diff --git a/docs/html/img100.png b/docs/html/img100.png index 453c0579..1244b45e 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 06cc29de..f8eef182 100644 Binary files a/docs/html/img101.png and b/docs/html/img101.png differ diff --git a/docs/html/img102.png b/docs/html/img102.png index b2133551..453c0579 100644 Binary files a/docs/html/img102.png and b/docs/html/img102.png differ diff --git a/docs/html/img103.png b/docs/html/img103.png index c34f3c6d..06cc29de 100644 Binary files a/docs/html/img103.png and b/docs/html/img103.png differ diff --git a/docs/html/img104.png b/docs/html/img104.png index a6135e0e..b2133551 100644 Binary files a/docs/html/img104.png and b/docs/html/img104.png differ diff --git a/docs/html/img105.png b/docs/html/img105.png index 706e64d0..c34f3c6d 100644 Binary files a/docs/html/img105.png and b/docs/html/img105.png differ diff --git a/docs/html/img106.png b/docs/html/img106.png index 750519a4..a6135e0e 100644 Binary files a/docs/html/img106.png and b/docs/html/img106.png differ diff --git a/docs/html/img92.png b/docs/html/img92.png index 80faaac9..a7d4ae33 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 6da35574..2135bd39 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 fcb1d80f..80faaac9 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 283f02fc..6da35574 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 fa31ee53..fcb1d80f 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 6e5db9a1..283f02fc 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 1244b45e..fa31ee53 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 f8eef182..6e5db9a1 100644 Binary files a/docs/html/img99.png and b/docs/html/img99.png differ diff --git a/docs/html/node12.html b/docs/html/node12.html index 56efc610..2e128b41 100644 --- a/docs/html/node12.html +++ b/docs/html/node12.html @@ -726,7 +726,7 @@ $w = y_1$; \begin{tabbing} \quad \=\quad... ...= y_l+r_l$\\ -\textbf{endfor} \ [1mm] +\textbf{endfor} [1mm] $w = y_1$; \end{tabbing}} \end{minipage}}"> diff --git a/docs/html/node18.html b/docs/html/node18.html index ca52b257..8a5bd398 100644 --- a/docs/html/node18.html +++ b/docs/html/node18.html @@ -191,7 +191,7 @@ according to their needs.


-
+
- + + (i.e. smoother): Jacobi (with diagonal local + solver), block Jacobi, AS. @@ -236,7 +236,7 @@ Parameters defining the type of multi-level preconditioner.


-
+
Table 2: Parameters defining the type of multi-level preconditioner. @@ -214,11 +214,11 @@ Parameters defining the type of multi-level preconditioner.
mld_smoother_type_
SMOOTHER_TYPE		 character(len=*)'DIAG' 'BJAC' 'AS''JACOBI' 'BJAC' 'AS' 'AS' Basic predefined one-level preconditioner - (i.e. smoother): diagonal, - block Jacobi, AS.
mld_smoother_pos_
SMOOTHER_POS		 character(len=*)
- - + ALT="$p,t$">), LU from UMFPACK, LU from + SuperLU (plus triangular solve). @@ -328,6 +332,27 @@ Parameters defining the one-level preconditioner used as smoother. reordering according to the global numbering of the rows and columns of the whole matrix. + + + + + + + + + + + +
Table 3: Parameters defining the one-level preconditioner used as smoother. @@ -277,21 +277,25 @@ Parameters defining the one-level preconditioner used as smoother.
mld_sub_solve_
SUB_SOLVE		 character(len=*)'ILU' 'MILU' 'ILUT' +'DIAG' + 'GS' + 'ILU' + 'MILU' 'ILUT' 'UMF' 'SLU' 'ILU'Predefined local solver: ILU(Predefined local solver: diagonal scaling, + Gauss-Seidel, ILU($p$), - MILU($p$), MILU($p$), ILU($p$), + ILU($p,t$), LU from UMFPACK, LU from SuperLU - (plus triangular solve).
mld_sub_fillin_
SUB_FILLIN		 integer
mld_solver_sweeps_
SOLVER_SWEEPS		integerAny int. num. $\ge 1$1Number of sweeps for iterative local solver + (currently only Gauss-Seidel).
mld_solver_eps_
SOLVER_EPS		realAny real num.0Stopping tolerance for iterative local solver + (currently only Gauss-Seidel); if $\le0$, then + perform prespecified number of iterations.
@@ -337,7 +362,7 @@ Parameters defining the one-level preconditioner used as smoother.


-
+
@@ -440,7 +465,7 @@ Parameters defining the aggregation algorithm. --> $4/(3\rho(D^{-1}A))$
Table 4: Parameters defining the aggregation algorithm. @@ -381,28 +406,28 @@ Parameters defining the aggregation algorithm.
real(kind_parameter) Any real num. $\in [0, 1]$ 0.05 Threshold $\theta$ in the aggregation algorithm.
mld_aggr_scale_
AGGR_SCALE		 real(kind_parameter) Any real num. $\in [0, 1]$ 1.0 Scale factor applied to the threshold going from level $ilev$ to level $ilev+1$.
mld_aggr_omega_alg_
AGGR_OMEGA_ALG		 Damping parameter $\rho(D^{-1}A)$ of

-
+
@@ -117,7 +117,7 @@ and hence it is completely transparent to the user. @@ -144,28 +144,28 @@ and hence it is completely transparent to the user. --> $op(M^{-1}) = M^{-1}$; if trans = 'T','t' then $op(M^{-1}) = M^{-T}$ (transpose of $M^{-1})$; if trans = 'C','c' then $op(M^{-1}) = M^{-C}$ (conjugate transpose of $M^{-1})$. diff --git a/docs/mld2p4-2.0-guide.pdf b/docs/mld2p4-2.0-guide.pdf deleted file mode 100644 index 7e4113c6..00000000 --- a/docs/mld2p4-2.0-guide.pdf +++ /dev/null @@ -1,8944 +0,0 @@ -%PDF-1.5 -% -105 0 obj -<< -/Length 1164 ->> -stream -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -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 -ET -q -1 0 0 1 93.6 573.564 cm -0 0 412.451 4.981 re f -Q -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 -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",)-326(Italy)]TJ -0 g 0 G -0 g 0 G - 100.3 -78.924 Td [(Soft)27(w)28(are)-327(v)27(ersion)1(:)-436(2.0)]TJ 37.459 -13.948 Td [(Oct.)-435(12,)-326(2015)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -114 0 obj -<< -/Length 32 ->> -stream -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -118 0 obj -<< -/Length 3728 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 503.021 740.002 Td [(i)]TJ -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)-342(the)-342(matrix)-342(to)-341(b)-28(e)-342(preconditioned.)-470(The)-342(matrix)-342(is)-342(assumed)-341(to)-342(b)-28(e)-342(square,)-344(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)-307(pac)28(k)55(age)-307(emplo)28(ys)-307(ob)-55(ject-orien)27(ted)-307(design)-306(te)-1(c)28(hniques)-307(in)-307(F)84(ortran)-307(2003,)-312(with)-307(in)28(ter-)]TJ -16.937 -13.55 Td [(faces)-222(to)-223(ad)1(ditional)-223(thi)1(rd)-223(part)28(y)-222(libraries)-222(suc)28(h)-223(as)-222(UMFP)84(A)27(CK,)-222(Sup)-27(e)-1(r)1(LU)-223(and)-222(Sup)-27(erLU)]TJ -ET -q -1 0 0 1 481.345 490.295 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 484.618 490.095 Td [(Dist,)]TJ -391.018 -13.549 Td [(that)-383(can)-384(b)-27(e)-384(exploited)-383(in)-383(building)-383(m)28(ulti-lev)27(el)-383(preconditioners.)-594(The)-383(parallel)-384(implemen-)]TJ 0 -13.549 Td [(tation)-345(is)-345(based)-345(on)-344(a)-345(Single)-345(Program)-345(Multiple)-345(Data)-345(\050)1(SPMD\051)-345(paradigm)-345(for)-345(distributed-)]TJ 0 -13.549 Td [(memory)-406(arc)28(hitectures;)-441(the)-406(in)28(ter-pro)-28(cess)-406(data)-405(comm)28(unication)-406(is)-405(based)-406(on)-405(MPI)-406(and)-405(is)]TJ 0 -13.549 Td [(managed)-333(mainly)-334(throu)1(gh)-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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -124 0 obj -<< -/Length 79 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(ii)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -ET - -endstream -endobj -152 0 obj -<< -/Length 6439 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 496.96 740.002 Td [(iii)]TJ -0 g 0 G -/F17 14.3462 Tf -403.36 -35.866 Td [(Con)31(ten)31(ts)]TJ -0 0 1 rg 0 0 1 RG -/F43 10.9091 Tf 0 -24.458 Td [(Abstract)]TJ -0 g 0 G - 408.966 0 Td [(i)]TJ -0 0 1 rg 0 0 1 RG - -408.966 -24.458 Td [(1)-925(General)-383(Ov)32(erview)]TJ -0 g 0 G - [-26677(1)]TJ -0 0 1 rg 0 0 1 RG - 0 -24.459 Td [(2)-925(Co)-32(de)-383(Distribution)]TJ -0 g 0 G - [-26593(3)]TJ -0 0 1 rg 0 0 1 RG - 0 -24.458 Td [(3)-925(Con\014guring)-383(and)-384(Building)-383(MLD2P4)]TJ -0 g 0 G - [-17973(4)]TJ -0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.549 Td [(3.1)-1022(Prerequisites)]TJ -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 -0 g 0 G - [-1781(4)]TJ -0 g 0 G -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 -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 -0 g 0 G - [-1781(4)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(3.3)-1022(Con\014guration)-333(options)]TJ -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 -0 g 0 G - [-1781(5)]TJ -0 g 0 G -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 -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 -0 g 0 G - [-1780(8)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(3.5)-1022(Example)-333(and)-334(test)-333(programs)]TJ -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 -0 g 0 G - [-1780(8)]TJ -0 g 0 G -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 -0 g 0 G - [-11152(10)]TJ -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 -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 -0 g 0 G - [-1281(11)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.55 Td [(4.2)-1022(Smo)-28(othed)-333(Aggregation)]TJ -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 -0 g 0 G - [-1281(13)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG -/F43 10.9091 Tf -16.364 -24.458 Td [(5)-925(Getting)-383(Started)]TJ -0 g 0 G - [-27184(16)]TJ -0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.549 Td [(5.1)-1022(Examples)]TJ -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 -0 g 0 G - [-1280(17)]TJ -0 g 0 G -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 -0 g 0 G - [-27997(21)]TJ -0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.55 Td [(6.1)-1022(Subroutine)-333(mld)]TJ -ET -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 -Q -BT -/F15 10.9091 Tf 212.952 410.985 Td [(precinit)]TJ -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 -0 g 0 G - [-1281(22)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -102.988 -13.549 Td [(6.2)-1022(Subroutine)-333(mld)]TJ -ET -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 -Q -BT -/F15 10.9091 Tf 212.952 397.436 Td [(precset)]TJ -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 -0 g 0 G - [-1281(23)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -102.988 -13.549 Td [(6.3)-1022(Subroutine)-333(mld)]TJ -ET -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 -Q -BT -/F15 10.9091 Tf 212.952 383.887 Td [(precbld)]TJ -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 -0 g 0 G - [-1281(29)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -102.988 -13.549 Td [(6.4)-1022(Subroutine)-333(mld)]TJ -ET -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 -Q -BT -/F15 10.9091 Tf 212.952 370.338 Td [(precaply)]TJ -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 -0 g 0 G - [-1281(30)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -102.988 -13.549 Td [(6.5)-1022(Subroutine)-333(mld)]TJ -ET -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 -Q -BT -/F15 10.9091 Tf 212.952 356.789 Td [(precfree)]TJ -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 -0 g 0 G - [-1281(31)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -102.988 -13.55 Td [(6.6)-1022(Subroutine)-333(mld)]TJ -ET -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 -Q -BT -/F15 10.9091 Tf 212.952 343.239 Td [(precdescr)]TJ -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 -0 g 0 G - [-1281(32)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG -/F43 10.9091 Tf -119.352 -24.458 Td [(7)-925(Error)-383(Handling)]TJ -0 g 0 G - [-27434(33)]TJ -0 0 1 rg 0 0 1 RG - 0 -24.458 Td [(A)-631(License)]TJ -0 g 0 G - [-31489(34)]TJ -0 0 1 rg 0 0 1 RG - 0 -24.459 Td [(References)]TJ -0 g 0 G - [-31259(35)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -158 0 obj -<< -/Length 79 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(iv)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -ET - -endstream -endobj -170 0 obj -<< -/Length 8133 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(1)]TJ -0 g 0 G - [-378(General)-378(O)30(ver)88(view)]TJ/F15 10.9091 Tf 406.997 0 Td [(1)]TJ -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 rg 1 0 0 RG - [(22)]TJ -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 -0 g 0 G -/F15 10.9091 Tf 182.57 0 Td [(\0501\051)]TJ -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 -0 g 0 G -/F25 10.9091 Tf 16.364 -21.386 Td [(\017)]TJ -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 -0 g 0 G -/F25 10.9091 Tf -10.909 -22.064 Td [(\017)]TJ -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 rg 1 0 0 RG - [(1)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-284(26)]TJ -0 g 0 G - [(].)]TJ -114.289 -21.385 Td [(V)83(ersion)-379(2.0)-380(of)-379(the)-380(pac)28(k)56(age)-380(is)-379(written)-380(in)]TJ/F18 10.9091 Tf 194.214 0 Td [(F)77(ortr)51(an)-400(2003)]TJ/F15 10.9091 Tf 62.505 0 Td [(,)-391(follo)28(wing)-380(an)]TJ/F18 10.9091 Tf 69.517 0 Td [(obje)51(ct-oriente)51(d)]TJ -343.173 -13.55 Td [(design)]TJ/F15 10.9091 Tf 34.51 0 Td [(through)-378(the)-377(exploitation)-378(of)-378(features)-378(suc)28(h)-378(as)-377(abstract)-378(data)-378(t)28(yp)-28(e)-378(creation,)-389(fun)1(c)-1(-)]TJ -34.51 -13.549 Td [(tional)-347(o)27(v)28(erloading)-347(and)-347(dynamic)-348(memory)-347(managemen)27(t.)