -s* gR(=֓ Am muE6V}.ɼ*CeYN -ނsƋ]<5&uwt.W J -endstream -endobj -538 0 obj << -/Type /FontDescriptor -/FontName /FRDBIF+CMTT10 -/Flags 4 -/FontBBox [-4 -235 731 800] -/Ascent 611 -/CapHeight 611 -/Descent -222 -/ItalicAngle 0 -/StemV 69 -/XHeight 431 -/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/a/asciitilde/asterisk/at/b/backslash/bracketleft/bracketright/c/colon/comma/d/dollar/e/eight/equal/exclam/f/five/four/g/greater/h/hyphen/i/j/k/l/less/m/n/nine/o/one/p/parenleft/parenright/period/plus/q/quotedbl/quoteleft/quoteright/r/s/semicolon/slash/t/three/two/u/underscore/v/w/x/y/z/zero) -/FontFile 537 0 R ->> endobj -158 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /RAJEKX+CMBX10 -/FontDescriptor 504 0 R -/FirstChar 12 -/LastChar 119 -/Widths 497 0 R ->> endobj -111 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /VZSPNB+CMBX12 -/FontDescriptor 506 0 R -/FirstChar 12 -/LastChar 122 -/Widths 502 0 R ->> endobj -124 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /WARYBH+CMCSC10 -/FontDescriptor 508 0 R -/FirstChar 39 -/LastChar 121 -/Widths 498 0 R ->> endobj -275 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /QZSJAN+CMEX10 -/FontDescriptor 510 0 R -/FirstChar 0 -/LastChar 112 -/Widths 488 0 R ->> endobj -175 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /SQUASS+CMMI10 -/FontDescriptor 512 0 R -/FirstChar 14 -/LastChar 122 -/Widths 495 0 R ->> endobj -274 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /OFGSEC+CMMI6 -/FontDescriptor 514 0 R -/FirstChar 14 -/LastChar 105 -/Widths 489 0 R ->> endobj -316 0 obj << +6^js u:(A8vQT0Af(FNC@jU1žP":ZCd޸m$WW޶7+X_K yK5R^X$1V#O2>*絶ph!{W.g~BX0t"!܌IhFKp0\i綀^U&oeG +Y|afeF*}^ +GD+Y|jXGf- ZSRs ū qv[b=ornLRD7o0n*X<rS ^'N`8i$)o/["84Yacqn T2>Nԩ9 ȨەDsc0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +116 0 obj << /Type /Font /Subtype /Type1 -/BaseFont /CFAIUE+CMMI7 -/FontDescriptor 516 0 R -/FirstChar 84 +/Encoding 553 0 R +/FirstChar 45 /LastChar 118 -/Widths 486 0 R +/Widths 554 0 R +/BaseFont /XQMAPN+CMTI12 +/FontDescriptor 114 0 R >> endobj -271 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /VCFHMD+CMMI8 -/FontDescriptor 518 0 R -/FirstChar 14 -/LastChar 115 -/Widths 492 0 R +114 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /XQMAPN+CMTI12 +/ItalicAngle -14.04 +/StemV 63 +/XHeight 431 +/FontBBox [-36 -251 1103 750] +/Flags 4 +/CharSet (/hyphen/A/B/D/L/M/P/S/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/r/s/t/u/v) +/FontFile 115 0 R >> endobj -123 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /KZBLKD+CMR10 -/FontDescriptor 520 0 R -/FirstChar 11 -/LastChar 127 -/Widths 499 0 R +554 0 obj +[350 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 727 688 0 738 0 0 0 0 0 0 0 613 877 0 0 663 0 0 550 0 0 0 0 0 0 0 0 0 0 0 0 0 500 450 450 500 450 300 450 500 300 0 450 250 800 550 500 500 0 413 400 325 525 450 ] +endobj +553 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 45/hyphen 46/.notdef 65/A/B 67/.notdef 68/D 69/.notdef 76/L/M 78/.notdef 80/P 81/.notdef 83/S 84/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 107/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v 119/.notdef] >> endobj +112 0 obj << +/Length1 1513 +/Length2 8660 +/Length3 532 +/Length 10705 +>> +stream +%!PS-AdobeFont-1.1: CMBX12 1.0 +%%CreationDate: 1991 Aug 20 16:34:54 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBX12) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /RKPWQJ+CMBX12 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 12 /fi put +dup 39 /quoteright put +dup 45 /hyphen put +dup 46 /period put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +dup 54 /six put +dup 55 /seven put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 76 /L put +dup 77 /M put +dup 79 /O put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 85 /U put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 113 /q put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 122 /z put +readonly def +/FontBBox{-53 -251 1139 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou_dV`Ky Z]uMYb[1[l',t\pڮԞZO4GJ7 i!U&Ϸݢh`ZṆhKGz; #1&()$J3KُօEsjFf"P$-I޵˕B +6=hqDV<` EkENrraƌJG ~L{6IE6U'y 0gK>&)o>2\U]$XW-1f@'B 1mW=L%5t.O-]N CT4>&wvNXŅCf עr1fׁVCȖ~q0 Xf^^$ӷ%G7dȱ\lFc0]g<銷_&W{>}N|ӷ 054H4ܞlG>T_cќ6Y1 nUr-u$zq1k.s+6'F2炁.rq5#3|u)pվc Nr3 p<~s?aG:m+-뢅^dҭG)qQE;%鬎F02y'9N#`=gh7+eC:é&3ˎMYn;96WLN(^r⼛nY#sdB1_èx/u!gcY';(/5t@aYkYeLYREz1o/bXK06P,)^^"!Hߪ7A3vćNB"Pij.:QV8yJ *Tۀ$F"yLX;5:E Gɢ|| UݢuɂSύRǷR B, fV6 ><=bPÊO6˸t9|bs6ݳ<CRC|C #(2nOr&ĝ=F)x־'c0$UnKޣl?ZP-} +0`3w='·~轙"IvAnVoK$դY*꬀QWͱzv/6䱢tkf R-+vV6A< +dWl`.b'v-= LJdٝd5qMc %s2pʚ?'OfKo('xm1`1{X?k>p:8mz}W,nfҲt5xmPٱ2YoAۓ1BK@fe>*\V FhsW rYSԁ_Hw-\% ¯5qBxLY^_)T1"b" 0rLizge8,ˮ6fP~曹 c6KOhj9l90 7E\8J0N( Z~e=+ʢiN],!#G5tHXS/ρM {Xr8 CYY^`J! /:xēQ9`f{tmFQܡ<Vh]PV%:G%H^z@Gww=Z .%9U^+_$J*\b]J2Q.‘؉Xd;R\&r {$}L[s6THr _%ߪHGيFHmBGN38][ S6<|kTu@Eh|tݳԱG4t3 $W2)d"*BN#\-LBb>p9j]UIĂ֎R-CET|Ac,[uϘe%BC[ (Zo(-pnӹJC0A;cHK.eire7&T]C--mK:wb SsߒF[6oq{{݂IvܯT֘Kjj})|s}WDfM#U;/ϴN'ھAOT@B_3˄̊jFnF?W0WI]Ke9TjE!#0Xdfųgp=|svhSpr5#rnAFNg}9XfczjNd +!A&RMQfg 8s]5c˾իWd!{;9+U:{x$SYR5A\7e~i:y236SK5U_JS+{.2{j-EQz|\fNO$z>M"g1|l3e# $^˥087'ĕDcۦхRo8ɿl>qIbB B̀_1@ݝT/]o[*FME"f*\*e6^cުvfǕѭkGF'Ni![r%bϋBԫPd~c#Y7jF;R'bg_?㒺[50bFm}W*TZ ep_Y~!dpLDbՔR"^9*Jw@{PV {&!N ^=j'#1VxǽږFPHYH̜BF^m +ٸDa[v`qyPYQ;{,._¿U\d0ly&(aʼnar +0gozМ7oˌ4C=rz4lsr>`K709"w[JURC*:'ҎBt76PKyj!{ٷ H%}9=K Y. ݂!]E%_bK-;>h II:͞P؀+?0Zھ+7 `c^T {rOr- b(P`YАV al9VKῒ UkOog z#gPőĭX`lZZ_ͣDoٝy(ICy bqO(\s5q|kj(> VE b$Cw-ٴ${ +ŹYre*~ڬ E +j'LzƐyèߛ/DPN-lQ"Iw,_owX)Axw'i S-jzЯ*xA@*;_#Ե%KSOFɴD7B_l~bGd5n/ ~$3XRm6;hc;!A@E}|-G @&5:+: }j7-=/2 :I<,SFh"ΒtY[k, +p®aI zEzќB['4}Aw.ѷ.oK3CJ߷TMAHAOXuigAD- +S=s|x2HՉM6{Z$*v`?|jq)/&\{g8yLJI8SR'He'AyI>-v6a~37rz$/m"=di={g0sYwl}xyֱyh8hNOA06jGg6nj{\!b#/g>k>`}Cfld84(ǩVi]}zWf\M.*;; + +Ÿ"s^]R9rkIXA"ט>SrWǮ54X|BhFኳ&7%Wtc$y V;)Jc6A\W * Aoyg" ckzl[OiZpZG2{/SMXdR\ob͹ĥ9hS*E&F8x57,EaR702+':p+,C%x0iO7U9Z*+i!+|cZ*Z*B \Aߑgi1wџNJ'揈/u f!(Nl%xFoBׯ~jdIēpUG?ӷIFn{[eͶQP+V:JtfbP|):S*yb4F# pʾVt^}2D%r8.>9S|8Nϳ eea$_4ZPWJD`!l~^fP_t CINrMeQ><8=4oΆU +}t|hO=N{FtNqăxŀQHi"7K\Nÿt_O\'4f/&5QgǶKøB G` -U`K {@H8xA&X'}:WJ + itHe,&}Fw92 55gY=lV@  hCwxBkȒ[; +,6Cխine6z'Jtv@g3SNS~cvꑌt +yY0X(prޜ-AYW&ZP j#mR̛uo=;mXՇ6rqA 4\{SkjnYl݉fh"py8.[Lcdjh>ym{''uSK珘kKg&ɉ6+ߩr`5P;e ωge8*R>O +:iC_a&N3 gPV7u*jldbKYMl%G|W6C}zq\7ӒQ8vЃK<_ը@+pE?LsAyz>JtVAbjq +;T|amQ2P#vwL@8cjڳ@oY ZEsv .F^4!_#> n=;${|Z6I`[8s9_u2_,B.ʲ98xAJz7r&̗q-/ )=GB $x`_&Шn f{q\cK-2M]z)vdQqźfe_ue4/+9ab`RjT7}?I7 RpGS/h |"IB+)NyJ7yq + +Oӽ:GvfVM7}0҄]R褼Y5-<0 +}aclܿ? AOK:7.mוAqZI!-uLE~MۨaH 6KA9Y*=OTF7 hGr=nFS~1])#כ5r +O;T Gu))yY\ z0;^'D !Lf{΀s6Sgy.~0T<; $Wc/nwov[8`ez>xϟ-g)J~Bjh> endobj -315 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /TQVOAL+CMR7 -/FontDescriptor 524 0 R -/FirstChar 43 -/LastChar 49 -/Widths 487 0 R ->> endobj -273 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /CGCFOU+CMR8 -/FontDescriptor 526 0 R -/FirstChar 48 -/LastChar 61 -/Widths 490 0 R ->> endobj -176 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /WYYAGH+CMSY10 -/FontDescriptor 528 0 R -/FirstChar 0 -/LastChar 110 -/Widths 494 0 R ->> endobj -317 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /PXBGHL+CMSY7 -/FontDescriptor 530 0 R -/FirstChar 0 -/LastChar 0 -/Widths 485 0 R ->> endobj -272 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /VOEFGO+CMSY8 -/FontDescriptor 532 0 R -/FirstChar 0 -/LastChar 2 -/Widths 491 0 R ->> endobj -173 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /CXHZKE+CMTI10 -/FontDescriptor 534 0 R -/FirstChar 11 +/Encoding 555 0 R +/FirstChar 12 /LastChar 122 -/Widths 496 0 R +/Widths 556 0 R +/BaseFont /RKPWQJ+CMBX12 +/FontDescriptor 111 0 R >> endobj -112 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /BABWJL+CMTI12 -/FontDescriptor 536 0 R -/FirstChar 45 -/LastChar 118 -/Widths 501 0 R +111 0 obj << +/Ascent 694 +/CapHeight 686 +/Descent -194 +/FontName /RKPWQJ+CMBX12 +/ItalicAngle 0 +/StemV 109 +/XHeight 444 +/FontBBox [-53 -251 1139 750] +/Flags 4 +/CharSet (/fi/quoteright/hyphen/period/one/two/three/four/five/six/seven/A/B/C/D/E/F/G/H/I/L/M/O/P/R/S/U/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z) +/FontFile 112 0 R >> endobj -200 0 obj << -/Type /Font -/Subtype /Type1 -/BaseFont /FRDBIF+CMTT10 -/FontDescriptor 538 0 R -/FirstChar 33 -/LastChar 126 -/Widths 493 0 R +556 0 obj +[625 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 312 0 0 0 0 0 375 312 0 0 562 562 562 562 562 562 562 0 0 0 0 0 0 0 0 0 850 800 812 862 738 707 884 880 419 0 0 676 1067 0 845 769 0 839 625 0 865 0 0 0 0 0 0 0 0 0 0 0 547 625 500 625 513 344 562 625 312 0 594 312 937 625 562 625 594 459 444 437 625 594 812 594 594 500 ] +endobj +555 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 12/fi 13/.notdef 39/quoteright 40/.notdef 45/hyphen/period 47/.notdef 49/one/two/three/four/five/six/seven 56/.notdef 65/A/B/C/D/E/F/G/H/I 74/.notdef 76/L/M 78/.notdef 79/O/P 81/.notdef 82/R/S 84/.notdef 85/U 86/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 107/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 123/.notdef] >> endobj -114 0 obj << +120 0 obj << /Type /Pages /Count 6 -/Parent 539 0 R -/Kids [106 0 R 116 0 R 120 0 R 126 0 R 154 0 R 160 0 R] +/Parent 557 0 R +/Kids [106 0 R 122 0 R 126 0 R 136 0 R 140 0 R 172 0 R] >> endobj -177 0 obj << +195 0 obj << /Type /Pages /Count 6 -/Parent 539 0 R -/Kids [171 0 R 192 0 R 197 0 R 210 0 R 223 0 R 230 0 R] +/Parent 557 0 R +/Kids [176 0 R 203 0 R 213 0 R 222 0 R 239 0 R 250 0 R] >> endobj -238 0 obj << +258 0 obj << /Type /Pages /Count 6 -/Parent 539 0 R -/Kids [235 0 R 240 0 R 251 0 R 268 0 R 289 0 R 300 0 R] +/Parent 557 0 R +/Kids [254 0 R 260 0 R 264 0 R 276 0 R 314 0 R 325 0 R] >> endobj -320 0 obj << +356 0 obj << /Type /Pages /Count 6 -/Parent 539 0 R -/Kids [312 0 R 325 0 R 345 0 R 360 0 R 377 0 R 384 0 R] +/Parent 557 0 R +/Kids [336 0 R 358 0 R 368 0 R 391 0 R 401 0 R 420 0 R] >> endobj -392 0 obj << +428 0 obj << /Type /Pages /Count 6 -/Parent 539 0 R -/Kids [389 0 R 395 0 R 402 0 R 414 0 R 423 0 R 427 0 R] +/Parent 557 0 R +/Kids [424 0 R 430 0 R 435 0 R 442 0 R 458 0 R 463 0 R] >> endobj -437 0 obj << +473 0 obj << /Type /Pages /Count 6 -/Parent 539 0 R -/Kids [433 0 R 439 0 R 447 0 R 452 0 R 458 0 R 463 0 R] +/Parent 557 0 R +/Kids [468 0 R 475 0 R 479 0 R 487 0 R 492 0 R 498 0 R] >> endobj -472 0 obj << +508 0 obj << /Type /Pages /Count 4 -/Parent 540 0 R -/Kids [469 0 R 474 0 R 478 0 R 482 0 R] +/Parent 558 0 R +/Kids [503 0 R 510 0 R 514 0 R 518 0 R] >> endobj -539 0 obj << +557 0 obj << /Type /Pages /Count 36 -/Parent 541 0 R -/Kids [114 0 R 177 0 R 238 0 R 320 0 R 392 0 R 437 0 R] +/Parent 559 0 R +/Kids [120 0 R 195 0 R 258 0 R 356 0 R 428 0 R 473 0 R] >> endobj -540 0 obj << +558 0 obj << /Type /Pages /Count 4 -/Parent 541 0 R -/Kids [472 0 R] +/Parent 559 0 R +/Kids [508 0 R] >> endobj -541 0 obj << +559 0 obj << /Type /Pages /Count 40 -/Kids [539 0 R 540 0 R] +/Kids [557 0 R 558 0 R] >> endobj -542 0 obj << +560 0 obj << /Type /Outlines /First 7 0 R /Last 7 0 R @@ -7342,707 +11080,609 @@ endobj 7 0 obj << /Title 8 0 R /A 5 0 R -/Parent 542 0 R +/Parent 560 0 R /First 11 0 R /Last 103 0 R /Count -10 >> endobj -543 0 obj << -/Names [(Doc-Start) 110 0 R (Item.1) 276 0 R (Item.10) 351 0 R (Item.11) 352 0 R (Item.12) 353 0 R (Item.13) 417 0 R] -/Limits [(Doc-Start) (Item.13)] ->> endobj -544 0 obj << -/Names [(Item.14) 418 0 R (Item.15) 419 0 R (Item.16) 420 0 R (Item.2) 277 0 R (Item.3) 278 0 R (Item.4) 303 0 R] -/Limits [(Item.14) (Item.4)] ->> endobj -545 0 obj << -/Names [(Item.5) 318 0 R (Item.6) 319 0 R (Item.7) 348 0 R (Item.8) 349 0 R (Item.9) 350 0 R (appendix.A) 98 0 R] -/Limits [(Item.5) (appendix.A)] ->> endobj -546 0 obj << -/Names [(cite.BLACS) 217 0 R (cite.BREZINA_VANEK) 179 0 R (cite.CAI_SARKIS) 292 0 R (cite.Cai_Widlund_92) 254 0 R (cite.EFSTATHIOU) 293 0 R (cite.MPI1) 183 0 R] -/Limits [(cite.BLACS) (cite.MPI1)] ->> endobj -547 0 obj << -/Names [(cite.MPI2) 216 0 R (cite.PSBLASGUIDE) 182 0 R (cite.SUPERLU) 227 0 R (cite.SUPERLUDIST) 228 0 R (cite.Saad_book) 284 0 R (cite.StubenGMD69_99) 279 0 R] -/Limits [(cite.MPI2) (cite.StubenGMD69_99)] ->> endobj -548 0 obj << -/Names [(cite.TUMINARO_TONG) 280 0 R (cite.UMFPACK) 226 0 R (cite.VANEK_MANDEL_BREZINA) 180 0 R (cite.aaecc_07) 282 0 R (cite.apnum_07) 283 0 R (cite.blas1) 215 0 R] -/Limits [(cite.TUMINARO_TONG) (cite.blas1)] ->> endobj -549 0 obj << -/Names [(cite.blas2) 214 0 R (cite.blas3) 213 0 R (cite.dd1_94) 255 0 R (cite.dd2_96) 178 0 R (cite.para_04) 281 0 R (cite.psblas_00) 181 0 R] -/Limits [(cite.blas2) (cite.psblas_00)] ->> endobj -550 0 obj << -/Names [(equation.1) 174 0 R (equation.2) 328 0 R (equation.3) 329 0 R (equation.4) 330 0 R (figure.1) 304 0 R (figure.2) 363 0 R] -/Limits [(equation.1) (figure.2)] ->> endobj -551 0 obj << -/Names [(figure.3) 380 0 R (figure.4) 381 0 R (figure.5) 382 0 R (page.1) 109 0 R (page.10) 270 0 R (page.11) 291 0 R] -/Limits [(figure.3) (page.11)] ->> endobj -552 