-486(The)-348(parallel)-347(implemen)28(tation)-348(is)]TJ 0 -13.549 Td [(based)-389(on)-389(a)-389(Single)-389(Program)-389(Multiple)-389(Data)-390(\050SPM)1(D\051)-390(p)1(aradigm)-390(for)-389(distribu)1(ted-m)-1(emory)]TJ 0 -13.549 Td [(arc)28(hitectures.)-654(Single)-403(and)-403(d)1(ouble)-403(precision)-403(implemen)27(tations)-403(of)-403(MLD2P)1(4)-403(are)-403(a)27(v)56(ailable)]TJ 0 -13.549 Td [(for)-333(b)-28(oth)-333(the)-334(real)-333(and)-333(the)-334(complex)-333(case,)-333(that)-334(can)-333(b)-28(e)-333(used)-333(through)-334(a)-333(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 28.375 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(17)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-436(16)]TJ -0 g 0 G - [(].)-753(PSBLAS)-436(is)-437(a)-436(library)-436(originally)-436(dev)28(elop)-28(ed)-436(to)-436(address)-436(the)-437(parallel)-436(im-)]TJ -28.375 -13.549 Td [(plemen)28(tation)-489(of)-489(iterativ)28(e)-489(solv)28(ers)-489(for)-489(sparse)-489(linear)-489(system,)-527(b)27(y)-488(pro)27(vi)1(ding)-489(basic)-489(linear)]TJ 0 -13.549 Td [(algebra)-453(op)-28(erators)-452(and)-453(data)-453(managemen)28(t)-453(facilities)-453(for)-453(distributed)-453(sparse)-453(matrices;)-512(it)]TJ 0 -13.549 Td [(also)-278(includes)-279(parallel)-278(Krylo)28(v)-278(solv)27(ers,)-289(built)-278(on)-278(the)-279(top)-278(of)-278(the)-278(basic)-279(PSBLAS)-278(k)28(ernels.)-426(The)]TJ 0 -13.55 Td [(preconditioners)-268(a)28(v)56(ailable)-268(in)-267(MLD2P4)-268(can)-267(b)-28(e)-268(used)-267(with)-268(these)-268(Krylo)28(v)-267(solv)27(ers.)-422(The)-268(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)-288(MLD2P4)-289(has)-288(led)-289(to)-288(some)-289(r)1(e)-1(vi)1(s)-1(ion)1(s)-289(and)-288(exten)27(ti)1(ons)-289(of)-288(the)-289(PSBLAS)-288(k)28(ernels,)-298(leading)-288(to)]TJ 0 -13.549 Td [(the)-352(PSBLAS)-352(2.0)-352(v)28(ersion)-353([)]TJ -1 0 0 rg 1 0 0 RG - [1(15)]TJ -0 g 0 G - [(].)-501(The)-352(in)27(ter-pr)1(o)-28(cess)-353(com)28(unication)-352(required)-352(b)28(y)-352(MLD2P4)-352(is)]TJ 0 -13.549 Td [(encapsulated)-353(in)27(to)-353(the)-354(PSBLAS)-353(routines,)-358(exce)-1(p)1(t)-354(few)-353(c)-1(ases)-353(where)-354(MPI)-353([)]TJ -1 0 0 rg 1 0 0 RG - [(23)]TJ -0 g 0 G - [(])-354(is)-353(explicitly)]TJ 0 -13.549 Td [(called.)-647(Therefore,)-417(MLD2P4)-401(can)-401(b)-27(e)-401(run)-401(on)-401(an)28(y)-401(par)1(alle)-1(l)-400(mac)27(h)1(ine)-401(where)-401(PSBLAS)-401(and)]TJ 0 -13.549 Td [(MPI)-333(implemen)27(tati)1(ons)-334(are)-333(a)28(v)55(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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -2 0 obj -<< -/Type /ObjStm -/N 100 -/First 815 -/Length 8844 ->> -stream -1 0 5 38 6 84 9 125 10 146 13 187 14 219 17 260 18 293 21 334 -22 381 25 427 26 458 29 504 30 552 33 598 34 637 37 683 38 714 41 760 -42 803 45 844 46 903 49 949 50 1002 53 1048 54 1086 57 1127 58 1158 61 1204 -62 1230 65 1271 66 1301 69 1347 70 1391 73 1437 74 1480 77 1526 78 1569 81 1615 -82 1659 85 1705 86 1749 89 1795 90 1840 93 1881 94 1911 97 1953 98 1976 101 2018 -102 2043 103 2088 106 2202 107 2256 3 2310 104 2362 113 2455 115 2569 112 2623 117 2659 -119 2773 7 2827 116 2879 123 2972 125 3086 122 3140 151 3207 126 3525 127 3671 128 3817 -129 3963 130 4109 131 4261 132 4413 133 4565 134 4716 135 4867 136 5013 137 5165 138 5317 -139 5463 140 5615 141 5760 142 5912 143 6064 144 6214 145 6364 146 6516 147 6668 148 6814 -149 6961 153 7108 154 7162 150 7216 157 7309 159 7423 156 7477 169 7544 167 7734 160 7880 -% 1 0 obj -<< /S /GoTo /D (title.0) >> -% 5 0 obj -(MLD2P4 User's and Reference Guide) -% 6 0 obj -<< /S /GoTo /D (section*.1) >> -% 9 0 obj -(Abstract) -% 10 0 obj -<< /S /GoTo /D (section.1) >> -% 13 0 obj -(1 General Overview) -% 14 0 obj -<< /S /GoTo /D (section.2) >> -% 17 0 obj -(2 Code Distribution) -% 18 0 obj -<< /S /GoTo /D (section.3) >> -% 21 0 obj -(3 Configuring and Building MLD2P4) -% 22 0 obj -<< /S /GoTo /D (subsection.3.1) >> -% 25 0 obj -(3.1 Prerequisites) -% 26 0 obj -<< /S /GoTo /D (subsection.3.2) >> -% 29 0 obj -(3.2 Optional third party libraries) -% 30 0 obj -<< /S /GoTo /D (subsection.3.3) >> -% 33 0 obj -(3.3 Configuration options) -% 34 0 obj -<< /S /GoTo /D (subsection.3.4) >> -% 37 0 obj -(3.4 Bug reporting) -% 38 0 obj -<< /S /GoTo /D (subsection.3.5) >> -% 41 0 obj -(3.5 Example and test programs) -% 42 0 obj -<< /S /GoTo /D (section.4) >> -% 45 0 obj -(4 Multi-level Domain Decomposition Background) -% 46 0 obj -<< /S /GoTo /D (subsection.4.1) >> -% 49 0 obj -(4.1 Multi-level Schwarz Preconditioners) -% 50 0 obj -<< /S /GoTo /D (subsection.4.2) >> -% 53 0 obj -(4.2 Smoothed Aggregation) -% 54 0 obj -<< /S /GoTo /D (section.5) >> -% 57 0 obj -(5 Getting Started) -% 58 0 obj -<< /S /GoTo /D (subsection.5.1) >> -% 61 0 obj -(5.1 Examples) -% 62 0 obj -<< /S /GoTo /D (section.6) >> -% 65 0 obj -(6 User Interface) -% 66 0 obj -<< /S /GoTo /D (subsection.6.1) >> -% 69 0 obj -(6.1 Subroutine mld\137precinit) -% 70 0 obj -<< /S /GoTo /D (subsection.6.2) >> -% 73 0 obj -(6.2 Subroutine mld\137precset) -% 74 0 obj -<< /S /GoTo /D (subsection.6.3) >> -% 77 0 obj -(6.3 Subroutine mld\137precbld) -% 78 0 obj -<< /S /GoTo /D (subsection.6.4) >> -% 81 0 obj -(6.4 Subroutine mld\137precaply) -% 82 0 obj -<< /S /GoTo /D (subsection.6.5) >> -% 85 0 obj -(6.5 Subroutine mld\137precfree) -% 86 0 obj -<< /S /GoTo /D (subsection.6.6) >> -% 89 0 obj -(6.6 Subroutine mld\137precdescr) -% 90 0 obj -<< /S /GoTo /D (section.7) >> -% 93 0 obj -(7 Error Handling) -% 94 0 obj -<< /S /GoTo /D (appendix.A) >> -% 97 0 obj -(A License) -% 98 0 obj -<< /S /GoTo /D (section*.3) >> -% 101 0 obj -(References) -% 102 0 obj -<< /S /GoTo /D [103 0 R /Fit] >> -% 103 0 obj -<< -/Type /Page -/Contents 105 0 R -/Resources 104 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 111 0 R ->> -% 106 0 obj -<< -/D [103 0 R /XYZ 92.6 752.957 null] ->> -% 107 0 obj -<< -/D [103 0 R /XYZ 93.6 715.095 null] ->> -% 3 0 obj -<< -/D [103 0 R /XYZ 93.6 715.095 null] ->> -% 104 0 obj -<< -/Font << /F17 108 0 R /F19 109 0 R /F37 110 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 113 0 obj -<< -/Type /Page -/Contents 114 0 R -/Resources 112 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 111 0 R ->> -% 115 0 obj -<< -/D [113 0 R /XYZ 85.4 752.957 null] ->> -% 112 0 obj -<< -/ProcSet [ /PDF ] ->> -% 117 0 obj -<< -/Type /Page -/Contents 118 0 R -/Resources 116 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 111 0 R ->> -% 119 0 obj -<< -/D [117 0 R /XYZ 92.6 752.957 null] ->> -% 7 0 obj -<< -/D [117 0 R /XYZ 93.6 722.069 null] ->> -% 116 0 obj -<< -/Font << /F15 120 0 R /F17 108 0 R /F41 121 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 123 0 obj -<< -/Type /Page -/Contents 124 0 R -/Resources 122 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 111 0 R ->> -% 125 0 obj -<< -/D [123 0 R /XYZ 85.4 752.957 null] ->> -% 122 0 obj -<< -/Font << /F15 120 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 151 0 obj -<< -/Type /Page -/Contents 152 0 R -/Resources 150 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 111 0 R -/Annots [ 126 0 R 127 0 R 128 0 R 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 ] ->> -% 126 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 678.682 142.598 688.25] -/A << /S /GoTo /D (section*.1) >> ->> -% 127 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 654.223 209.755 663.792] -/A << /S /GoTo /D (section.1) >> ->> -% 128 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 629.765 210.673 639.333] -/A << /S /GoTo /D (section.2) >> ->> -% 129 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 603.186 304.709 614.875] -/A << /S /GoTo /D (section.3) >> ->> -% 130 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 589.636 197.294 601.205] -/A << /S /GoTo /D (subsection.3.1) >> ->> -% 131 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 576.087 276.233 587.777] -/A << /S /GoTo /D (subsection.3.2) >> ->> -% 132 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 562.538 239.779 574.228] -/A << /S /GoTo /D (subsection.3.3) >> ->> -% 133 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 548.989 202.93 560.557] -/A << /S /GoTo /D (subsection.3.4) >> ->> -% 134 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 535.44 268.203 547.129] -/A << /S /GoTo /D (subsection.3.5) >> ->> -% 135 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 510.981 372.854 522.671] -/A << /S /GoTo /D (section.4) >> ->> -% 136 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 499.553 307.263 509.122] -/A << /S /GoTo /D (subsection.4.1) >> ->> -% 137 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 483.883 245.172 495.572] -/A << /S /GoTo /D (subsection.4.2) >> ->> -% 138 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 459.425 197.952 471.114] -/A << /S /GoTo /D (section.5) >> ->> -% 139 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 445.875 182.021 457.565] -/A << /S /GoTo /D (subsection.5.1) >> ->> -% 140 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 423.538 189.09 433.107] -/A << /S /GoTo /D (section.6) >> ->> -% 141 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 407.868 250.342 419.557] -/A << /S /GoTo /D (subsection.6.1) >> ->> -% 142 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 394.319 247.372 406.008] -/A << /S /GoTo /D (subsection.6.2) >> ->> -% 143 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 380.77 249.13 392.459] -/A << /S /GoTo /D (subsection.6.3) >> ->> -% 144 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 367.22 254.282 378.91] -/A << /S /GoTo /D (subsection.6.4) >> ->> -% 145 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 353.671 251.282 365.361] -/A << /S /GoTo /D (subsection.6.5) >> ->> -% 146 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 340.122 258.312 351.811] -/A << /S /GoTo /D (subsection.6.6) >> ->> -% 147 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 315.664 195.225 327.353] -/A << /S /GoTo /D (section.7) >> ->> -% 148 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 293.326 150.984 302.895] -/A << /S /GoTo /D (appendix.A) >> ->> -% 149 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 268.868 153.499 278.436] -/A << /S /GoTo /D (section*.3) >> ->> -% 153 0 obj -<< -/D [151 0 R /XYZ 92.6 752.957 null] ->> -% 154 0 obj -<< -/D [151 0 R /XYZ 93.6 722.069 null] ->> -% 150 0 obj -<< -/Font << /F15 120 0 R /F17 108 0 R /F43 155 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 157 0 obj -<< -/Type /Page -/Contents 158 0 R -/Resources 156 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 111 0 R ->> -% 159 0 obj -<< -/D [157 0 R /XYZ 85.4 752.957 null] ->> -% 156 0 obj -<< -/Font << /F15 120 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 169 0 obj -<< -/Type /Page -/Contents 170 0 R -/Resources 168 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 175 0 R -/Annots [ 167 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 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.1) >> ->> -% 160 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [488.085 665.239 500.987 674.261] -/A << /S /GoTo /D (cite.dd2_96) >> ->> - -endstream -endobj -193 0 obj -<< -/Length 4592 ->> -stream -0 g 0 G -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 -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 [(The)-359(user)-358(in)27(terface)-358(of)-359(v)28(ersion)-359(2.0)-358(is)-359(essen)27(t)1(ially)-359(iden)28(tical)-359(to)-359(that)-358(of)-359(v)28(ersion)-359(1.1.)-520(The)]TJ -16.936 -13.549 Td [(in)28(ternal)-479(implem)-1(en)28(tation)-479(ho)28(w)28(e)-1(v)28(er)-479(has)-480(b)-27(een)-480(c)28(hanged)-479(signi\014can)28(tly;)-553(as)-479(a)-480(result,)-516(it)-479(has)]TJ 0 -13.549 Td [(b)-28(ecome)-443(m)28(uc)27(h)-443(easier)-443(to)-443(extend)-444(the)-443(library)-443(b)28(y)-443(adding)-444(n)1(e)-1(w)-443(smo)-28(others)-443(and/or)-443(solv)28(ers,)]TJ 0 -13.55 Td [(thanks)-333(to)-334(the)-333(F)83(ort)1(ran)-334(2003)-333(features)-333(exploited)-334(in)-333(the)-333(design)-334(of)-333(PSBLAS)-333(3.0.)]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 -0 0 1 rg 0 0 1 RG - [-239(2)]TJ -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 -0 0 1 rg 0 0 1 RG - [-280(3)]TJ -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 -13.549 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 -0 0 1 rg 0 0 1 RG - [-353(4)]TJ -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 -13.55 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)-487(in)-487(Section)]TJ -0 0 1 rg 0 0 1 RG - [-488(5)]TJ -0 g 0 G - [(,)-525(where)-488(the)-487(F)83(ortr)1(an)-488(co)-28(des)-487(of)-487(a)-487(few)-488(sample)-487(programs)-487(are)-488(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 -13.549 Td [(in)28(terface,)-328(is)-326(pro)27(vid)1(e)-1(d)-326(in)-326(Section)]TJ -0 0 1 rg 0 0 1 RG - [-327(6)]TJ -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 -13.55 Td [(is)-359(b)1(rie\015y)-359(describ)-28(ed)-358(in)-359(Section)]TJ -0 0 1 rg 0 0 1 RG - [-358(7)]TJ -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 -0 0 1 rg 0 0 1 RG - [-333(A)]TJ -0 g 0 G - [(.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -198 0 obj -<< -/Length 1682 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(2)]TJ -0 g 0 G - [-378(Code)-378(D)1(istri)-1(bution)]TJ/F15 10.9091 Tf 406.997 0 Td [(3)]TJ -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 -0 g 0 G -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 -0 0 1 rg 0 0 1 RG - [-299(A)]TJ -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 16.937 -13.549 Td [(The)-333(library)-333(de\014nes)-334(a)-333(v)28(ersion)-334(string)-333(with)-333(the)-334(constan)28(t)]TJ/F44 10.9091 Tf 134.88 -24.508 Td [(mld_version_string_)]TJ/F15 10.9091 Tf -151.817 -24.508 Td [(whose)-333(curren)27(t)-333(v)56(alue)-334(is)]TJ/F44 10.9091 Tf 109.273 0 Td [(2.0.0)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -211 0 obj -<< -/Length 6591 ->> -stream -0 g 0 G -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 -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 -24.567 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 -13.66 Td [(MLD2P4)-390(is)-390(implemen)28(ted)-391(almost)-390(en)28(tirely)-390(in)-390(F)83(ortran)-390(2003,)-404(with)-390(some)-390(in)28(terfaces)-391(to)]TJ -16.936 -13.549 Td [(external)-373(libraries)-374(in)-373(C;)-373(the)-374(F)84(ortran)-373(compiler)-374(m)28(ust)-373(supp)-28(ort)-373(the)-374(F)84(ortran)-374(2003)-373(standard)]TJ 0 -13.549 Td [(plus)-480(the)-480(extension)]TJ/F44 10.9091 Tf 94.928 0 Td [(MOLD=)]TJ/F15 10.9091 Tf 33.875 0 Td [(feature,)-517(whic)28(h)-480(enhances)-481(the)-480(usabilit)28(y)-480(of)]TJ/F44 10.9091 Tf 202.591 0 Td [(ALLOCATE)]TJ/F15 10.9091 Tf 45.818 0 Td [(.)-480(Man)28(y)]TJ -377.212 -13.549 Td [(compiles)-442(do)-442(th)1(is;)-496(in)-442(particular,)-469(this)-441(is)-442(supp)-28(orted)-442(b)28(y)-442(the)-441(GNU)-442(F)83(ortran)-441(compiler,)-469(for)]TJ 0 -13.55 Td [(whic)28(h)-308(w)28(e)-307(recomm)-1(end)-307(to)-307(use)-308(at)-307(least)-308(v)28(ersion)-308(4.7.2.)-435(The)-308(soft)28(w)28(are)-308(de\014nes)-307(data)-308(t)28(yp)-28(es)-307(and)]TJ 0 -13.549 Td [(in)28(terfaces)-334(for)-333(real)-333(and)-333(complex)-334(data,)-333(in)-333(b)-28(oth)-333(single)-334(and)-333(double)-333(precision.)]TJ/F17 11.9552 Tf 0 -29.846 Td [(3.1)-1125(Prerequisites)]TJ/F15 10.9091 Tf 0 -20.81 Td [(The)-333(follo)28(wing)-334(base)-333(libraries)-333(are)-334(needed:)]TJ -0 g 0 G -/F43 10.9091 Tf 0 -22.959 Td [(BLAS)]TJ -0 g 0 G -/F15 10.9091 Tf 38.378 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(11)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-315(12)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-316(19)]TJ -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 -13.55 Td [(Sup)-28(erLU)-333(third)-333(part)28(y)-334(libr)1(aries)-1(.)]TJ -0 g 0 G -/F43 10.9091 Tf -27.273 -22.959 Td [(MPI)]TJ -0 g 0 G -/F15 10.9091 Tf 30.697 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(18)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-340(23)]TJ -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;)]TJ -0 g 0 G -/F43 10.9091 Tf -27.273 -22.959 Td [(PSBLAS)]TJ -0 g 0 G -/F15 10.9091 Tf 53.924 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(15)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(17)]TJ -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(3.3)-337(\050or)-338(later\051)-337(is)-338(required.)-456(Indeed,)]TJ -183.27 -13.549 Td [(all)-333(the)-334(prerequ)1(is)-1(i)1(te)-1(s)-333(listed)-333(so)-334(far)-333(are)-333(also)-334(prerequ)1(is)-1(i)1(te)-1(s)-333(of)-333(PSBLAS.)]TJ -27.273 -22.959 Td [(Please)-430(note)-431(that)-430(the)-430(four)-430(previous)-430(libraries)-431(m)28(ust)-430(ha)28(v)28(e)-431(F)84(ortran)-431(in)28(terfaces)-430(compatible)]TJ 0 -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 -13.55 Td [(as)-333(MLD2P4.)]TJ/F17 11.9552 Tf 0 -29.846 Td [(3.2)-1125(Optional)-375(third)-375(part)31(y)-375(libraries)]TJ/F15 10.9091 Tf 0 -20.81 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(bu)1(t)-370(if)-370(y)28(ou)-370(enable)-370(them)-370(some)-370(defau)1(lts)-370(for)-370(m)28(ultilev)28(el)-370(preconditioners)-370(ma)28(y)]TJ 0 -13.549 Td [(c)28(hange)-334(to)-333(re\015ect)-333(their)-334(p)1(res)-1(ence.)]TJ -0 g 0 G -/F43 10.9091 Tf 0 -26.059 Td [(UMFP)96(A)32(CK)]TJ -0 g 0 G -/F15 10.9091 Tf 70.469 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(9)]TJ -0 g 0 G - [(])-333(A)-334(sparse)-333(direct)-333(factorization)-334(pac)28(k)56(age)-334(a)28(v)56(ailable)-334(f)1(rom)]TJ/F44 10.9091 Tf -43.196 -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(serial)-351(factor-)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -223 0 obj -<< -/Length 5149 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(3)]TJ -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 -0 g 0 G - -379.724 -35.866 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(5.4.)]TJ -0 g 0 G -/F43 10.9091 Tf -27.273 -22.542 Td [(Sup)-32(erLU)]TJ -0 g 0 G -/F15 10.9091 Tf 54.826 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(10)]TJ -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 -13.549 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 -13.55 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(ersion)-334(4.3)-333(and)-333(5.0.)]TJ -0 g 0 G -/F43 10.9091 Tf -27.273 -22.542 Td [(Sup)-32(erLU)]TJ -ET -q -1 0 0 1 143.724 605.054 cm -[]0 d 0 J 0.398 w 0 0 m 3.764 0 l S -Q -BT -/F43 10.9091 Tf 147.487 604.855 Td [(Dist)]TJ -0 g 0 G -/F15 10.9091 Tf 28.388 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(20)]TJ -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(3.3)-333(and)-333(4.2.)]TJ/F17 11.9552 Tf -27.273 -29.251 Td [(3.3)-1125(Con\014guration)-375(options)]TJ/F15 10.9091 Tf 0 -20.608 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 -13.556 Td [(As)-333(a)-334(minimal)-333(example)-333(consider)-334(the)-333(follo)28(wing:)]TJ -0 g 0 G -0 g 0 G -/F44 10.9091 Tf -16.937 -22.549 Td [(./configure)-525(--with-psblas=PSB-INSTALL-DIR)]TJ/F15 10.9091 Tf 0 -22.542 Td [(whic)28(h)-411(assumes)-412(th)1(at)-412(the)-411(v)56(arious)-411(MPI)-411(compilers)-411(and)-411(supp)-28(ort)-411(libraries)-411(are)-411(a)28(v)55(ailable)-411(in)]TJ 0 -13.55 Td [(the)-290(standard)-290(directories)-291(on)-290(the)-290(system,)-299(and)-290(sp)-28(eci\014es)-290(only)-290(the)-291(PS)1(B)-1(LAS)-290(install)-290(directory)]TJ 0 -13.549 Td [(\050note)-386(th)1(at)-386(the)-386(lat)1(te)-1(r)-385(directory)-386(m)28(ust)-385(b)-28(e)-386(sp)-27(eci\014ed)-386(with)-385(an)]TJ/F18 10.9091 Tf 278.635 0 Td [(absolute)]TJ/F15 10.9091 Tf 42.12 0 Td [(path\051.)-601(The)-386(f)1(ull)-386(set)]TJ -320.755 -13.549 Td [(of)-487(options)-487(ma)28(y)-488(b)-27(e)-487(lo)-28(ok)28(ed)-488(at)-487(b)28(y)-487(issuing)-487(the)-487(command)]TJ/F44 10.9091 Tf 273.022 0 Td [(./configure)-525(--help)]TJ/F15 10.9091 Tf 103.089 0 Td [(,)-526(whic)28(h)]TJ -376.111 -13.549 Td [(pro)-28(duces:)]TJ -0 g 0 G -0 g 0 G -/F44 10.9091 Tf 0 -22.549 Td [(`configure')-525(configures)-525(MLD2P4)-525(2.0)-525(to)-525(adapt)-525(to)-525(many)-525(kinds)-525(of)-525(systems.)]TJ 0 -27.099 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 -13.549 Td [(--help=short)-4200(display)-525(options)-525(specific)-525(to)-525(this)-525(package)]TJ 0 -13.55 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 0 -13.549 Td [(-q,)-525(--quiet,)-525(--silent)-1575(do)-525(not)-525(print)-525(`checking...')-525(messages)]TJ 22.908 -13.549 Td [(--cache-file=FILE)-1575(cache)-525(test)-525(results)-525(in)-525(FILE)-525([disabled])]TJ -22.908 -13.549 Td [(-C,)-525(--config-cache)-3150(alias)-525(for)-525(`--cache-file=config.cache')]TJ 0 -13.55 Td [(-n,)-525(--no-create)-4725(do)-525(not)-525(create)-525(output)-525(files)]TJ 22.908 -13.549 Td [(--srcdir=DIR)-4200(find)-525(the)-525(sources)-525(in)-525(DIR)-525([configure)-525(dir)-525(or)-525(`..'])]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -229 0 obj -<< -/Length 3725 ->> -stream -0 g 0 G -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 -0 g 0 G -/F44 10.9091 Tf -203.265 -35.866 Td [(Installation)-525(directories:)]TJ 11.454 -13.549 Td [(--prefix=PREFIX)-4725(install)-525(architecture-independent)-525(files)-525(in)-525(PREFIX)]TJ 137.453 -13.549 Td [([/usr/local])]TJ -137.453 -13.549 Td [(--exec-prefix=EPREFIX)-1575(install)-525(architecture-dependent)-525(files)-525(in)-525(EPREFIX)]TJ 137.453 -13.549 Td [([PREFIX])]TJ -148.907 -27.099 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 -13.549 Td [(for)-525(instance)-525(`--prefix=$HOME'.)]TJ 0 -27.099 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 -13.549 Td [(--bindir=DIR)-6300(user)-525(executables)-525([EPREFIX/bin])]TJ 0 -13.55 Td [(--sbindir=DIR)-5775(system)-525(admin)-525(executables)-525([EPREFIX/sbin])]TJ 0 -13.549 Td [(--libexecdir=DIR)-4200(program)-525(executables)-525([EPREFIX/libexec])]TJ 0 -13.549 Td [(--sysconfdir=DIR)-4200(read-only)-525(single-machine)-525(data)-525([PREFIX/etc])]TJ 0 -13.549 Td [(--sharedstatedir=DIR)-2100(modifiable)-525(architecture-independent)-525(data)-525([PREFIX/com])]TJ 0 -13.549 Td [(--localstatedir=DIR)-2625(modifiable)-525(single-machine)-525(data)-525([PREFIX/var])]TJ 0 -13.55 Td [(--libdir=DIR)-6300(object)-525(code)-525(libraries)-525([EPREFIX/lib])]TJ 0 -13.549 Td [(--includedir=DIR)-4200(C)-525(header)-525(files)-525([PREFIX/include])]TJ 0 -13.549 Td [(--oldincludedir=DIR)-2625(C)-525(header)-525(files)-525(for)-525(non-gcc)-525([/usr/include])]TJ 0 -13.549 Td [(--datarootdir=DIR)-3675(read-only)-525(arch.-independent)-525(data)-525(root)-525([PREFIX/share])]TJ 0 -13.549 Td [(--datadir=DIR)-5775(read-only)-525(architecture-independent)-525(data)-525([DATAROOTDIR])]TJ 0 -13.549 Td [(--infodir=DIR)-5775(info)-525(documentation)-525([DATAROOTDIR/info])]TJ 0 -13.55 Td [(--localedir=DIR)-4725(locale-dependent)-525(data)-525([DATAROOTDIR/locale])]TJ 0 -13.549 Td [(--mandir=DIR)-6300(man)-525(documentation)-525([DATAROOTDIR/man])]TJ 0 -13.549 Td [(--docdir=DIR)-6300(documentation)-525(root)-525([DATAROOTDIR/doc/mld2p4])]TJ 0 -13.549 Td [(--htmldir=DIR)-5775(html)-525(documentation)-525([DOCDIR])]TJ 0 -13.549 Td [(--dvidir=DIR)-6300(dvi)-525(documentation)-525([DOCDIR])]TJ 0 -13.55 Td [(--pdfdir=DIR)-6300(pdf)-525(documentation)-525([DOCDIR])]TJ 0 -13.549 Td [(--psdir=DIR)-6825(ps)-525(documentation)-525([DOCDIR])]TJ -11.454 -27.098 Td [(Optional)-525(Features:)]TJ 11.454 -13.549 Td [(--disable-option-checking)-1050(ignore)-525(unrecognized)-525(--enable/--with)-525(options)]TJ 0 -13.55 Td [(--disable-FEATURE)-3675(do)-525(not)-525(include)-525(FEATURE)-525(\050same)-525(as)-525(--enable-FEATURE=no\051)]TJ 0 -13.549 Td [(--enable-FEATURE[=ARG])-1050(include)-525(FEATURE)-525([ARG=yes])]TJ 0 -13.549 Td [(--enable-serial)-4725(Specify)-525(whether)-525(to)-525(enable)-525(a)-525(fake)-525(mpi)-525(library)-525(to)-525(run)]TJ 137.453 -13.549 Td [(in)-525(serial)-525(mode.)]TJ -148.907 -27.099 Td [(Optional)-525(Packages:)]TJ 11.454 -13.549 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 g 0 G -0 g 0 G -ET - -endstream -endobj -234 0 obj -<< -/Length 3624 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(3)]TJ -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 -0 g 0 G -/F44 10.9091 Tf -395.542 -35.866 Td [(--with-psblas=DIR)-3675(The)-525(install)-525(directory)-525(for)-525(PSBLAS,)-525(for)-525(example,)]TJ 137.453 -13.549 Td [(--with-psblas=/opt/packages/psblas-3.3)]TJ -137.453 -13.549 Td [(--with-psblas-incdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(PSBLAS)-525(includes.)]TJ -137.453 -13.549 Td [(--with-psblas-libdir=DIR)]TJ 137.453 -13.55 Td [(Specify)-525(the)-525(directory)-525(for)-525(PSBLAS)-525(library.)]TJ -137.453 -13.549 Td [(--with-extra-libs)-3675(List)-525(additional)-525(link)-525(flags)-525(here.)-525(For)-525(example,)]TJ 137.453 -13.549 Td [(--with-extra-libs=-lspecial_system_lib)-525(or)]TJ 0 -13.549 Td [(--with-extra-libs=-L/path/to/libs)]TJ -137.453 -13.549 Td [(--with-umfpack=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(UMFPACK)-525(and)-525(its)-525(support)]TJ 137.453 -13.55 Td [(libraries.)-525(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-umfpackincdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(UMFPACK)-525(includes.)]TJ -137.453 -13.55 Td [(--with-umfpacklibdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(UMFPACK)-525(library.)]