0 obj << -/Names [(page.12) 302 0 R (page.13) 314 0 R (page.14) 327 0 R (page.15) 347 0 R (page.16) 362 0 R (page.17) 379 0 R] -/Limits [(page.12) (page.17)] ->> endobj -553 0 obj << -/Names [(page.18) 386 0 R (page.19) 391 0 R (page.2) 118 0 R (page.20) 397 0 R (page.21) 404 0 R (page.22) 416 0 R] -/Limits [(page.18) (page.22)] ->> endobj -554 0 obj << -/Names [(page.23) 425 0 R (page.24) 429 0 R (page.25) 435 0 R (page.26) 441 0 R (page.27) 449 0 R (page.28) 454 0 R] -/Limits [(page.23) (page.28)] ->> endobj -555 0 obj << -/Names [(page.29) 460 0 R (page.3) 199 0 R (page.30) 465 0 R (page.31) 471 0 R (page.32) 476 0 R (page.33) 480 0 R] -/Limits [(page.29) (page.33)] ->> endobj -556 0 obj << -/Names [(page.34) 484 0 R (page.4) 212 0 R (page.5) 225 0 R (page.6) 232 0 R (page.7) 237 0 R (page.8) 242 0 R] -/Limits [(page.34) (page.8)] ->> endobj -557 0 obj << -/Names [(page.9) 253 0 R (page.i) 122 0 R (page.ii) 128 0 R (page.iii) 156 0 R (page.iv) 162 0 R (section*.1) 10 0 R] -/Limits [(page.9) (section*.1)] ->> endobj -558 0 obj << -/Names [(section*.2) 157 0 R (section*.3) 102 0 R (section.1) 14 0 R (section.2) 18 0 R (section.3) 22 0 R (section.4) 46 0 R] -/Limits [(section*.2) (section.4)] ->> endobj -559 0 obj << -/Names [(section.5) 58 0 R (section.6) 66 0 R (section.7) 94 0 R (subsection.3.1) 26 0 R (subsection.3.2) 30 0 R (subsection.3.3) 34 0 R] -/Limits [(section.5) (subsection.3.3)] ->> endobj -560 0 obj << -/Names [(subsection.3.4) 38 0 R (subsection.3.5) 42 0 R (subsection.4.1) 50 0 R (subsection.4.2) 54 0 R (subsection.5.1) 62 0 R (subsection.6.1) 70 0 R] -/Limits [(subsection.3.4) (subsection.6.1)] ->> endobj 561 0 obj << -/Names [(subsection.6.2) 74 0 R (subsection.6.3) 78 0 R (subsection.6.4) 82 0 R (subsection.6.5) 86 0 R (subsection.6.6) 90 0 R (table.1) 354 0 R] -/Limits [(subsection.6.2) (table.1)] +/Names [(Doc-Start) 110 0 R (Item.1) 303 0 R (Item.10) 381 0 R (Item.11) 382 0 R (Item.12) 383 0 R (Item.13) 450 0 R (Item.14) 451 0 R (Item.15) 452 0 R (Item.16) 453 0 R (Item.2) 304 0 R (Item.3) 305 0 R (Item.4) 333 0 R (Item.5) 349 0 R (Item.6) 350 0 R (Item.7) 373 0 R (Item.8) 374 0 R (Item.9) 376 0 R (cite.BLACS) 237 0 R (cite.BREZINA_VANEK) 197 0 R (cite.CAI_SARKIS) 322 0 R (cite.Cai_Widlund_92) 273 0 R (cite.EFSTATHIOU) 323 0 R (cite.MPI1) 201 0 R (cite.MPI2) 236 0 R (cite.PSBLASGUIDE) 200 0 R (cite.SUPERLU) 247 0 R (cite.SUPERLUDIST) 248 0 R (cite.Saad_book) 312 0 R (cite.StubenGMD69_99) 307 0 R (cite.TUMINARO_TONG) 308 0 R (cite.UMFPACK) 246 0 R (cite.VANEK_MANDEL_BREZINA) 198 0 R (cite.aaecc_07) 310 0 R (cite.apnum_07) 311 0 R (cite.blas1) 235 0 R (cite.blas2) 234 0 R (cite.blas3) 233 0 R (cite.dd1_94) 274 0 R (cite.dd2_96) 196 0 R (cite.para_04) 309 0 R (cite.psblas_00) 199 0 R (equation.1) 183 0 R (equation.2) 361 0 R (equation.3) 362 0 R (equation.4) 365 0 R (figure.1) 334 0 R (figure.2) 399 0 R (figure.3) 416 0 R (figure.4) 417 0 R (figure.5) 418 0 R (page.1) 109 0 R (page.10) 278 0 R (page.11) 316 0 R (page.12) 327 0 R (page.13) 338 0 R (page.14) 360 0 R (page.15) 370 0 R (page.16) 393 0 R (page.17) 403 0 R (page.18) 422 0 R (page.19) 426 0 R (page.2) 124 0 R (page.20) 432 0 R (page.21) 437 0 R (page.22) 444 0 R (page.23) 460 0 R (page.24) 465 0 R (page.25) 470 0 R (page.26) 477 0 R (page.27) 481 0 R (page.28) 489 0 R (page.29) 494 0 R (page.3) 215 0 R (page.30) 500 0 R (page.31) 505 0 R (page.32) 512 0 R (page.33) 516 0 R (page.34) 520 0 R (page.4) 224 0 R (page.5) 241 0 R (page.6) 252 0 R (page.7) 256 0 R (page.8) 262 0 R (page.9) 266 0 R (page.i) 128 0 R (page.ii) 138 0 R (page.iii) 142 0 R (page.iv) 174 0 R (section*.1) 10 0 R (section*.2) 143 0 R (section*.3) 102 0 R (section.1) 14 0 R (section.2) 18 0 R (section.3) 22 0 R (section.4) 46 0 R (section.5) 58 0 R (section.6) 66 0 R (section.7) 94 0 R (section.A) 98 0 R (subsection.3.1) 26 0 R (subsection.3.2) 30 0 R (subsection.3.3) 34 0 R (subsection.3.4) 38 0 R (subsection.3.5) 42 0 R (subsection.4.1) 50 0 R (subsection.4.2) 54 0 R (subsection.5.1) 62 0 R (subsection.6.1) 70 0 R (subsection.6.2) 74 0 R (subsection.6.3) 78 0 R (subsection.6.4) 82 0 R (subsection.6.5) 86 0 R (subsection.6.6) 90 0 R (table.1) 387 0 R (table.2) 388 0 R (table.3) 466 0 R (table.4) 472 0 R (table.5) 389 0 R (title.0) 6 0 R] +/Limits [(Doc-Start) (title.0)] >> endobj 562 0 obj << -/Names [(table.2) 355 0 R (table.3) 430 0 R (table.4) 436 0 R (table.5) 356 0 R (title.0) 6 0 R] -/Limits [(table.2) (title.0)] +/Kids [561 0 R] >> endobj 563 0 obj << -/Kids [543 0 R 544 0 R 545 0 R 546 0 R 547 0 R 548 0 R] -/Limits [(Doc-Start) (cite.blas1)] +/Dests 562 0 R >> endobj 564 0 obj << -/Kids [549 0 R 550 0 R 551 0 R 552 0 R 553 0 R 554 0 R] -/Limits [(cite.blas2) (page.28)] ->> endobj -565 0 obj << -/Kids [555 0 R 556 0 R 557 0 R 558 0 R 559 0 R 560 0 R] -/Limits [(page.29) (subsection.6.1)] ->> endobj -566 0 obj << -/Kids [561 0 R 562 0 R] -/Limits [(subsection.6.2) (title.0)] ->> endobj -567 0 obj << -/Kids [563 0 R 564 0 R 565 0 R 566 0 R] -/Limits [(Doc-Start) (title.0)] ->> endobj -568 0 obj << -/Dests 567 0 R ->> endobj -569 0 obj << /Type /Catalog -/Pages 541 0 R -/Outlines 542 0 R -/Names 568 0 R - /PageMode/UseOutlines/PageLabels << /Nums [0 << /S /D >> 2 << /S /r >> 6 << /S /D >> ] >> +/Pages 559 0 R +/Outlines 560 0 R +/Names 563 0 R + /PageMode /UseOutlines /PageLabels << /Nums [0 << /S /D >> 2 << /S /r >> 6 << /S /D >> ] >> /OpenAction 105 0 R >> endobj -570 0 obj << - /Title (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS, V. 1.0) /Subject (MultiLevel Domain Decomposition Parallel Preconditioners Package) /Keywords (Parallel Numerical Software, Algebraic Multilevel Preconditioners, Sparse Iterative Solvers, PSBLAS, MPI) /Creator (pdfLaTeX) /Producer ($Id: userguide.tex 2008-04-08 Pasqua D'Ambra, Daniela di Serafino, Salvatore Filippone$) /Author()/Title()/Subject()/Creator(LaTeX with hyperref package)/Producer(pdfTeX-1.40.3)/Keywords() -/CreationDate (D:20080904134744+02'00') -/ModDate (D:20080904134744+02'00') -/Trapped /False -/PTEX.Fullbanner (This is pdfTeX using libpoppler, Version 3.141592-1.40.3-2.2 (Web2C 7.5.6) kpathsea version 3.5.6) +565 0 obj << + /Title (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS, V. 1.0) /Subject (MultiLevel Domain Decomposition Parallel Preconditioners Package) /Keywords (Parallel Numerical Software, Algebraic Multilevel Preconditioners, Sparse Iterative Solvers, PSBLAS, MPI) /Creator (pdfLaTeX) /Producer ($Id: userguide.tex 2008-04-08 Pasqua D'Ambra, Daniela di Serafino, Salvatore Filippone$) /Author()/Title()/Subject()/Creator(LaTeX with hyperref package)/Producer(pdfeTeX-1.21a)/Keywords() +/CreationDate (D:20080909143504+02'00') +/PTEX.Fullbanner (This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) kpathsea version 3.5.4) >> endobj xref -0 571 +0 566 0000000001 65535 f 0000000002 00000 f 0000000003 00000 f 0000000004 00000 f 0000000000 00000 f -0000000015 00000 n -0000003823 00000 n -0000423307 00000 n -0000000058 00000 n -0000000109 00000 n -0000008280 00000 n -0000423235 00000 n -0000000155 00000 n -0000000182 00000 n -0000029341 00000 n -0000423149 00000 n -0000000228 00000 n -0000000265 00000 n -0000036757 00000 n -0000423063 00000 n -0000000311 00000 n -0000000349 00000 n -0000045440 00000 n -0000422940 00000 n -0000000395 00000 n -0000000447 00000 n -0000045498 00000 n -0000422866 00000 n -0000000498 00000 n -0000000534 00000 n -0000052181 00000 n -0000422779 00000 n -0000000585 00000 n -0000000638 00000 n -0000052239 00000 n -0000422692 00000 n -0000000689 00000 n -0000000733 00000 n -0000065964 00000 n -0000422605 00000 n -0000000784 00000 n -0000000820 00000 n -0000066022 00000 n -0000422531 00000 n -0000000871 00000 n -0000000919 00000 n -0000075605 00000 n -0000422408 00000 n -0000000965 00000 n -0000001029 00000 n -0000092460 00000 n -0000422334 00000 n -0000001080 00000 n -0000001138 00000 n -0000120507 00000 n -0000422260 00000 n -0000001189 00000 n -0000001232 00000 n -0000148355 00000 n -0000422137 00000 n -0000001278 00000 n -0000001314 00000 n -0000158627 00000 n -0000422076 00000 n -0000001365 00000 n -0000001396 00000 n -0000184873 00000 n -0000421953 00000 n -0000001442 00000 n -0000001477 00000 n -0000188920 00000 n -0000421879 00000 n -0000001528 00000 n -0000001577 00000 n -0000195733 00000 n -0000421792 00000 n -0000001628 00000 n -0000001676 00000 n -0000235522 00000 n -0000421705 00000 n -0000001727 00000 n -0000001775 00000 n -0000245208 00000 n -0000421618 00000 n -0000001826 00000 n -0000001875 00000 n -0000247574 00000 n -0000421531 00000 n -0000001926 00000 n -0000001975 00000 n -0000250436 00000 n -0000421457 00000 n -0000002026 00000 n -0000002076 00000 n -0000252997 00000 n -0000421371 00000 n -0000002122 00000 n -0000002157 00000 n -0000257402 00000 n -0000421283 00000 n -0000002204 00000 n -0000002233 00000 n -0000264466 00000 n -0000421207 00000 n -0000002281 00000 n -0000002311 00000 n -0000003586 00000 n -0000003880 00000 n -0000002363 00000 n -0000003705 00000 n -0000003764 00000 n -0000417638 00000 n -0000419778 00000 n -0000418786 00000 n -0000420066 00000 n +0000000009 00000 n +0000004495 00000 n +0000517281 00000 n +0000000052 00000 n +0000000103 00000 n +0000010148 00000 n +0000517209 00000 n +0000000149 00000 n +0000000176 00000 n +0000041823 00000 n +0000517123 00000 n +0000000222 00000 n +0000000259 00000 n +0000052400 00000 n +0000517037 00000 n +0000000305 00000 n +0000000343 00000 n +0000064811 00000 n +0000516914 00000 n +0000000389 00000 n +0000000441 00000 n +0000064873 00000 n +0000516840 00000 n +0000000492 00000 n +0000000528 00000 n +0000073803 00000 n +0000516753 00000 n +0000000579 00000 n +0000000632 00000 n +0000073865 00000 n +0000516666 00000 n +0000000683 00000 n +0000000727 00000 n +0000089539 00000 n +0000516579 00000 n +0000000778 00000 n +0000000814 00000 n +0000089601 00000 n +0000516505 00000 n +0000000865 00000 n +0000000913 00000 n +0000102586 00000 n +0000516382 00000 n +0000000959 00000 n +0000001023 00000 n +0000123457 00000 n +0000516308 00000 n +0000001074 00000 n +0000001132 00000 n +0000156797 00000 n +0000516234 00000 n +0000001183 00000 n +0000001226 00000 n +0000193212 00000 n +0000516111 00000 n +0000001272 00000 n +0000001308 00000 n +0000207168 00000 n +0000516050 00000 n +0000001359 00000 n +0000001390 00000 n +0000240962 00000 n +0000515927 00000 n +0000001436 00000 n +0000001471 00000 n +0000246186 00000 n +0000515853 00000 n +0000001522 00000 n +0000001571 00000 n +0000256379 00000 n +0000515766 00000 n +0000001622 00000 n +0000001670 00000 n +0000307742 00000 n +0000515679 00000 n +0000001721 00000 n +0000001769 00000 n +0000318914 00000 n +0000515592 00000 n +0000001820 00000 n +0000001869 00000 n +0000322060 00000 n +0000515505 00000 n +0000001920 00000 n +0000001969 00000 n +0000325750 00000 n +0000515431 00000 n +0000002020 00000 n +0000002070 00000 n +0000329159 00000 n +0000515345 00000 n +0000002116 00000 n +0000002151 00000 n +0000333911 00000 n +0000515257 00000 n +0000002197 00000 n +0000002226 00000 n +0000344206 00000 n +0000515181 00000 n +0000002274 00000 n +0000002304 00000 n 0000004247 00000 n -0000004069 00000 n -0000003978 00000 n -0000004188 00000 n -0000008338 00000 n -0000008102 00000 n -0000004288 00000 n -0000008221 00000 n -0000418643 00000 n -0000417782 00000 n -0000008752 00000 n -0000008574 00000 n -0000008436 00000 n -0000008693 00000 n -0000015644 00000 n -0000015795 00000 n -0000015946 00000 n -0000016097 00000 n -0000016248 00000 n -0000016405 00000 n -0000016562 00000 n -0000016719 00000 n -0000016875 00000 n -0000017031 00000 n -0000017182 00000 n -0000017339 00000 n -0000017496 00000 n -0000017647 00000 n -0000017804 00000 n -0000017954 00000 n -0000018111 00000 n -0000018268 00000 n -0000018423 00000 n -0000018578 00000 n -0000018735 00000 n -0000018892 00000 n -0000019043 00000 n -0000019195 00000 n -0000019465 00000 n -0000015321 00000 n -0000008824 00000 n -0000019347 00000 n -0000019406 00000 n -0000417494 00000 n -0000019879 00000 n -0000019701 00000 n -0000019563 00000 n -0000019820 00000 n -0000028391 00000 n -0000028545 00000 n -0000028706 00000 n -0000028874 00000 n -0000029031 00000 n -0000029189 00000 n +0000004556 00000 n +0000002356 00000 n +0000004369 00000 n +0000004432 00000 n +0000512985 00000 n +0000502018 00000 n +0000512823 00000 n +0000501274 00000 n +0000493239 00000 n +0000501112 00000 n +0000492172 00000 n +0000482952 00000 n +0000492011 00000 n +0000514040 00000 n +0000005033 00000 n +0000004848 00000 n +0000004654 00000 n +0000004970 00000 n +0000010210 00000 n +0000009963 00000 n +0000005074 00000 n +0000010085 00000 n +0000481401 00000 n +0000463202 00000 n +0000481240 00000 n +0000462194 00000 n +0000451797 00000 n +0000462031 00000 n +0000010774 00000 n +0000010589 00000 n +0000010308 00000 n +0000010711 00000 n 