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("-lsuperlu")]TJ -137.453 -13.549 Td [(--with-superludir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(library)-525(and)]TJ 137.453 -13.55 Td [(includes.)]TJ -137.453 -13.549 Td [(--with-superluincdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(includes.)]TJ -137.453 -13.549 Td [(--with-superlulibdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(library.)]TJ -137.453 -13.549 Td [(--with-superludist=LIBNAME)]TJ 137.453 -13.55 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:)]TJ 0 -13.549 Td [("-lsuperlu_dist")]TJ -137.453 -13.549 Td [(--with-superludistdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(library)-525(and)]TJ 0 -13.55 Td [(includes.)]TJ -137.453 -13.549 Td [(--with-superludistincdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(includes.)]TJ -137.453 -13.549 Td [(--with-superludistlibdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(library.)]TJ -148.908 -27.099 Td [(Some)-525(influential)-525(environment)-525(variables:)]TJ 11.455 -13.549 Td [(FC)-5250(Fortran)-525(compiler)-525(command)]TJ 0 -13.549 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 -13.55 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 g 0 G -0 g 0 G -ET - -endstream -endobj -239 0 obj -<< -/Length 4780 ->> -stream -0 g 0 G -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 -0 g 0 G -/F44 10.9091 Tf -191.811 -35.866 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 68.727 -13.549 Td [(you)-525(have)-525(headers)-525(in)-525(a)-525(nonstandard)-525(directory)-525()]TJ -68.727 -13.549 Td [(CPP)-4725(C)-525(preprocessor)]TJ 0 -13.549 Td [(MPICC)-3675(MPI)-525(C)-525(compiler)-525(command)]TJ 0 -13.55 Td [(F77)-4725(Fortran)-525(77)-525(compiler)-525(command)]TJ 0 -13.549 Td [(FFLAGS)-3150(Fortran)-525(77)-525(compiler)-525(flags)]TJ 0 -13.549 Td [(MPIF77)-3150(MPI)-525(Fortran)-525(77)-525(compiler)-525(command)]TJ 0 -13.549 Td [(MPIFC)-3675(MPI)-525(Fortran)-525(compiler)-525(command)]TJ -11.454 -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 0 -27.098 Td [(Report)-525(bugs)-525(to)-525(.)]TJ/F15 10.9091 Tf 0 -22.534 Td [(F)83(or)-277(instance,)-289(if)-277(a)-277(user)-278(has)-277(built)-277(and)-278(installed)-277(PSBLAS)-277(3.3)-277(under)-278(the)]TJ/F44 10.9091 Tf 323.126 0 Td [(/opt)]TJ/F15 10.9091 Tf 25.935 0 Td [(directory)-277(and)]TJ -349.061 -13.549 Td [(is)-300(using)-299(the)-300(SuiteSparse)-300(pac)28(k)56(age)-300(\050whic)28(h)-300(includes)-300(UMFP)84(A)28(CK\051,)-300(then)-300(MLD2P4)-299(migh)27(t)-299(b)-28(e)]TJ 0 -13.549 Td [(con\014gured)-333(with:)]TJ -0 g 0 G -0 g 0 G -/F44 10.9091 Tf 5.727 -22.538 Td [(./configure)-525(--with-psblas=/opt/psblas-3.3/)-525(\134)]TJ 0 -13.549 Td [(--with-umfpackincdir=/usr/include/suitesparse)]TJ/F15 10.9091 Tf -5.727 -22.533 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 -13.55 Td [(Make.inc)]TJ/F15 10.9091 Tf 49.144 0 Td [(whic)28(h)-305(will)-305(then)-305(b)-28(e)-305(used)-305(b)28(y)-305(all)-305(Mak)28(e\014les)-305(in)-305(the)-305(directory)-305(t)1(re)-1(e;)-314(this)-305(\014le)-305(will)-305(b)-27(e)]TJ -49.144 -13.549 Td [(copied)-333(in)-334(the)-333(install)-333(directory)-333(under)-334(the)-333(name)]TJ/F44 10.9091 Tf 223.485 0 Td [(Make.inc.MLD2P4)]TJ/F15 10.9091 Tf 85.908 0 Td [(.)]TJ -292.457 -13.553 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 -0 g 0 G -0 g 0 G -/F44 10.9091 Tf -16.936 -22.538 Td [(make)]TJ/F15 10.9091 Tf 0 -22.534 Td [(follo)28(w)28(ed)-334(\050optionally\051)-333(b)28(y)]TJ -0 g 0 G -0 g 0 G -/F44 10.9091 Tf 0 -22.538 Td [(make)-525(install)]TJ/F17 11.9552 Tf 0 -29.238 Td [(3.4)-1125(Bug)-375(rep)-31(orting)]TJ/F15 10.9091 Tf 0 -20.603 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 -29.239 Td [(3.5)-1125(Example)-375(and)-375(test)-375(programs)]TJ/F15 10.9091 Tf 0 -20.603 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 -13.549 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 -0 g 0 G -/F44 10.9091 Tf -169.272 -22.534 Td [(examples)]TJ -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 -13.549 Td [(with)-333(the)-334(m)28(ultilev)28(el)-333(preconditioners.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -244 0 obj -<< -/Length 1460 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(3)]TJ -0 g 0 G - [-378(Configuring)-378(and)-377(B)-1(uilding)-377(MLD2P4)]TJ/F15 10.9091 Tf 406.997 0 Td [(9)]TJ -0 g 0 G -0 g 0 G -/F44 10.9091 Tf -406.997 -35.866 Td [(tests)]TJ -0 g 0 G -/F15 10.9091 Tf 34.091 0 Td [(con)28(tains)-380(a)-380(set)-380(of)-380(more)-380(soph)1(istic)-1(at)1(e)-1(d)-379(examples)-380(that)-380(will)-380(allo)28(w)-380(the)-380(user,)-391(via)-380(the)]TJ -6.818 -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(to)-286(exp)-28(erimen)28(t)-286(with)-287(the)-286(full)-286(range)-287(of)-286(precon-)]TJ -106.472 -13.549 Td [(ditioners)-333(implemen)27(t)1(e)-1(d)-333(in)-333(the)-333(library)83(.)]TJ -27.273 -22.516 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(e)-1(i)1(ng)-286(storage)-285(format;)-301(the)]TJ/F44 10.9091 Tf 378.088 0 Td [(pdegen)]TJ/F15 10.9091 Tf -378.088 -13.549 Td [(instead)-272(generate)-272(matrices)-272(in)-272(full)-272(parallel)-272(mo)-28(de)-272(f)1(rom)-272(the)-272(discretiz)-1(at)1(ion)-272(of)-272(a)-272(sample)-272(PDE.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -254 0 obj -<< -/Length 8148 ->> -stream -0 g 0 G -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 -0 g 0 G -/F17 14.3462 Tf -203.265 -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(i)1(n)-316(the)-315(parallel)-315(solution)-315(of)-316(large)-315(and)-315(sparse)-315(linear)-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(th)1(e)]TJ 0 -13.55 Td [(whole)-407(original)-406(m)-1(at)1(rix.)-665(This)-407(pro)-28(cess)-407(often)-407(corresp)-27(onds)-407(to)-407(dividing)-407(a)-406(ph)28(ysic)-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(ol)1(ving)-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(origin)1(al)-334(problem)-333(from)-333(the)-334(lo)-27(cal)-334(solutions)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(6)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(7)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-334(22)]TJ -0 g 0 G - [(].)]TJ/F18 10.9091 Tf 16.936 -14.011 Td [(A)51(dditive)-468(Schwarz)]TJ/F15 10.9091 Tf 89.059 0 Td [(preconditioners)-453(are)-453(DD)-454(precondi)1(tioners)-454(using)-453(o)28(v)28(erlapping)-454(sub)1(-)]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 rg 1 0 0 RG - [(22)]TJ -0 g 0 G - [(]\051.)-530(The)-362(main)-362(motiv)56(ation)-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)-361(of)-362(th)1(e)-1(se)-361(preconditioners)-361(is)-361(that)]TJ 0 -13.549 Td [(the)-388(n)28(um)27(b)-27(er)-388(of)-389(iteration)1(s)-389(of)-388(the)-388(preconditioned)-388(solv)28(ers)-388(generally)-389(gr)1(o)27(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)-403(s)-1(u)1(bmatrice)-1(s)-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)-369(b)27(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(inf)1(ormation)-323(related)]TJ 0 -13.549 Td [(to)-333(the)-334(single)-333(submatrices.)]TJ/F18 10.9091 Tf 16.936 -14.012 Td [(Two-level)-308(Schwarz)]TJ/F15 10.9091 Tf 91.53 0 Td [(preconditioners)-279(are)-280(obtained)-279(b)27(y)-279(com)28(bining)-280(basic)-279(\050one-le)-1(v)28(el\051)-279(Sc)27(h)1(-)]TJ -108.466 -13.549 Td [(w)28(arz)-362(preconditioners)-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)-344(`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(th)1(e)-371(w)27(a)28(y)]TJ 0 -13.549 Td [(they)-374(are)-373(com)27(bined)-373([)]TJ -1 0 0 rg 1 0 0 RG - [(22)]TJ -0 g 0 G - [(].)-566(The)-373(same)-374(reasoning)-374(can)-373(b)-28(e)-374(applied)-373(s)-1(t)1(arting)-374(from)-374(the)-373(coarse-)]TJ 0 -13.55 Td [(lev)28(el)-281(system,)-291(i.e.)-281(a)-280(coarse-s)-1(p)1(ac)-1(e)-280(correction)-281(can)-280(b)-28(e)-281(built)-280(from)-281(this)-280(sys)-1(t)1(e)-1(m,)-291(th)28(us)-280(obtaining)]TJ/F18 10.9091 Tf 0 -13.549 Td [(multi-level)]TJ/F15 10.9091 Tf 53.83 0 Td [(preconditioners.)]TJ -36.894 -14.011 Td [(It)-443(is)-444(w)28(orth)-443(noting)-444(that)-443(optimal)-444(p)1(rec)-1(on)1(ditioners)-444(do)-443(not)-444(necessarily)-443(corresp)-28(ond)-443(to)]TJ -16.936 -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(ee)-1(n)-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(Th)1(e)-384(c)27(hoice)-383(of)-384(the)-384(n)28(um)28(b)-28(er)-384(of)-383(lev)27(els,)-396(i.e.)-384(of)]TJ 0 -13.549 Td [(the)-379(coarse-space)-379(corr)1(e)-1(ctions,)-390(al)1(s)-1(o)-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)28(v)27(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 16.936 -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 -16.936 -13.549 Td [(approac)28(h)-412(applies)-413(coarsening)-412(strategies)-413(b)1(as)-1(ed)-412(on)-412(the)-412(kno)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(matrix)-280(and)-279(requires)-280(the)-279(user)-280(to)-280(d)1(e)-1(\014)1(ne)-280(grid)-279(transfer)-280(op)-28(erators)-279(from)-280(the)]TJ 0 -13.549 Td [(\014ne)-393(to)-394(the)-394(coarse)-393(lev)28(e)-1(l)1(s)-394(and)-394(vice)-393(v)28(ersa.)-626(Th)1(is)-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)28(e)-1(l)-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(consid)1(e)-1(r)1(e)-1(d)1(.)-695(The)-416(alge)-1(b)1(raic)-417(approac)28(h)-417(builds)-416(coarse-s)-1(p)1(ac)-1(e)-416(corrections)-417(using)]TJ 0 -13.549 Td [(only)-442(matrix)-442(information.)-770(It)-442(p)-28(erforms)-442(a)-442(fully)-442(automatic)-442(coarsening)-442(and)-442(enforces)-443(th)1(e)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -273 0 obj -<< -/Length 14867 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -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 [(11)]TJ -0 g 0 G - -401.542 -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(s)-1(u)1(itably)-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 rg 1 0 0 RG - [(24)]TJ -0 g 0 G - [(].)]TJ 16.937 -13.643 Td [(MLD2P4)-255(uses)-255(a)-255(pu)1(re)-255(algebraic)-255(approac)28(h)-255(for)-255(building)-255(t)1(he)-255(sequence)-255(of)-255(coarse)-255(matrices)]TJ -16.937 -13.549 Td [(starting)-425(from)-425(the)-425(original)-425(matrix.)-720(The)-426(algebrai)1(c)-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 58.613 0 Td [(algorithm)-402([)]TJ -1 0 0 rg 1 0 0 RG - [(1)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-402(26)]TJ -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 -58.613 -13.549 Td [(where)-347(the)-346(smo)-28(othed)-347(aggregation)-346(is)-347(applied)-347(lo)-27(cally)-347(to)-347(eac)28(h)-346(s)-1(u)1(bmatrix)-347([)]TJ -1 0 0 rg 1 0 0 RG - [(25)]TJ -0 g 0 G - [(].)-484(In)-347(the)-347(next)]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(e)-1(l)-248(Sc)28(h)27(w)28(arz)-249(pr)1(e)-1(cond)1(itioners)]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(MLD)1(2P4.)-613(F)83(or)-390(f)1(urther)]TJ 0 -13.549 Td [(details)-333(the)-334(reader)-333(is)-333(referred)-334(to)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(2)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(3)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-334(4)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(8)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(22)]TJ -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)-270(p)1(re)-1(cond)1(itioners)-270(implemen)28(ted)-270(in)-270(MLD2P4)-269(are)-270(obtained)-270(b)28(y)-269(com)27(bining)-269(AS)]TJ 0 -13.549 Td [(preconditioners)-315(with)-315(coarse-space)-315(corrections;)-321(therefore)-316(w)28(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 16.937 -13.643 Td [(Giv)28(en)-303(th)1(e)-303(linear)-302(system)-303(\050)]TJ -0 0 1 rg 0 0 1 RG - [(1)]TJ -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 15.757 0 Td [(a)]TJ/F23 7.9701 Tf 5.767 -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 18.181 3.959 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 8.935 -3.959 Td [(is)-302(a)-303(nonsingular)-302(sparse)-302(matrix)]TJ -270.137 -13.549 Td [(with)-321(a)-321(symmetric)-321(nonzero)-321(pattern,)-324(let)]TJ/F22 10.9091 Tf 184.527 0 Td [(G)]TJ/F15 10.9091 Tf 11.607 0 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.758 0 Td [(W)28(;)-167(E)]TJ/F15 10.9091 Tf 23.53 0 Td [(\051)-321(b)-28(e)-321(the)-321(adjacency)-321(graph)-321(of)]TJ/F22 10.9091 Tf 134.379 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)-323(where)]TJ/F22 10.9091 Tf -377.983 -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 5.455 0 Td [(;)]TJ/F15 10.9091 Tf 4.848 0 Td [(2)]TJ/F22 10.9091 Tf 5.455 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(n)]TJ/F25 10.9091 Tf 30.79 0 Td [(g)]TJ/F15 10.9091 Tf 9.433 0 Td [(and)]TJ/F22 10.9091 Tf 21.555 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 5.454 0 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(i;)-167(j)]TJ/F15 10.9091 Tf 13.723 0 Td [(\051)-330(:)]TJ/F22 10.9091 Tf 14.475 0 Td [(a)]TJ/F23 7.9701 Tf 5.767 -1.637 Td [(ij)]TJ/F25 10.9091 Tf 10.866 1.637 Td [(6)]TJ/F15 10.9091 Tf 0 0 Td [(=)-330(0)]TJ/F25 10.9091 Tf 17.541 0 Td [(g)]TJ/F15 10.9091 Tf 9.433 0 Td [(are)-365(the)-364(v)27(ertex)-364(se)-1(t)-364(and)-365(the)-365(edge)-364(set)-365(of)]TJ/F22 10.9091 Tf 184.477 0 Td [(G)]TJ/F15 10.9091 Tf 8.577 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)-341(is)-340(an)-341(edge)-341(connecting)-340(them.)