0000028240 00000 n -0000029460 00000 n -0000028053 00000 n -0000019951 00000 n -0000419634 00000 n -0000029399 00000 n -0000418070 00000 n -0000419211 00000 n -0000420183 00000 n -0000272084 00000 n -0000264525 00000 n -0000272320 00000 n -0000271789 00000 n -0000271730 00000 n -0000272143 00000 n -0000033676 00000 n -0000033828 00000 n -0000033980 00000 n -0000034131 00000 n -0000034282 00000 n -0000034432 00000 n -0000034584 00000 n -0000034736 00000 n -0000033489 00000 n -0000029597 00000 n -0000036545 00000 n -0000036394 00000 n -0000036815 00000 n -0000036247 00000 n -0000034821 00000 n -0000036698 00000 n -0000419922 00000 n -0000044153 00000 n -0000044306 00000 n -0000044459 00000 n -0000044612 00000 n -0000044763 00000 n -0000044914 00000 n -0000045067 00000 n -0000045225 00000 n -0000045556 00000 n -0000043958 00000 n -0000036926 00000 n -0000045381 00000 n -0000265056 00000 n -0000265115 00000 n -0000271907 00000 n -0000271848 00000 n -0000265174 00000 n -0000051655 00000 n -0000051810 00000 n -0000051963 00000 n -0000051504 00000 n -0000052297 00000 n -0000051341 00000 n -0000045680 00000 n -0000052122 00000 n -0000264938 00000 n -0000264997 00000 n -0000271966 00000 n -0000056476 00000 n -0000056298 00000 n -0000052434 00000 n -0000056417 00000 n -0000060642 00000 n -0000060852 00000 n -0000060503 00000 n -0000056574 00000 n -0000060793 00000 n -0000420300 00000 n -0000066080 00000 n -0000065786 00000 n -0000060950 00000 n -0000065905 00000 n -0000074771 00000 n -0000074933 00000 n -0000075087 00000 n -0000075241 00000 n -0000075394 00000 n -0000090827 00000 n -0000074620 00000 n -0000075663 00000 n -0000074441 00000 n -0000066191 00000 n -0000075546 00000 n -0000264820 00000 n -0000264879 00000 n -0000090988 00000 n -0000091148 00000 n -0000091313 00000 n -0000091472 00000 n -0000091627 00000 n -0000091783 00000 n -0000091939 00000 n -0000092092 00000 n -0000092244 00000 n -0000107127 00000 n -0000107284 00000 n -0000092695 00000 n -0000090616 00000 n -0000075774 00000 n -0000092401 00000 n -0000418500 00000 n -0000419494 00000 n -0000419070 00000 n -0000418214 00000 n -0000417927 00000 n -0000092518 00000 n -0000092577 00000 n -0000092636 00000 n -0000272202 00000 n -0000272261 00000 n -0000264584 00000 n -0000264643 00000 n -0000264702 00000 n -0000272025 00000 n -0000107442 00000 n -0000107596 00000 n -0000106976 00000 n -0000107809 00000 n -0000106805 00000 n -0000092897 00000 n -0000107750 00000 n -0000264761 00000 n -0000271671 00000 n -0000119665 00000 n -0000119818 00000 n -0000119970 00000 n -0000120119 00000 n -0000120280 00000 n -0000120624 00000 n -0000119494 00000 n -0000107998 00000 n -0000120448 00000 n -0000120565 00000 n -0000132212 00000 n -0000131358 00000 n -0000131514 00000 n -0000131681 00000 n -0000131837 00000 n -0000131993 00000 n -0000131207 00000 n -0000132392 00000 n -0000131028 00000 n -0000120813 00000 n -0000132153 00000 n -0000418929 00000 n -0000418357 00000 n -0000419354 00000 n -0000132274 00000 n -0000132333 00000 n -0000420417 00000 n -0000136696 00000 n -0000136857 00000 n -0000137019 00000 n -0000137423 00000 n -0000136541 00000 n -0000132606 00000 n -0000137178 00000 n -0000137237 00000 n -0000137299 00000 n -0000137361 00000 n -0000146918 00000 n -0000147077 00000 n -0000147225 00000 n -0000147380 00000 n -0000147532 00000 n -0000147681 00000 n -0000147831 00000 n -0000147982 00000 n -0000148139 00000 n -0000157744 00000 n -0000157899 00000 n -0000158055 00000 n -0000146767 00000 n -0000148767 00000 n -0000146556 00000 n -0000137612 00000 n -0000148296 00000 n -0000148413 00000 n -0000148472 00000 n -0000148531 00000 n -0000148590 00000 n -0000148649 00000 n -0000148708 00000 n -0000158566 00000 n -0000200916 00000 n -0000231297 00000 n -0000158207 00000 n -0000158357 00000 n -0000158685 00000 n -0000157573 00000 n -0000148891 00000 n -0000158507 00000 n -0000173676 00000 n -0000168207 00000 n -0000168362 00000 n -0000168521 00000 n -0000168673 00000 n -0000168824 00000 n -0000168979 00000 n -0000169129 00000 n -0000169279 00000 n -0000169429 00000 n -0000169580 00000 n -0000169731 00000 n -0000168056 00000 n -0000169941 00000 n -0000167829 00000 n -0000158822 00000 n -0000169882 00000 n -0000177267 00000 n -0000177329 00000 n -0000177391 00000 n -0000173737 00000 n -0000173498 00000 n -0000170052 00000 n -0000173617 00000 n -0000177057 00000 n -0000177453 00000 n -0000176918 00000 n -0000173835 00000 n -0000177208 00000 n -0000420534 00000 n -0000184657 00000 n -0000184931 00000 n -0000184518 00000 n -0000177551 00000 n -0000184814 00000 n -0000188561 00000 n -0000188709 00000 n -0000188410 00000 n -0000188978 00000 n -0000188255 00000 n -0000185107 00000 n -0000188861 00000 n -0000194474 00000 n -0000194623 00000 n -0000194773 00000 n -0000194923 00000 n -0000195073 00000 n -0000195225 00000 n -0000195373 00000 n -0000195522 00000 n -0000196027 00000 n -0000194279 00000 n -0000189102 00000 n -0000195674 00000 n -0000195791 00000 n -0000195850 00000 n -0000195909 00000 n -0000195968 00000 n -0000200706 00000 n -0000200979 00000 n -0000200567 00000 n -0000196151 00000 n -0000200857 00000 n -0000211082 00000 n -0000210840 00000 n -0000201077 00000 n -0000210959 00000 n -0000211018 00000 n -0000221586 00000 n -0000221859 00000 n -0000221447 00000 n -0000211219 00000 n -0000221737 00000 n -0000221796 00000 n -0000420651 00000 n -0000231361 00000 n -0000231119 00000 n -0000222022 00000 n -0000231238 00000 n -0000234993 00000 n -0000235152 00000 n -0000235311 00000 n -0000234842 00000 n -0000235580 00000 n -0000234679 00000 n -0000231498 00000 n -0000235463 00000 n -0000244998 00000 n -0000245266 00000 n -0000244859 00000 n -0000235704 00000 n -0000245149 00000 n -0000247363 00000 n -0000247212 00000 n -0000247632 00000 n -0000247065 00000 n -0000245442 00000 n -0000247515 00000 n -0000250225 00000 n -0000250494 00000 n -0000250086 00000 n -0000247756 00000 n -0000250377 00000 n -0000252779 00000 n -0000252628 00000 n -0000253055 00000 n -0000252481 00000 n -0000250618 00000 n -0000252938 00000 n -0000420768 00000 n -0000257460 00000 n -0000257224 00000 n -0000253166 00000 n -0000257343 00000 n -0000265233 00000 n -0000264288 00000 n -0000257571 00000 n -0000264407 00000 n -0000272379 00000 n -0000271493 00000 n -0000265357 00000 n -0000271612 00000 n -0000272490 00000 n -0000272515 00000 n -0000272746 00000 n -0000272805 00000 n -0000273501 00000 n -0000274065 