-467(F)84(or)]TJ 0 -13.55 Td [(an)28(y)-238(in)27(teger)]TJ/F22 10.9091 Tf 54.621 0 Td [(\016)-316(>)]TJ/F15 10.9091 Tf 19.807 0 Td [(0,)-257(a)]TJ/F22 10.9091 Tf 19.344 0 Td [(\016)]TJ/F15 10.9091 Tf 5.261 0 Td [(-o)28(v)28(erlap)-239(part)1(ition)-239(of)]TJ/F22 10.9091 Tf 96.341 0 Td [(W)]TJ/F15 10.9091 Tf 14.416 0 Td [(can)-238(b)-28(e)-238(de\014ned)-238(recursiv)28(e)-1(l)1(y)-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(erlappin)1(g\051)-344(partition)-344(of)]TJ/F22 10.9091 Tf 216.25 0 Td [(W)]TJ/F15 10.9091 Tf 11.818 0 Td [(,)-346(i.e.)-344(a)-343(set)-344(of)]TJ/F22 10.9091 Tf 63.377 0 Td [(m)]TJ/F15 10.9091 Tf 13.327 0 Td [(disjoin)28(t)-344(nonempt)28(y)-343(s)-1(ets)]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 7.273 3.959 Td [(m)]TJ 0 -7.015 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F22 10.9091 Tf 11.319 3.056 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/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 [(,)-289(a)]TJ/F22 10.9091 Tf 14.682 0 Td [(\016)]TJ/F15 10.9091 Tf 5.261 0 Td [(-o)28(v)28(erlap)-279(partition)-278(of)]TJ/F22 10.9091 Tf 97.662 0 Td [(W)]TJ/F15 10.9091 Tf 14.856 0 Td [(is)-279(obtain)1(e)-1(d)-278(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 9.09 3.056 Td [(\033)]TJ/F22 10.9091 Tf 11.515 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 4.588 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 -7.845 Td [(i)]TJ/F15 10.9091 Tf 20.225 3.257 Td [(obtained)-306(b)27(y)-306(including)-307(the)-306(v)28(ertices)-307(that)-307(are)-306(adjacen)28(t)-307(to)-307(an)28(y)-306(v)27(ertex)]TJ -100.974 -13.549 Td [(in)]TJ/F22 10.9091 Tf 12.728 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 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -12.147 -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 63.705 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 20.457 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F25 10.9091 Tf 7.659 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 4.089 2.582 Td [(\002)]TJ/F23 7.9701 Tf 6.587 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 -211.56 -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 -0.391 -7.015 Td [(i)]TJ/F25 10.9091 Tf 8.249 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 144.984 0 Td [(v)]TJ/F15 10.9091 Tf 9.485 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 11.819 3.959 Td [(\016)]TJ -1.516 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.06 3.055 Td [(.)-551(The)-369(transp)-28(ose)-369(of)]TJ/F22 10.9091 Tf 94 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.959 Td [(\016)]TJ -0.085 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.654 3.055 Td [(is)-369(a)-369(prolongation)-369(op)-28(erator)-368(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 13.723 0 Td [(<)]TJ/F23 7.9701 Tf 7.878 3.959 Td [(n)]TJ/F15 10.9091 Tf 5.637 -3.959 Td [(.)-551(The)]TJ -384.618 -14.974 Td [(matrix)]TJ/F22 10.9091 Tf 35.134 0 Td [(A)]TJ/F23 7.9701 Tf 8.181 3.959 Td [(\016)]TJ 0 -7.015 Td [(i)]TJ/F15 10.9091 Tf 7.575 3.056 Td [(=)]TJ/F22 10.9091 Tf 11.515 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 4.629 3.056 Td [(A)]TJ/F15 10.9091 Tf 8.181 0 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 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 4.243 3.959 Td [(T)]TJ/F25 10.9091 Tf 9.634 -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 6.587 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 7.872 -1.376 Td [(can)-301(b)-28(e)-301(considered)-301(as)-301(a)-301(restriction)-301(of)]TJ/F22 10.9091 Tf 172.964 0 Td [(A)]TJ/F15 10.9091 Tf 11.466 0 Td [(corresp)-28(onding)]TJ -345.966 -13.549 Td [(to)-333(the)-334(set)]TJ/F22 10.9091 Tf 49.152 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.958 Td [(\016)]TJ -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.059 3.056 Td [(.)]TJ -48.577 -13.643 Td [(The)]TJ/F18 10.9091 Tf 22.424 0 Td [(classic)51(al)-358(one-l)1(evel)-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 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(AS)]TJ/F15 10.9091 Tf 15.538 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 8.368 4.505 Td [(\016)]TJ -0.085 -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 6.605 -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 -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 8.972 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 283.186 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 10.064 -3.958 Td [(within)-406(a)]TJ -372.267 -13.55 Td [(Krylo)28(v)-333(s)-1(ol)1(v)27(er)-333(requires)-333(the)-334(follo)28(wing)-333(three)-333(ste)-1(p)1(s)-1(:)]TJ -0 g 0 G - 13.334 -22.89 Td [(1.)]TJ -0 g 0 G - [-500(restriction)-333(of)]TJ/F22 10.9091 Tf 78.606 0 Td [(v)]TJ/F15 10.9091 Tf 9.315 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 6.412 1.636 Td [(=)]TJ/F22 10.9091 Tf 11.515 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 5.68 0 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 -0 g 0 G - -207.366 -22.89 Td [(2.)]TJ -0 g 0 G - [-500(solution)-333(of)-333(the)-334(linear)-333(systems)]TJ/F22 10.9091 Tf 157.242 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 6.412 1.637 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(v)]TJ/F23 7.9701 Tf 5.288 -1.637 Td [(i)]TJ/F15 10.9091 Tf 3.381 1.637 Td [(,)]TJ/F22 10.9091 Tf 6.667 0 Td [(i)]TJ/F15 10.9091 Tf 6.788 0 Td [(=)-278(1)]TJ/F22 10.9091 Tf 16.97 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(m)]TJ/F15 10.9091 Tf 33.821 0 Td [(;)]TJ -0 g 0 G - -268.62 -22.89 Td [(3.)]TJ -0 g 0 G - [-500(prolongation)-333(and)-333(sum)-334(of)-333(the)]TJ/F22 10.9091 Tf 153.121 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 4.243 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 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 4.243 3.958 Td [(T)]TJ/F22 10.9091 Tf 6.604 -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(that)-472(the)-473(l)1(inear)-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 rg 1 0 0 RG - [(21)]TJ -0 g 0 G - [(,)-334(Chapter)-333(10].)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -294 0 obj -<< -/Length 13838 ->> -stream -0 g 0 G -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 -0 g 0 G -/F15 10.9091 Tf -186.329 -35.866 Td [(A)-318(v)56(arian)28(t)-318(of)-318(the)-317(class)-1(ical)-317(AS)-318(preconditioner)-318(th)1(at)-318(outp)-28(erforms)-318(it)-317(in)-318(terms)-318(of)-317(c)-1(on)28(v)28(er-)]TJ -16.936 -13.549 Td [(gence)-265(rate)-266(and)-265(of)-265(computation)-265(and)-265(comm)27(un)1(ication)-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 105.993 0 Td [(preconditioner)-387([)]TJ -1 0 0 rg 1 0 0 RG - [(5)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-387(14)]TJ -0 g 0 G - [(].)-605(It)-387(is)-386(obtained)]TJ -235.209 -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(erlappin)1(g)-408(v)28(ertices)-408(when)-407(ap-)]TJ -163.715 -13.549 Td [(plying)-349(the)-348(prolongation.)-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 182.691 2.758 Td [(~)]TJ/F22 10.9091 Tf -2.365 -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 4.816 3.055 Td [(\051)]TJ/F23 7.9701 Tf 4.243 3.959 Td [(T)]TJ/F25 10.9091 Tf 10.613 -3.959 Td [(2)-368(<)]TJ/F23 7.9701 Tf 19.161 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 5.637 -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 -0.085 -7.014 Td [(i)]TJ/F15 10.9091 Tf 9.041 3.055 Td [(is)-387(obtained)-387(b)28(y)-388(zeroing)]TJ -305.75 -13.549 Td [(the)-333(ro)28(w)-1(s)-333(of)]TJ/F22 10.9091 Tf 56.454 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.264 3.055 Td [(corresp)-28(onding)-333(to)-333(the)-334(v)28(ertices)-333(in)]TJ/F22 10.9091 Tf 154.455 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.959 Td [(\016)]TJ -1.515 -7.014 Td [(i)]TJ/F25 10.9091 Tf 6.059 3.055 Td [(n)]TJ/F22 10.9091 Tf 5.455 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 6.247 3.055 Td [(:)]TJ/F22 10.9091 Tf -127.804 -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 -7.776 -8.022 Td [(R)-6(AS)]TJ/F15 10.9091 Tf 21.895 3.434 Td [(=)]TJ/F23 7.9701 Tf 15.648 13.637 Td [(m)]TJ/F28 10.9091 Tf -4.133 -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 11.847 13.087 Td [(\050)]TJ 6.608 2.758 Td [(~)]TJ/F22 10.9091 Tf -2.365 -2.758 Td [(R)]TJ/F20 7.9701 Tf 8.367 4.505 Td [(0)]TJ/F23 7.9701 Tf -0.084 -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 4.242 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 -271.401 -30.78 Td [(Analogously)83(,)-333(the)-333(AS)-333(v)55(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 -207.736 -29.306 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 [(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 -4.134 -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 13.088 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 4.504 Td [(\016)]TJ -0.085 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.629 2.697 Td [(\051)]TJ/F23 7.9701 Tf 4.242 4.504 Td [(T)]TJ/F15 10.9091 Tf 6.605 -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 -2.366 -2.757 Td [(R)]TJ/F20 7.9701 Tf 8.368 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 8.315 0 Td [(=)-280(0)-335(the)-334(three)-335(v)56(arian)27(ts)-334(of)-335(the)-335(AS)-334(preconditioner)-335(are)-334(all)-335(equal)-335(to)-334(the)]TJ -91.737 -13.55 Td [(blo)-28(c)28(k-Jacobi)-333(preconditioner.)]TJ 16.936 -13.549 Td [(As)-358(already)-359(ob)1(s)-1(erv)28(ed,)-364(the)-358(c)-1(on)28(v)28(ergence)-358(rate)-359(of)-358(the)-358(one-lev)28(el)-359(S)1(c)27(h)28(w)28(arz)-358(preconditioned)]TJ -16.936 -13.549 Td [(iterativ)28(e)-358(s)-1(olv)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 75.453 0 Td [(W)]TJ/F15 10.9091 Tf 15.727 0 Td [(increases)-358([)]TJ -1 0 0 rg 1 0 0 RG - [(7)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-359(22)]TJ -0 g 0 G - [(].)-519(T)83(o)]TJ -316.089 -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(parall)1(e)-1(li)1(s)-1(m)-307(w)27(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)-275(o)27(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(pur)1(e)-275(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(buil)1(t)-275(with)]TJ -318.789 -13.549 Td [(the)-321(Galerkin)-322(appr)1(oac)27(h.)-440(Giv)28(en)-322(a)-321(set)]TJ/F22 10.9091 Tf 171.697 0 Td [(W)]TJ/F23 7.9701 Tf 10.303 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.602 1.689 Td [(of)]TJ/F18 10.9091 Tf 12.294 0 Td [(c)51(o)51(arse)-346(vertic)51(es)]TJ/F15 10.9091 Tf 68.461 0 Td [(,)-324(with)-321(size)]TJ/F22 10.9091 Tf 51.815 0 Td [(n)]TJ/F23 7.9701 Tf 6.548 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.097 1.689 Td [(,)-324(and)-321(a)-321(suitable)]TJ -338.817 -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 8.181 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.734 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(coars)-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 11.772 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/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 8.181 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -6.587 -8.022 Td [(C)]TJ/F22 10.9091 Tf 11.319 3.434 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F22 10.9091 Tf 7.097 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 8.181 -1.689 Td [(C)]TJ/F15 10.9091 Tf 11.098 1.689 Td [(is)-367(assumed)-366(to)-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 -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 16.509 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(olv)1(ing)]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 20.947 0 Td [(M)]TJ/F20 7.9701 Tf 10.584 -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 11.772 4.587 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 3.435 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 6.586 0 Td [(A)]TJ/F15 10.9091 Tf 11.406 3.434 Td [(to)-418(a)-419(v)28(ector)]TJ/F22 10.9091 Tf 57.967 0 Td [(v)]TJ/F15 10.9091 Tf 10.245 0 Td [(within)-418(a)-419(Krylo)28(v)-418(solv)28(e)-1(r)-418(corresp)-28(onds)-418(to)-419(app)1(lying)]TJ/F22 10.9091 Tf 234.378 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/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 6.586 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 11.91 3.434 Td [(to)]TJ/F22 10.9091 Tf 13.333 0 Td [(v)]TJ/F15 10.9091 Tf 9.316 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)-333(the)-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 11.772 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/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 11.133 0 Td [(=)]TJ/F22 10.9091 Tf 11.516 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 12.508 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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -306 