00000 n -0000274168 00000 n -0000274205 00000 n -0000274834 00000 n -0000275229 00000 n -0000275865 00000 n -0000276486 00000 n -0000277155 00000 n -0000277770 00000 n -0000278282 00000 n -0000278926 00000 n -0000279410 00000 n -0000279767 00000 n -0000280408 00000 n -0000291717 00000 n -0000292072 00000 n -0000302344 00000 n -0000302707 00000 n -0000312408 00000 n -0000312757 00000 n -0000316129 00000 n -0000316455 00000 n -0000326219 00000 n -0000326548 00000 n -0000328896 00000 n -0000329124 00000 n -0000331882 00000 n -0000332109 00000 n -0000338092 00000 n -0000338351 00000 n -0000355856 00000 n -0000356426 00000 n -0000364952 00000 n -0000365303 00000 n -0000367320 00000 n -0000367545 00000 n -0000369908 00000 n -0000370143 00000 n -0000373613 00000 n -0000373959 00000 n -0000375382 00000 n -0000375607 00000 n -0000377214 00000 n -0000377448 00000 n -0000393309 00000 n -0000393723 00000 n -0000401063 00000 n -0000401344 00000 n -0000416936 00000 n -0000420869 00000 n -0000420987 00000 n -0000421064 00000 n -0000421134 00000 n -0000423405 00000 n -0000423578 00000 n -0000423744 00000 n -0000423913 00000 n -0000424132 00000 n -0000424360 00000 n -0000424593 00000 n -0000424799 00000 n -0000424987 00000 n -0000425160 00000 n -0000425330 00000 n -0000425499 00000 n -0000425669 00000 n -0000425838 00000 n -0000426002 00000 n -0000426175 00000 n -0000426360 00000 n -0000426560 00000 n -0000426780 00000 n -0000426987 00000 n -0000427137 00000 n -0000427251 00000 n -0000427363 00000 n -0000427479 00000 n -0000427563 00000 n -0000427658 00000 n -0000427696 00000 n -0000427893 00000 n +0000024002 00000 n +0000010846 00000 n +0000028114 00000 n +0000028177 00000 n +0000024328 00000 n +0000450739 00000 n +0000438735 00000 n +0000450577 00000 n +0000024481 00000 n +0000024634 00000 n +0000024788 00000 n +0000024942 00000 n +0000025103 00000 n +0000025264 00000 n +0000025424 00000 n +0000025583 00000 n +0000025744 00000 n +0000025898 00000 n +0000026059 00000 n +0000026220 00000 n +0000026373 00000 n +0000026534 00000 n +0000026686 00000 n +0000026847 00000 n +0000027008 00000 n +0000027168 00000 n +0000027329 00000 n +0000027490 00000 n +0000027651 00000 n +0000027805 00000 n +0000027959 00000 n +0000028804 00000 n +0000028619 00000 n +0000028338 00000 n +0000028741 00000 n +0000041949 00000 n +0000040507 00000 n +0000028876 00000 n +0000040697 00000 n +0000437584 00000 n +0000421028 00000 n +0000437422 00000 n +0000040851 00000 n +0000041885 00000 n +0000419939 00000 n +0000409480 00000 n +0000419777 00000 n +0000408546 00000 n +0000404382 00000 n +0000408385 00000 n +0000041008 00000 n +0000041173 00000 n +0000041344 00000 n +0000041505 00000 n +0000041667 00000 n +0000514157 00000 n +0000354879 00000 n +0000344269 00000 n +0000355131 00000 n +0000354564 00000 n +0000354501 00000 n +0000354942 00000 n +0000049634 00000 n +0000048356 00000 n +0000042086 00000 n +0000048546 00000 n +0000048701 00000 n +0000048857 00000 n +0000049013 00000 n +0000049168 00000 n +0000049324 00000 n +0000049479 00000 n +0000052462 00000 n +0000051877 00000 n +0000049719 00000 n +0000052337 00000 n +0000052027 00000 n +0000402949 00000 n +0000386662 00000 n +0000402787 00000 n +0000052181 00000 n +0000064935 00000 n +0000063287 00000 n +0000052573 00000 n +0000064748 00000 n +0000063485 00000 n +0000063641 00000 n +0000063798 00000 n +0000063955 00000 n +0000064111 00000 n +0000064267 00000 n +0000064424 00000 n +0000064587 00000 n +0000344835 00000 n +0000344898 00000 n +0000354690 00000 n +0000354627 00000 n +0000344960 00000 n +0000073927 00000 n +0000072940 00000 n +0000065059 00000 n +0000073740 00000 n +0000073106 00000 n +0000073260 00000 n +0000073418 00000 n +0000073577 00000 n +0000344709 00000 n +0000344772 00000 n +0000354753 00000 n +0000078330 00000 n +0000078145 00000 n +0000074064 00000 n +0000078267 00000 n +0000083039 00000 n +0000082680 00000 n +0000078428 00000 n +0000082976 00000 n +0000082822 00000 n +0000514274 00000 n +0000089663 00000 n +0000089354 00000 n +0000083137 00000 n +0000089476 00000 n +0000102648 00000 n +0000101391 00000 n +0000089774 00000 n +0000102523 00000 n +0000101573 00000 n +0000101727 00000 n +0000101893 00000 n +0000102051 00000 n +0000102209 00000 n +0000102366 00000 n +0000344583 00000 n +0000344646 00000 n +0000123708 00000 n +0000121558 00000 n +0000102759 00000 n +0000123394 00000 n +0000121772 00000 n +0000121938 00000 n +0000122103 00000 n +0000122275 00000 n +0000122439 00000 n +0000122598 00000 n +0000122758 00000 n +0000122918 00000 n +0000123076 00000 n +0000385896 00000 n +0000379219 00000 n +0000385735 00000 n +0000378878 00000 n +0000376580 00000 n +0000378720 00000 n +0000376198 00000 n +0000373143 00000 n +0000376039 00000 n +0000372604 00000 n +0000369562 00000 n +0000372443 00000 n +0000368757 00000 n +0000364691 00000 n +0000368596 00000 n +0000123519 00000 n +0000123582 00000 n +0000123645 00000 n +0000123233 00000 n +0000355005 00000 n +0000355068 00000 n +0000344332 00000 n +0000344395 00000 n +0000344458 00000 n +0000354816 00000 n +0000141183 00000 n +0000140152 00000 n +0000123910 00000 n +0000141120 00000 n +0000140326 00000 n +0000140480 00000 n +0000140642 00000 n +0000140804 00000 n +0000140962 00000 n +0000344520 00000 n +0000354438 00000 n +0000156922 00000 n +0000155753 00000 n +0000141372 00000 n +0000156734 00000 n +0000155927 00000 n +0000156084 00000 n +0000156242 00000 n +0000156397 00000 n +0000156562 00000 n +0000156859 00000 n +0000171226 00000 n +0000171415 00000 n +0000170011 00000 n +0000157111 00000 n +0000171163 00000 n +0000170193 00000 n +0000364347 00000 n +0000361638 00000 n +0000364188 00000 n +0000361176 00000 n +0000357724 00000 n +0000361015 00000 n +0000357419 00000 n +0000355305 00000 n +0000357261 00000 n +0000171289 00000 n +0000171352 00000 n +0000170347 00000 n +0000170507 00000 n +0000170679 00000 n +0000170839 00000 n +0000170998 00000 n +0000514391 00000 n +0000177944 00000 n +0000177038 00000 n +0000171629 00000 n +0000177690 00000 n +0000177753 00000 n +0000177817 00000 n +0000177196 00000 n +0000177361 00000 n +0000177881 00000 n +0000177527 00000 n +0000193652 00000 n +0000191365 00000 n +0000178133 00000 n +0000193149 00000 n +0000191579 00000 n +0000191733 00000 n +0000193274 00000 n +0000193337 00000 n +0000191896 00000 n +0000193400 00000 n +0000192050 00000 n +0000192210 00000 n +0000192366 00000 n +0000192520 00000 n +0000193463 00000 n +0000193526 00000 n +0000193589 00000 n +0000192674 00000 n +0000192828 00000 n +0000192989 00000 n +0000207104 00000 n +0000263237 00000 n +0000302086 00000 n +0000207230 00000 n +0000206083 00000 n +0000193776 00000 n +0000207041 00000 n +0000206257 00000 n +0000206417 00000 n +0000206577 00000 n +0000206733 00000 n +0000206888 00000 n +0000226874 00000 n +0000222625 00000 n +0000220464 00000 n +0000207367 00000 n +0000222562 00000 n +0000220694 00000 n +0000220848 00000 n +0000221005 00000 n +0000221167 00000 n +0000221323 00000 n +0000221477 00000 n +0000221635 00000 n +0000221790 00000 n +0000221944 00000 n +0000222098 00000 n +0000222253 00000 n +0000222408 00000 n +0000231536 00000 n +0000231599 00000 n +0000231663 00000 n +0000226938 00000 n +0000226689 00000 n +0000222736 00000 n +0000226811 00000 n +0000231727 00000 n +0000231177 00000 n +0000227036 00000 n +0000231473 00000 n +0000231319 00000 n +0000514508 00000 n +0000241024 00000 n +0000240597 00000 n +0000231825 00000 n +0000240899 00000 n +0000240739 00000 n +0000246248 00000 n +0000245501 00000 n +0000241200 00000 n +0000246123 00000 n +0000245659 00000 n +0000245813 00000 n +0000245967 00000 n +0000256693 00000 n +0000254884 00000 n +0000246372 00000 n +0000256316 00000 n +0000255082 00000 n +0000255236 00000 n +0000255389 00000 n +0000255543 00000 n +0000255697 00000 n +0000256441 00000 n +0000256504 00000 n +0000256567 00000 n +0000256630 00000 n +0000255853 00000 n +0000256007 00000 n +0000256161 00000 n +0000263301 00000 n +0000262878 00000 n +0000256817 00000 n +0000263174 00000 n +0000263020 00000 n +0000276273 00000 n +0000276024 00000 n +0000263399 00000 n +0000276146 00000 n +0000276209 00000 n +0000290006 00000 n +0000289583 00000 n +0000276410 00000 n +0000289879 00000 n +0000289725 00000 n +0000289942 00000 n +0000514625 00000 n +0000302149 00000 n +0000301901 00000 n +0000290169 00000 n +0000302023 00000 n +0000307804 00000 n +0000306878 00000 n +0000302286 00000 n +0000307679 00000 n +0000307044 00000 n +0000307198 00000 n +0000307360 00000 n +0000307523 00000 n +0000318976 00000 n +0000318553 00000 n +0000307928 00000 n +0000318851 00000 n +0000318695 00000 n +0000322122 00000 n +0000321537 00000 n +0000319152 00000 n +0000321997 00000 n +0000321687 00000 n +0000321841 00000 n +0000325812 00000 n +0000325389 00000 n +0000322246 00000 n +0000325687 00000 n +0000325531 00000 n +0000329221 00000 n +0000328629 00000 n +0000325936 00000 n +0000329096 00000 n +0000328779 00000 n +0000328933 00000 n +0000514742 00000 n +0000333973 00000 n +0000333726 00000 n +0000329332 00000 n +0000333848 00000 n +0000345023 00000 n +0000344021 00000 n +0000334084 00000 n +0000344143 00000 n +0000355194 00000 n +0000354253 00000 n +0000345147 00000 n +0000354375 00000 n +0000357650 00000 n +0000357626 00000 n +0000361484 00000 n +0000361384 00000 n +0000364588 00000 n +0000364550 00000 n +0000369326 00000 n +0000369061 00000 n +0000373023 00000 n +0000372813 00000 n +0000376467 00000 n +0000376411 00000 n +0000379124 00000 n +0000379094 00000 n +0000386396 00000 n +0000386136 00000 n +0000403859 00000 n +0000403485 00000 n +0000409140 00000 n +0000408874 00000 n +0000420563 00000 n +0000420249 00000 n +0000438349 00000 n +0000437979 00000 n +0000451407 00000 n +0000451072 00000 n +0000462799 00000 n +0000462521 00000 n +0000482377 00000 n +0000481949 00000 n +0000492777 00000 n +0000492501 00000 n +0000501760 00000 n +0000501536 00000 n +0000513673 00000 n +0000513326 00000 n +0000514843 00000 n +0000514961 00000 n +0000515038 00000 n +0000515108 00000 n +0000517379 00000 n +0000519847 00000 n +0000519886 00000 n +0000519924 00000 n +0000520123 00000 n trailer -<< /Size 571 -/Root 569 0 R -/Info 570 0 R -/ID [<136871EED177BE6899DEDAD9C7B9BCDB> <136871EED177BE6899DEDAD9C7B9BCDB>] >> +<< +/Size 566 +/Root 564 0 R +/Info 565 0 R +/ID [ ] +>> startxref -428636 +520798 %%EOF diff --git a/docs/src/userhtml.tex b/docs/src/userhtml.tex index 2dbc75f1..0f575c24 100644 --- a/docs/src/userhtml.tex +++ b/docs/src/userhtml.tex @@ -104,7 +104,7 @@ based on PSBLAS}\\[3ex] %\today Software version: 1.0\\ %\today -July 24, 2008 +Sept. 9th, 2008 \clearpage \ \\ \thispagestyle{empty} diff --git a/examples/fileread/data_input.f90 b/examples/fileread/data_input.f90 index 32aae9fb..9a3c145b 100644 --- a/examples/fileread/data_input.f90 +++ b/examples/fileread/data_input.f90 @@ -40,52 +40,144 @@ module data_input interface read_data module procedure read_char, read_int,& - & read_double, read_single + & read_double, read_single,& + & string_read_char, string_read_int,& + & string_read_double, string_read_single end interface read_data - + interface trim_string + module procedure trim_string + end interface + + character(len=4096), private :: charbuf + character, private, parameter :: def_marker="!" + contains - subroutine read_char(val,file) + subroutine read_char(val,file,marker) character(len=*), intent(out) :: val integer, intent(in) :: file + character(len=1), optional, intent(in) :: marker + + read(file,'(a)')charbuf + call read_data(val,charbuf,marker) + + end subroutine read_char + + subroutine read_int(val,file,marker) + integer, intent(out) :: val + integer, intent(in) :: file + character(len=1), optional, intent(in) :: marker + + read(file,'(a)')charbuf + call read_data(val,charbuf,marker) + + end subroutine read_int + subroutine read_single(val,file,marker) + use psb_base_mod + real(psb_spk_), intent(out) :: val + integer, intent(in) :: file + character(len=1), optional, intent(in) :: marker + + read(file,'(a)')charbuf + call read_data(val,charbuf,marker) + + end subroutine read_single + subroutine read_double(val,file,marker) + use psb_base_mod + real(psb_dpk_), intent(out) :: val + integer, intent(in) :: file + character(len=1), optional, intent(in) :: marker + + read(file,'(a)')charbuf + call read_data(val,charbuf,marker) + + end subroutine read_double + + subroutine string_read_char(val,file,marker) + character(len=*), intent(out) :: val + character(len=*), intent(in) :: file + character(len=1), optional, intent(in) :: marker + character(len=1) :: marker_ character(len=1024) :: charbuf integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if read(file,'(a)')charbuf charbuf = adjustl(charbuf) - idx=index(charbuf,"!") + idx=index(charbuf,marker_) read(charbuf(1:idx-1),'(a)') val - end subroutine read_char - subroutine