0 obj -<< -/Length 11371 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -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 - -401.542 -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)51(othe)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 -25.536 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.775 -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(R)-6(E)]TJ/F15 10.9091 Tf 23.153 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 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 14.932 3.435 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 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.021 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 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.021 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.434 Td [(:)]TJ/F15 10.9091 Tf -300.208 -25.537 Td [(On)-368(the)-369(other)-368(hand,)-378(b)28(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 -13.549 Td [(computing)]TJ/F22 10.9091 Tf 150.506 -13.871 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/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F22 10.9091 Tf 12.508 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 -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.235 0 Td [(L)]TJ/F15 10.9091 Tf 8.274 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/F22 10.9091 Tf 4.242 0 Td [(;)]TJ/F15 10.9091 Tf -258.915 -20.312 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 148.757 0 Td [(Sc)28(h)28(w)27(arz)-333(preconditioner)-333(is)-333(obtained:)]TJ/F22 10.9091 Tf -60.973 -25.537 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(O)-29(S)-56(T)]TJ/F15 10.9091 Tf 28.436 3.434 Td [(=)]TJ/F22 10.9091 Tf 11.516 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 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 4.235 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.434 Td [(A)]TJ/F28 10.9091 Tf 8.181 8.836 Td [(\001)]TJ/F22 10.9091 Tf 6.819 -8.836 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 [(:)]TJ/F15 10.9091 Tf -302.849 -25.537 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(preconditi)1(oner)-223(is)-222(obtained)-222(b)28(y)-222(applying)-222(the)-223(smo)-28(oth)1(e)-1(r)]TJ 0 -13.549 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(symm)-1(etric)]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 6.667 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 9.894 1.689 Td [(and)]TJ/F22 10.9091 Tf 21.212 0 Td [(M)]TJ/F23 7.9701 Tf 10.583 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.733 1.689 Td [(are)-333(symme)-1(tr)1(ic.)]TJ -75.151 -13.892 Td [(As)-533(p)1(reviously)-533(noted,)-582(on)-533(parallel)-532(computers)-533(the)-532(n)28(um)28(b)-28(er)-533(of)-532(submatrices)-533(usually)]TJ -16.937 -13.549 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(th)1(e)-307(size)-307(of)-307(the)-307(system)-307(to)-307(b)-28(e)-306(precon-)]TJ 0 -13.55 Td [(ditioned)-300(is)-300(v)28(ery)-301(l)1(arge)-1(,)-306(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(sys)-1(tem,)-317(whose)-315(solu)1(tion)-314(ma)27(y)-314(b)-27(e)-314(c)-1(ompu)1(tationally)-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)-424(on)-423(s)-1(i)1(ngle)-424(pro)-28(cessors,)-447(b)-28(ecause)-424(of)-424(memory)-424(and/or)-424(com-)]TJ 0 -13.549 Td [(puting)-324(requiremen)28(ts.)-441(Therefore,)-326(it)-324(seems)-324(natural)-324(to)-324(use)-324(a)-324(r)1(e)-1(cur)1(s)-1(iv)28(e)-324(approac)28(h,)-326(in)-323(whic)27(h)]TJ 0 -13.55 Td [(the)-394(coarse)-1(-lev)28(el)-394(correction)-395(is)-394(re-applied)-394(starting)-395(from)-394(the)-394(c)-1(u)1(rren)27(t)-394(coarse-lev)28(el)-395(system.)]TJ 0 -13.549 Td [(The)-321(corresp)-28(onding)-321(p)1(rec)-1(on)1(ditioners,)-324(called)]TJ/F18 10.9091 Tf 202.455 0 Td [(multi-level)]TJ/F15 10.9091 Tf 53.695 0 Td [(preconditioners,)-323(can)-321(signi\014can)28(tly)]TJ -256.15 -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 rg 1 0 0 RG - [(22)]TJ -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 rg 1 0 0 RG - [(22)]TJ -0 g 0 G - [(,)-324(Chap)1(te)-1(r)-321(3].)-440(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 15.429 0 Td [(to)-335(a)-335(v)28(ec)-1(tor)]TJ/F22 10.9091 Tf 55.241 0 Td [(v)]TJ/F15 10.9091 Tf 5.679 0 Td [(,)-336(i.e.)-335(for)-335(the)-335(computation)-335(of)]TJ/F22 10.9091 Tf 135.911 0 Td [(w)]TJ/F15 10.9091 Tf 11.166 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 4.733 -3.959 Td [(v)]TJ/F15 10.9091 Tf 5.679 0 Td [(,)]TJ -409.421 -13.549 Td [(is)-425(rep)-28(orted,)-448(for)-425(example,)-448(in)-425(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-425(1)]TJ -0 g 0 G - [(.)-720(Here)-425(the)-425(n)28(um)27(b)-27(er)-425(of)-426(lev)28(els)-425(is)-425(denoted)-425(b)28(y)]TJ/F22 10.9091 Tf 391.675 0 Td [(nl)-20(ev)]TJ/F15 10.9091 Tf -391.675 -13.549 Td [(and)-410(the)-411(lev)28(els)-411(are)-410(n)28(um)27(b)-27(ered)-411(in)-410(increasing)-411(order)-410(starting)-411(from)-410(the)-411(\014nest)-410(one,)-430(i.e.)-410(the)]TJ 0 -13.549 Td [(\014nest)-361(lev)28(el)-361(is)-362(lev)28(el)-361(1;)-375(the)-361(coarse)-361(matrix)-361(and)-361(the)-361(corresp)-28(onding)-361(basic)-361(preconditioner)-361(at)]TJ 0 -13.55 Td [(eac)28(h)-415(lev)28(el)]TJ/F22 10.9091 Tf 51.17 0 Td [(l)]TJ/F15 10.9091 Tf 7.995 0 Td [(are)-415(denoted)-414(b)27(y)]TJ/F22 10.9091 Tf 77.24 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.777 Td [(l)]TJ/F15 10.9091 Tf 7.645 1.777 Td [(and)]TJ/F22 10.9091 Tf 22.1 0 Td [(M)]TJ/F23 7.9701 Tf 10.583 -1.777 Td [(l)]TJ/F15 10.9091 Tf 3.121 1.777 Td [(,)-435(resp)-28(ectiv)28(ely)83(,)-435(with)]TJ/F22 10.9091 Tf 96.23 0 Td [(A)]TJ/F20 7.9701 Tf 8.182 -1.636 Td [(1)]TJ/F15 10.9091 Tf 9.242 1.636 Td [(=)]TJ/F22 10.9091 Tf 12.996 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)-435(while)-415(the)-415(r)1(e)-1(lated)]TJ -322.868 -13.549 Td [(restriction)-333(op)-28(erator)-333(is)-334(denoted)-333(b)28(y)]TJ/F22 10.9091 Tf 163.576 0 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.777 Td [(l)]TJ/F15 10.9091 Tf 3.12 1.777 Td [(.)]TJ/F17 11.9552 Tf -174.979 -31.172 Td [(4.2)-1125(Smo)-31(othed)-375(Aggregation)]TJ/F15 10.9091 Tf 0 -21.261 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 8.284 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.096 1.689 Td [(,)-430(whic)27(h)-411(is)-411(used)-411(to)-411(compute)-411(th)1(e)-412(coarse-)]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 7.097 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)-27(e)-1(d)-280(in)-281([)]TJ -1 0 0 rg 1 0 0 RG - [(1)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-281(26)]TJ -0 g 0 G - [(].)]TJ -271.894 -13.549 Td [(The)-443(basic)-442(idea)-443(of)-443(this)-442(algorithm)-443(is)-442(to)-443(build)-443(a)-442(coarse)-443(set)-443(of)-442(v)27(ertices)]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 11.926 1.689 Td [(b)28(y)-443(suitably)]TJ -358.168 -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(subse)-1(t)1(s)-330(\050aggregates\051,)-331(and)-329(to)-330(de\014ne)-329(the)-330(coarse-)]TJ -131.434 -13.549 Td [(to-\014ne)-253(s)-1(p)1(ac)-1(e)-253(transfer)-253(op)-28(erator)]TJ/F22 10.9091 Tf 144.031 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 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(apply)1(ing)-254(a)-253(suitable)-254(smo)-28(other)-253(to)-254(a)-253(simple)-254(piecewise)]TJ -162.177 -13.549 Td [(constan)28(t)-334(pr)1(olongation)-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 16.937 -13.892 Td [(Three)-333(main)-334(steps)-333(can)-333(b)-28(e)-333(iden)27(ti\014ed)-333(in)-333(the)-334(smo)-27(othed)-334(aggregation)-333(pro)-28(cedure:)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -177 0 obj -<< -/Type /ObjStm -/N 100 -/First 899 -/Length 13302 ->> -stream -161 0 162 156 163 319 164 471 165 621 166 774 11 921 172 974 168 1030 192 1162 -184 1344 185 1491 186 1638 187 1782 188 1929 189 2075 190 2222 191 2369 197 2449 195 2591 -194 2737 199 2885 15 2939 196 2992 210 3098 201 3288 202 3436 203 3584 204 3732 205 3879 -206 4026 207 4180 208 4332 212 4481 19 4535 23 4588 27 4641 209 4694 222 4813 220 4963 -218 5109 219 5258 224 5412 31 5466 221 5519 228 5651 230 5765 227 5819 233 5912 231 6046 -235 6192 232 6246 238 6339 240 6453 35 6507 39 6560 237 6613 243 6719 241 6853 245 6999 -242 7053 253 7146 246 7312 247 7469 248 7617 249 7766 250 7914 255 8061 43 8115 252 8168 -272 8274 270 8496 251 8642 258 8798 259 8953 260 9113 261 9267 262 9417 263 9567 264 9718 -265 9871 266 10020 267 10169 274 10321 47 10375 280 10428 281 10482 282 10536 271 10590 293 10787 -268 10945 269 11097 290 11250 291 11399 295 11548 292 11602 305 11786 303 11960 298 12106 299 12254 -% 161 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [476.497 467.091 483.944 476.114] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 162 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [488.085 467.091 500.987 476.114] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 163 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [124.009 337.312 136.911 346.335] -/A << /S /GoTo /D (cite.psblas_00) >> ->> -% 164 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [142.708 337.312 155.609 346.335] -/A << /S /GoTo /D (cite.PSBLAS3) >> ->> -% 165 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [215.787 201.82 228.689 210.843] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 166 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [432.433 188.271 445.335 197.293] -/A << /S /GoTo /D (cite.MPI1) >> ->> -% 11 0 obj -<< -/D [169 0 R /XYZ 93.6 715.095 null] ->> -% 172 0 obj -<< -/D [169 0 R /XYZ 280.58 643.083 null] ->> -% 168 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F17 108 0 R /F18 171 0 R /F22 173 0 R /F25 174 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 192 0 obj -<< -/Type /Page -/Contents 193 0 R -/Resources 191 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 175 0 R -/Annots [ 184 0 R 185 0 R 186 0 R 187 0 R 188 0 R 189 0 R 190 0 R ] ->> -% 184 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [243.651 538.429 251.098 550.118] -/A << /S /GoTo /D (section.2) >> ->> -% 185 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [238.905 524.879 246.352 536.569] -/A << /S /GoTo /D (section.3) >> ->> -% 186 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [347.75 511.33 355.197 523.02] -/A << /S /GoTo /D (section.4) >> ->> -% 187 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [185.352 470.683 192.799 482.372] -/A << /S /GoTo /D (section.5) >> ->> -% 188 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [239.103 443.584 246.55 455.274] -/A << /S /GoTo /D (section.6) >> ->> -% 189 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [230.595 430.035 238.042 441.724] -/A << /S /GoTo /D (section.7) >> ->> -% 190 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [332.616 416.486 342.79 428.175] -/A << /S /GoTo /D (appendix.A) >> ->> -% 191 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 197 0 obj -<< -/Type /Page -/Contents 198 0 R -/Resources 196 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 175 0 R -/Annots [ 195 0 R 194 0 R ] ->> -% 195 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.2) >> ->> -% 194 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [493.843 618.086 504.017 629.776] -/A << /S /GoTo /D (appendix.A) >> ->> -% 199 0 obj -<< -/D [197 0 R /XYZ 92.6 752.957 null] ->> -% 15 0 obj -<< -/D [197 0 R /XYZ 93.6 715.095 null] ->> -% 196 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F17 108 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 210 0 obj -<< -/Type /Page -/Contents 211 0 R -/Resources 209 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 175 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 ] ->> -% 201 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [126.812 482.904 139.714 491.926] -/A << /S /GoTo /D (cite.blas3) >> ->> -% 202 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [144.192 482.904 157.094 491.926] -/A << /S /GoTo /D (cite.blas2) >> ->> -% 203 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [161.572 482.904 174.474 491.926] -/A << /S /GoTo /D (cite.blas1) >> ->> -% 204 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [119.131 351.551 132.032 360.574] -/A << /S /GoTo /D (cite.MPI2) >> ->> -% 205 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [136.782 351.551 149.683 360.574] -/A << /S /GoTo /D (cite.MPI1) >> ->> -% 206 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [142.358 315.043 155.259 324.066] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 207 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [159.934 315.043 172.835 324.066] -/A << /S /GoTo /D (cite.psblas_00) >> ->> -% 208 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [158.903 134.074 166.35 143.097] -/A << /S /GoTo /D (cite.UMFPACK) >> ->> -% 212 0 obj -<< -/D [210 0 R /XYZ 85.4 752.957 null] ->> -% 19 0 obj -<< -/D [210 0 R /XYZ 86.4 715.095 null] ->> -% 23 0 obj -<< -/D [210 0 R /XYZ 86.4 539.606 null] ->> -% 27 0 obj -<< -/D [210 0 R /XYZ 86.4 223.096 null] ->> -% 209 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F17 108 0 R /F44 200 0 R /F43 155 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 222 0 obj -<< -/Type /Page -/Contents 223 0 R -/Resources 221 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 175 0 R -/Annots [ 220 0 R 218 0 R 219 0 R ] ->> -% 220 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.3) >> ->> -% 218 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [150.46 667.049 163.361 676.071] -/A << /S /GoTo /D (cite.SUPERLU) >> ->> -% 219 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [177.909 603.859 190.811 612.881] -/A << /S /GoTo /D (cite.SUPERLUDIST) >> ->> -% 224 0 obj -<< -/D [222 0 R /XYZ 92.6 752.957 null] ->> -% 31 0 obj -<< -/D [222 0 R /XYZ 93.6 560.339 null] ->> -% 221 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F43 155 0 R /F44 200 0 R /F17 108 0 R /F18 171 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 228 0 obj -<< -/Type /Page -/Contents 229 0 R -/Resources 227 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 175 0 R ->> -% 230 0 obj -<< -/D [228 0 R /XYZ 85.4 752.957 null] ->> -% 227 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 233 0 obj -<< -/Type /Page -/Contents 234 0 R -/Resources 232 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 236 0 R -/Annots [ 231 0 R ] ->> -% 231 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.3) >> ->> -% 235 0 obj -<< -/D [233 0 R /XYZ 92.6 752.957 null] ->> -% 232 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 238 0 obj -<< -/Type /Page -/Contents 239 0 R -/Resources 237 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 236 0 R ->> -% 240 0 obj -<< -/D [238 0 R /XYZ 85.4 752.957 null] ->> -% 35 0 obj -<< -/D [238 0 R /XYZ 86.4 296.197 null] ->> -% 39 0 obj -<< -/D [238 0 R /XYZ 86.4 217.136 null] ->> -% 237 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F44 200 0 R /F17 108 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 243 0 obj -<< -/Type /Page -/Contents 244 0 R -/Resources 242 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 236 0 R -/Annots [ 241 0 R ] ->> -% 241 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.3) >> ->> -% 245 0 obj -<< -/D [243 0 R /XYZ 92.6 752.957 null] ->> -% 242 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 253 0 obj -<< -/Type /Page -/Contents 254 0 R -/Resources 252 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 236 0 R -/Annots [ 246 0 R 247 0 R 248 0 R 249 0 R 250 0 R ] ->> -% 246 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [436.919 569.496 444.366 578.519] -/A << /S /GoTo /D (cite.Cai_Widlund_92) >> ->> -% 247 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [449.04 569.496 456.487 578.519] -/A << /S /GoTo /D (cite.dd1_94) >> ->> -% 248 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [461.161 569.496 474.063 578.519] -/A << /S /GoTo /D (cite.dd2_96) >> ->> -% 249 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [197.616 528.387 210.517 537.41] -/A << /S /GoTo /D (cite.dd2_96) >> ->> -% 250 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [181.3 351.785 194.201 360.808] -/A << /S /GoTo /D (cite.dd2_96) >> ->> -% 255 0 obj -<< -/D [253 0 R /XYZ 85.4 752.957 null] ->> -% 43 0 obj -<< -/D [253 0 R /XYZ 86.4 715.095 null] ->> -% 252 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F17 108 0 R /F18 171 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 272 0 obj -<< -/Type /Page -/Contents 273 0 R -/Resources 271 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 236 0 R -/Annots [ 270 0 R 251 0 R 258 0 R 259 0 R 260 0 R 261 0 R 262 0 R 263 0 R 264 0 R 265 0 R 266 0 R 267 0 R ] ->> -% 270 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.4) >> ->> -% 251 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [246.059 689.591 258.96 698.614] -/A << /S /GoTo /D (cite.StubenGMD69_99) >> ->> -% 258 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [204.726 648.85 212.173 657.872] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 259 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [217.599 648.85 230.5 657.872] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 260 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [429.177 635.3 442.079 644.323] -/A << /S /GoTo /D (cite.TUMINARO_TONG) >> ->> -% 261 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [247.119 594.653 254.566 603.676] -/A << /S /GoTo /D (cite.para_04) >> ->> -% 262 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [259.24 594.653 266.688 603.676] -/A << /S /GoTo /D (cite.aaecc_07) >> ->> -% 263 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [271.362 594.653 278.809 603.676] -/A << /S /GoTo /D (cite.apnum_07) >> ->> -% 264 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [283.483 594.653 290.93 603.676] -/A << /S /GoTo /D (cite.MLD2P4_TOMS) >> ->> -% 265 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [295.604 594.653 308.506 603.676] -/A << /S /GoTo /D (cite.dd2_96) >> ->> -% 266 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [229.325 500.66 236.772 513.561] -/A << /S /GoTo /D (equation.1.1) >> ->> -% 267 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [427.767 120.525 440.669 129.547] -/A << /S /GoTo /D (cite.Saad_book) >> ->> -% 274 0 obj -<< -/D [272 0 R /XYZ 92.6 752.957 null] ->> -% 47 0 obj -<< -/D [272 0 R /XYZ 93.6 577.215 null] ->> -% 280 0 obj -<< -/D [272 0 R /XYZ 93.6 219.839 null] ->> -% 281 0 obj -<< -/D [272 0 R /XYZ 93.6 196.015 null] ->> -% 282 0 obj -<< -/D [272 0 R /XYZ 93.6 173.125 null] ->> -% 271 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F18 171 0 R /F17 108 0 R /F22 173 0 R /F23 275 0 R /F25 174 0 R /F26 276 0 R /F20 277 0 R /F24 278 0 R /F28 279 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 293 0 obj -<< -/Type /Page -/Contents 294 0 R -/Resources 292 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 236 0 R -/Annots [ 268 0 R 269 0 R 290 0 R 291 0 R ] ->> -% 268 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [396.41 676.042 403.857 685.065] -/A << /S /GoTo /D (cite.CAI_SARKIS) >> ->> -% 269 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [409.115 676.042 422.017 685.065] -/A << /S /GoTo /D (cite.EFSTATHIOU) >> ->> -% 290 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [450.402 461.302 457.849 470.324] -/A << /S /GoTo /D (cite.dd1_94) >> ->> -% 291 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [462.795 461.302 475.697 470.324] -/A << /S /GoTo /D (cite.dd2_96) >> ->> -% 295 0 obj -<< -/D [293 0 R /XYZ 85.4 752.957 null] ->> -% 292 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F18 171 0 R /F22 173 0 R /F23 275 0 R /F20 277 0 R /F25 174 0 R /F24 278 0 R /F26 276 0 R /F28 279 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 305 0 obj -<< -/Type /Page -/Contents 306 0 R -/Resources 304 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 308 0 R -/Annots [ 303 0 R 298 0 R 299 0 R 300 0 R 301 0 R 302 0 R ] ->> -% 303 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.4) >> ->> -% 298 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [95.634 362.989 108.536 372.012] -/A << /S /GoTo /D (cite.dd2_96) >> ->> -% 299 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [159.929 335.891 172.831 344.914] -/A << /S /GoTo /D (cite.dd2_96) >> ->> - -endstream -endobj -318 0 obj -<< -/Length 10394 ->> -stream -0 g 0 G -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 -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -/F22 9.9626 Tf -124.174 -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 5.186 0 Td [(;)]TJ/F43 9.9626 Tf -27.768 -17.625 Td [(for)]TJ/F22 9.9626 Tf 17.766 0 Td [(l)]TJ/F15 9.9626 Tf 5.936 0 Td [(=)-278(2)]TJ/F22 9.9626 Tf 15.498 0 Td [(;)-167(nl)-19(ev)]TJ/F43 9.9626 Tf 27.221 0 Td [(do)]TJ/F15 9.9626 Tf -56.459 -14.789 Td [(!)-444(transfer)]TJ/F22 9.9626 Tf 44.113 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 -65.519 -11.956 Td [(v)]TJ/F10 6.9738 Tf 4.83 -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 6.226 0 Td [(1)]TJ/F43 9.9626 Tf -55.371 -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 4.884 -1.494 Td [(nl)-6(ev)]TJ/F15 9.9626 Tf 18.766 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 4.427 0 Td [(1)]TJ/F22 9.9626 Tf 4.982 0 Td [(;)]TJ/F25 9.9626 Tf 4.427 0 Td [(\000)]TJ/F15 9.9626 Tf 7.749 0 Td [(1)]TJ/F43 9.9626 Tf 8.801 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 2.559 0 Td [(+1)]TJ/F15 9.9626 Tf 13.907 1.495 Td [(to)-333(the)-334(next)-333(\014ner)-333(lev)28(el)]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 5.825 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.517 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 10.585 2.821 Td [(y)]TJ/F10 6.9738 Tf 4.885 -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(compute)-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 4.494 -1.495 Td [(l)]TJ/F15 9.9626 Tf 5.826 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 9.962 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 -7.268 Td [(l)]TJ/F22 9.9626 Tf 10.696 3.006 Td [(y)]TJ/F10 6.9738 Tf 4.885 -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 4.494 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.826 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 4.494 -1.494 Td [(l)]TJ/F43 9.9626 Tf -55.802 -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 4.884 -1.494 Td [(1)]TJ/F15 9.9626 Tf 4.47 1.494 Td [(;)]TJ -ET -q -1 0 0 1 158.467 714.896 cm -[]0 d 0 J 0.398 w 0 0 m 268.316 0 l S -Q -q -1 0 0 1 158.666 443.282 cm -[]0 d 0 J 0.398 w 0 0 m 0 271.614 l S -Q -q -1 0 0 1 426.584 443.282 cm -[]0 d 0 J 0.398 w 0 0 m 0 271.614 l S -Q -q -1 0 0 1 158.467 443.282 cm -[]0 d 0 J 0.398 w 0 0 m 268.316 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 106.974 424.548 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(rec)-1(on)1(ditioner.)]TJ -0 g 0 G -0 g 0 G -0 g 0 G - -7.241 -42.981 Td [(1.)]TJ -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 -0 g 0 G - -231.824 -21.526 Td [(2.)]TJ -0 g 0 G - [-500(construction)-333(of)-334(th)1(e)-334(prolongator)]TJ/F22 10.9091 Tf 166.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.959 Td [(T)]TJ -0.084 -7.192 Td [(C)]TJ/F15 10.9091 Tf 7.096 3.233 Td [(;)]TJ -0 g 0 G - -181.895 -21.526 Td [(3.)]TJ -0 g 0 G - [-500(application)-333(of)]TJ/F22 10.9091 Tf 82.728 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 8.367 3.959 Td [(T)]TJ -0.084 -7.192 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 -20.041 Td [(T)83(o)-426(p)-28(erform)-426(the)-426(coarsening)-427(step,)-449(w)28(e)-427(ha)28(v)28(e)-426(implemen)27(ted)-426(the)-426(aggregation)-426(algorithm)]TJ -16.936 -13.549 Td [(sk)28(etc)27(h)1(e)-1(d)-388(in)-388([)]TJ -1 0 0 rg 1 0 0 RG - [(4)]TJ -0 g 0 G - [(].)-610(According)-389(to)-388([)]TJ -1 0 0 rg 1 0 0 RG - [(26)]TJ -0 g 0 G - [(],)-402(a)-389(mo)-28(di\014cation)-388(of)-389(this)-388(algorithm)-388(has)-389(b)-28(een)-388(actually)]TJ 0 -13.55 Td [(considered,)-257(in)-237(whic)28(h)-238(eac)28(h)-237(aggregate)]TJ/F22 10.9091 Tf 169.04 0 Td [(N)]TJ/F23 7.9701 Tf 8.765 -1.636 Td [(r)]TJ/F15 10.9091 Tf 7.145 1.636 Td [(is)-238(made)-237(of)-237(v)27(ertices)-237(of)]TJ/F22 10.9091 Tf 99.165 0 Td [(W)]TJ/F15 10.9091 Tf 14.409 0 Td [(that)-237(are)]TJ/F18 10.9091 Tf 39.756 0 Td [(str)51(ongly)-269(c)51(ouple)51(d)]TJ/F15 10.9091 Tf -338.28 -13.549 Td [(to)-333(a)-334(certain)-333(ro)-28(ot)-333(v)28(ertex)]TJ/F22 10.9091 Tf 115.242 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 -39.683 -23.653 Td [(N)]TJ/F23 7.9701 Tf 8.765 -1.636 Td [(r)]TJ/F15 10.9091 Tf 7.585 1.636 Td [(=)]TJ/F28 10.9091 Tf 11.515 12.11 Td [(n)]TJ/F22 10.9091 Tf 7.273 -12.11 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 5.766 -1.636 Td [(r)-30(s)]TJ/F25 10.9091 Tf 8.471 1.636 Td [(j)]TJ/F22 10.9091 Tf 6.061 0 Td [(>)-278(\022)]TJ/F28 10.9091 Tf 16.939 9.86 Td [(p)]TJ -ET -q -1 0 0 1 318.005 264.251 cm -[]0 d 0 J 0.436 w 0 0 m 34.535 0 l S -Q -BT -/F25 10.9091 Tf 318.005 254.173 Td [(j)]TJ/F22 10.9091 Tf 3.03 0 Td [(a)]TJ/F23 7.9701 Tf 5.767 -1.636 Td [(r)-29(r)]TJ/F22 10.9091 Tf 8.611 1.636 Td [(a)]TJ/F23 7.9701 Tf 5.766 -1.636 Td [(ss)]TJ/F25 10.9091 Tf 8.33 1.636 Td [(j)]TJ/F28 10.9091 Tf 3.031 12.109 Td [(o)]TJ/F25 10.9091 Tf 9.697 -12.109 Td [([)-222(f)]TJ/F22 10.9091 Tf 15.151 0 Td [(r)]TJ/F25 10.9091 Tf 5.225 0 Td [(g)]TJ/F22 10.9091 Tf 7.273 0 Td [(;)]TJ/F15 10.9091 Tf -303.486 -24.259 Td [(for)-341(a)-340(giv)27(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 10.438 0 Td [([0)]TJ/F22 10.9091 Tf 8.485 0 Td [(;)]TJ/F15 10.9091 Tf 4.849 0 Td [(1].)-467(Since)-341(th)1(is)-341(algorithm)-341(has)-341(a)-341(sequen)28(tial)-341(n)1(ature,)-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(een)-399(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 8.11 0 Td [(indep)-28(enden)28(tly)-399(applies)-399(the)-399(algor)1(ithm)-399(to)]TJ -224.346 -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)-420(is)]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)-250(c)-1(omm)28(unication.)