read_int(val,file) + end subroutine string_read_char + + subroutine string_read_int(val,file,marker) integer, intent(out) :: val - integer, intent(in) :: file + character(len=*), intent(in) :: file + character(len=1), optional, intent(in) :: marker + character(len=1) :: marker_ character(len=1024) :: charbuf integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if read(file,'(a)')charbuf charbuf = adjustl(charbuf) - idx=index(charbuf,"!") + idx=index(charbuf,marker_) read(charbuf(1:idx-1),*) val - end subroutine read_int - subroutine read_single(val,file) + end subroutine string_read_int + subroutine string_read_single(val,file,marker) use psb_base_mod real(psb_spk_), intent(out) :: val - integer, intent(in) :: file + character(len=*), intent(in) :: file + character(len=1), optional, intent(in) :: marker + character(len=1) :: marker_ character(len=1024) :: charbuf integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if read(file,'(a)')charbuf charbuf = adjustl(charbuf) - idx=index(charbuf,"!") + idx=index(charbuf,marker_) read(charbuf(1:idx-1),*) val - end subroutine read_single - subroutine read_double(val,file) + end subroutine string_read_single + subroutine string_read_double(val,file,marker) use psb_base_mod real(psb_dpk_), intent(out) :: val - integer, intent(in) :: file + character(len=*), intent(in) :: file + character(len=1), optional, intent(in) :: marker + character(len=1) :: marker_ character(len=1024) :: charbuf integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if read(file,'(a)')charbuf charbuf = adjustl(charbuf) - idx=index(charbuf,"!") + idx=index(charbuf,marker_) read(charbuf(1:idx-1),*) val - end subroutine read_double + end subroutine string_read_double + + function trim_string(string,marker) + character(len=*), intent(in) :: string + character(len=1), optional, intent(in) :: marker + character(len=len(string)) :: trim_string + character(len=1) :: marker_ + integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if + idx=index(string,marker_) + trim_string = adjustl(string(idx:)) + end function trim_string end module data_input diff --git a/tests/fileread/data_input.f90 b/tests/fileread/data_input.f90 index 32aae9fb..9a3c145b 100644 --- a/tests/fileread/data_input.f90 +++ b/tests/fileread/data_input.f90 @@ -40,52 +40,144 @@ module data_input interface read_data module procedure read_char, read_int,& - & read_double, read_single + & read_double, read_single,& + & string_read_char, string_read_int,& + & string_read_double, string_read_single end interface read_data - + interface trim_string + module procedure trim_string + end interface + + character(len=4096), private :: charbuf + character, private, parameter :: def_marker="!" + contains - subroutine read_char(val,file) + subroutine read_char(val,file,marker) character(len=*), intent(out) :: val integer, intent(in) :: file + character(len=1), optional, intent(in) :: marker + + read(file,'(a)')charbuf + call read_data(val,charbuf,marker) + + end subroutine read_char + + subroutine read_int(val,file,marker) + integer, intent(out) :: val + integer, intent(in) :: file + character(len=1), optional, intent(in) :: marker + + read(file,'(a)')charbuf + call read_data(val,charbuf,marker) + + end subroutine read_int + subroutine read_single(val,file,marker) + use psb_base_mod + real(psb_spk_), intent(out) :: val + integer, intent(in) :: file + character(len=1), optional, intent(in) :: marker + + read(file,'(a)')charbuf + call read_data(val,charbuf,marker) + + end subroutine read_single + subroutine read_double(val,file,marker) + use psb_base_mod + real(psb_dpk_), intent(out) :: val + integer, intent(in) :: file + character(len=1), optional, intent(in) :: marker + + read(file,'(a)')charbuf + call read_data(val,charbuf,marker) + + end subroutine read_double + + subroutine string_read_char(val,file,marker) + character(len=*), intent(out) :: val + character(len=*), intent(in) :: file + character(len=1), optional, intent(in) :: marker + character(len=1) :: marker_ character(len=1024) :: charbuf integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if read(file,'(a)')charbuf charbuf = adjustl(charbuf) - idx=index(charbuf,"!") + idx=index(charbuf,marker_) read(charbuf(1:idx-1),'(a)') val - end subroutine read_char - subroutine read_int(val,file) + end subroutine string_read_char + + subroutine string_read_int(val,file,marker) integer, intent(out) :: val - integer, intent(in) :: file + character(len=*), intent(in) :: file + character(len=1), optional, intent(in) :: marker + character(len=1) :: marker_ character(len=1024) :: charbuf integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if read(file,'(a)')charbuf charbuf = adjustl(charbuf) - idx=index(charbuf,"!") + idx=index(charbuf,marker_) read(charbuf(1:idx-1),*) val - end subroutine read_int - subroutine read_single(val,file) + end subroutine string_read_int + subroutine string_read_single(val,file,marker) use psb_base_mod real(psb_spk_), intent(out) :: val - integer, intent(in) :: file + character(len=*), intent(in) :: file + character(len=1), optional, intent(in) :: marker + character(len=1) :: marker_ character(len=1024) :: charbuf integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if read(file,'(a)')charbuf charbuf = adjustl(charbuf) - idx=index(charbuf,"!") + idx=index(charbuf,marker_) read(charbuf(1:idx-1),*) val - end subroutine read_single - subroutine read_double(val,file) + end subroutine string_read_single + subroutine string_read_double(val,file,marker) use psb_base_mod real(psb_dpk_), intent(out) :: val - integer, intent(in) :: file + character(len=*), intent(in) :: file + character(len=1), optional, intent(in) :: marker + character(len=1) :: marker_ character(len=1024) :: charbuf integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if read(file,'(a)')charbuf charbuf = adjustl(charbuf) - idx=index(charbuf,"!") + idx=index(charbuf,marker_) read(charbuf(1:idx-1),*) val - end subroutine read_double + end subroutine string_read_double + + function trim_string(string,marker) + character(len=*), intent(in) :: string + character(len=1), optional, intent(in) :: marker + character(len=len(string)) :: trim_string + character(len=1) :: marker_ + integer :: idx + if (present(marker)) then + marker_ = marker + else + marker_ = def_marker + end if + idx=index(string,marker_) + trim_string = adjustl(string(idx:)) + end function trim_string end module data_input