-416(On)-251(th)1(e)-251(other)]TJ 0 -13.549 Td [(hand,)-312(it)-306(ma)28(y)-306(pro)-28(duce)-306(non-uniform)-306(aggregate)-1(s)-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(strongl)1(y)-404(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 263.565 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 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(t)1(he)-260(implemen)28(tation)-260(in)-260(M)1(LD2P4,)-275(since)-259(it)-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 -1 0 0 rg 1 0 0 RG - [(3)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(4)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(25)]TJ -0 g 0 G - [(].)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -332 0 obj -<< -/Length 3919 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -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 [(15)]TJ -0 g 0 G - -384.605 -35.866 Td [(The)-277(prolongator)]TJ/F22 10.9091 Tf 80.038 0 Td [(P)]TJ/F23 7.9701 Tf 7.004 -1.688 Td [(C)]TJ/F15 10.9091 Tf 10.127 1.688 Td [(=)]TJ/F22 10.9091 Tf 11.515 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 102.595 0 Td [(P)]TJ/F25 10.9091 Tf 11.549 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 6.586 0 Td [(n)]TJ/F24 5.9776 Tf 5.139 -1.339 Td [(C)]TJ/F15 10.9091 Tf 6.692 -2.62 Td [(,)]TJ -409.421 -13.549 Td [(de\014ned)-333(as)]TJ/F22 10.9091 Tf 114.819 -17.818 Td [(P)]TJ/F15 10.9091 Tf 11.549 0 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.757 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 4.243 0 Td [(;)-1167(p)]TJ/F23 7.9701 Tf 21.246 -1.637 Td [(ij)]TJ/F15 10.9091 Tf 10.296 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 35.72 0 Td [(i)]TJ/F25 10.9091 Tf 6.789 0 Td [(2)]TJ/F22 10.9091 Tf 10.303 0 Td [(V)]TJ/F23 7.9701 Tf 8.787 5.307 Td [(j)]TJ -2.424 -8.741 Td [(C)]TJ/F15 10.9091 Tf -59.175 -10.116 Td [(0)-1913(otherwise)]TJ/F22 10.9091 Tf 79.261 7.304 Td [(:)]TJ -0 g 0 G -/F15 10.9091 Tf 103.909 0 Td [(\0502\051)]TJ -0 g 0 G -/F22 10.9091 Tf -398.512 -27.614 Td [(P)]TJ/F23 7.9701 Tf 7.004 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.733 1.689 Td [(is)-333(obtained)-334(b)28(y)-333(applying)-333(to)]TJ/F22 10.9091 Tf 128.849 0 Td [(P)]TJ/F15 10.9091 Tf 12.155 0 Td [(a)-333(smo)-28(other)]TJ/F22 10.9091 Tf 56.758 0 Td [(S)]TJ/F25 10.9091 Tf 10.348 0 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.182 3.958 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 5.636 -3.958 Td [(:)]TJ/F22 10.9091 Tf -79.224 -24.508 Td [(P)]TJ/F23 7.9701 Tf 7.004 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.127 1.689 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(S)-58(P)-27(;)]TJ -0 g 0 G -/F15 10.9091 Tf 187.7 0 Td [(\0503\051)]TJ -0 g 0 G - -398.512 -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(the)-303(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)-434(S)1(c)27(h)28(w)28(arz)-433(m)-1(etho)-27(d)-434([)]TJ -1 0 0 rg 1 0 0 RG - [(1)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-433(24)]TJ -0 g 0 G - [(].)-744(A)]TJ 0 -13.549 Td [(simple)-333(c)27(hoice)-333(for)]TJ/F22 10.9091 Tf 83.122 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 10.348 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(I)]TJ/F25 10.9091 Tf 8.076 0 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(!)-36(D)]TJ/F26 7.9701 Tf 16.517 4.504 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.733 -4.504 Td [(A;)]TJ -0 g 0 G -/F15 10.9091 Tf 164.459 0 Td [(\0504\051)]TJ -0 g 0 G - -398.512 -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 283.399 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 4.732 -3.959 Td [(A)]TJ/F15 10.9091 Tf -404.269 -13.549 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(1)]TJ -0 g 0 G - [(].)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -351 0 obj -<< -/Length 8842 ->> -stream -0 g 0 G -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 -0 g 0 G -/F17 14.3462 Tf -203.265 -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(an)1(d)-442(applying)-441(MLD2P4)-441(one-lev)27(el)-441(and)-441(m)27(u)1(lti-lev)27(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)28(e)-1(rs)-313(included)-313(in)-313(PSBLAS)-313([)]TJ -1 0 0 rg 1 0 0 RG - [(15)]TJ -0 g 0 G - [(].)-437(The)-314(follo)28(w-)]TJ 0 -13.549 Td [(ing)-333(steps)-334(are)-333(required:)]TJ -0 g 0 G - 13.333 -21.06 Td [(1.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 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 22.908 0 Td [(,)-322(where)]TJ/F18 10.9091 Tf 37.923 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 [(,)-321(ac)-1(cord)1(ing)-319(to)-319(th)1(e)-319(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 9.789 0 Td [(=)-372(real)-373(double)-372(precision;)]TJ/F44 10.9091 Tf 119.008 0 Td [(c)]TJ/F15 10.9091 Tf 9.79 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(omp)1(le)-1(x)-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(thr)1(ough)-334(the)-333(MLD2P4)-333(routines,)-334(fol)1(lo)27(wing)-333(an)-333(ob)-56(ject-orien)28(ted)-333(approac)28(h.)]TJ -0 g 0 G - -13.94 -21.934 Td [(2.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 0 Td [(A)26(l)-52(l)1(o)51(c)51(ate)-364(and)-365(i)1(nitialize)-364(the)-365(pr)52(e)51(c)51(onditioner)-364(data)-364(structur)51(e,)-366(ac)51(c)51(or)51(di)1(n)-1(g)-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 144.004 0 Td [(.)-503(This)-353(is)-354(p)-27(erformed)-353(b)28(y)-353(the)-353(routine)]TJ/F44 10.9091 Tf 169.417 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)-405(defaults)-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 -0 0 1 rg 0 0 1 RG - [-404(1)]TJ -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 74.445 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 72.057 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(cor-)]TJ 0 -13.549 Td [(resp)-28(onding)-333(lo)28(w)28(ercase)-334(ones.)]TJ -0 g 0 G - -13.94 -21.933 Td [(3.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 0 Td [(Mo)51(dify)-340(the)-341(sele)51(cte)52(d)-341(pr)51(e)51(c)51(onditi)1(o)-1(ner)-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(routin)1(e)]TJ/F44 10.9091 Tf 155.169 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 63 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)-364(the)-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)-467(of)-468(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 -0 0 1 rg 0 0 1 RG - [-395(5.1)]TJ -0 g 0 G - [(;)-425(a)-394(complete)-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 -0 0 1 rg 0 0 1 RG - [-333(6)]TJ -0 g 0 G - [(,)-334(T)84(ables)]TJ -0 0 1 rg 0 0 1 RG - [-334(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(5)]TJ -0 g 0 G - [(.)]TJ -0 g 0 G - -13.94 -21.934 Td [(4.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 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)-441(p)-28(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 -0 g 0 G - -76.939 -21.933 Td [(5.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 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)-333(s)-1(ol)1(v)27(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 -0 g 0 G - -267.121 -21.933 Td [(6.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 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(erf)1(orme)-1(d)-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 45.817 0 Td [(.)-502(Thi)1(s)-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 -45.817 -13.549 Td [(the)-333(preconditioner)-333(is)-334(no)-333(more)-333(use)-1(d)1(.)]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 -0 0 1 rg 0 0 1 RG - [-384(6)]TJ -0 g 0 G - [(.)-596(Examples)-384(sho)28(wing)]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 -0 0 1 rg 0 0 1 RG - [-334(5.1)]TJ -0 g 0 G - [(.)]TJ 16.936 -13.549 Td [(Note)-422(th)1(at)-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 68.727 0 Td [(,)-443(c)-1(on)28(taining)-421(the)-422(d)1(e)-1(\014)1(nition)-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(pr)1(ogram)-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(matri)1(x)]TJ -309.224 -13.549 Td [(and)-405(com)-1(m)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(f)1(or)-406(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 -0 0 1 rg 0 0 1 RG - [-333(5.1)]TJ -0 g 0 G - [(\051.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -369 0 obj -<< -/Length 9087 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(5)]TJ -0 g 0 G - [-378(Getting)-378(St)67(ar)67(ted)]TJ/F15 10.9091 Tf 401.542 0 Td [(17)]TJ -0 g 0 G -/F43 10.9091 Tf -401.542 -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)27(o-lev)28(el)-344(preconditioner)-344(has)]TJ -62.779 -13.549 Td [(b)-28(een)-432(c)28(hosen)-432(b)28(y)-432(takin)1(g)-432(in)28(to)-432(accoun)28(t)-432(that,)-456(on)-432(parallel)-432(mac)28(hines,)-457(i)1(t)-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(system)-1(s)-421(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(preconditioners)-223([)]TJ -1 0 0 rg 1 0 0 RG - [(3)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-223(4)]TJ -0 g 0 G - [(].)-408(Ho)28(w)28(e)-1(v)28(er,)-245(this)-223(solv)27(er)-223(do)-28(es)-223(not)-224(necessarily)-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(ite)-1(r)1(ations)-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(tori)1(z)-1(ati)1(on)-312(\050see)-312(Section)]TJ -0 0 1 rg 0 0 1 RG - [-312(6)]TJ -0 g 0 G - [-312(for)-311(the)-312(coarsest-lev)27(el)-311(solv)27(ers)-311(a)27(v)56(ailable)-312(in)-311(MLD2P4\051.)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -ET -q -1 0 0 1 105.524 581.154 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S -Q -q -1 0 0 1 105.524 567.406 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 111.501 571.471 Td [(type)]TJ -ET -q -1 0 0 1 203.297 567.406 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 209.275 571.471 Td [(string)]TJ -ET -q -1 0 0 1 261.07 567.406 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 267.048 571.471 Td [(def)89(a)22(ul)67(t)-378(preconditioner)]TJ -ET -q -1 0 0 1 494.128 567.406 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 105.524 567.207 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S -Q -q -1 0 0 1 105.524 539.909 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 111.501 557.523 Td [(No)-333(preconditioner)]TJ -ET -q -1 0 0 1 203.297 539.909 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 209.275 557.523 Td [('NOPREC')]TJ -ET -q -1 0 0 1 261.07 539.909 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 267.048 557.523 Td [(Considered)-507(only)-507(to)-507(use)-507(the)-508(PSBLAS)-506(Krylo)27(v)]TJ 0 -13.549 Td [(solv)28(ers)-334(with)-333(no)-333(preconditioner.)]TJ -ET -q -1 0 0 1 494.128 539.909 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 105.524 539.71 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S -Q -q -1 0 0 1 105.524 525.961 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 111.501 530.026 Td [(Diagonal)]TJ -ET -q -1 0 0 1 203.297 525.961 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F44 10.9091 Tf 209.275 530.026 Td [('DIAG')]TJ -ET -q -1 0 0 1 261.07 525.961 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 267.048 530.026 Td [(|)]TJ -ET -q -1 0 0 1 494.128 525.961 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 105.524 525.762 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S -Q -q -1 0 0 1 105.524 512.014 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 111.501 516.078 Td [(Blo)-28(c)28(k)-333(Jacobi)]TJ -ET -q -1 0 0 1 203.297 512.014 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F44 10.9091 Tf 209.275 516.078 Td [('BJAC')]TJ -ET -q -1 0 0 1 261.07 512.014 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 267.048 516.078 Td [(Blo)-28(c)28(k)-333(Jacobi)-334(with)-333(ILU\0500\051)-333(on)-334(th)1(e)-334(lo)-28(cal)-333(blo)-28(c)28(ks.)]TJ -ET -q -1 0 0 1 494.128 512.014 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 105.524 511.814 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S -Q -q -1 0 0 1 105.524 484.517 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 111.501 502.131 Td [(Additiv)28(e)-333(Sc)27(h)28(w)28(arz)]TJ -ET -q -1 0 0 1 203.297 484.517 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 209.275 502.131 Td [('AS')]TJ -ET -q -1 0 0 1 261.07 484.517 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 267.048 502.131 Td [(Restricted)-267(Additiv)27(e)-267(Sc)28(h)28(w)27(arz)-267(\050RAS\051,)-267(with)-268(o)28(v)28(er-)]TJ 0 -13.549 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 -ET -q -1 0 0 1 494.128 484.517 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 105.524 484.318 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S -Q -q -1 0 0 1 105.524 307.979 cm -[]0 d 0 J 0.398 w 0 0 m 0 176.14 l S -Q -BT -/F15 10.9091 Tf 111.501 474.634 Td [(Multilev)28(el)]TJ -ET -q -1 0 0 1 203.297 307.979 cm -[]0 d 0 J 0.398 w 0 0 m 0 176.14 l S -Q -BT -/F44 10.9091 Tf 209.275 474.634 Td [('ML')]TJ -ET -q -1 0 0 1 261.07 307.979 cm -[]0 d 0 J 0.398 w 0 0 m 0 176.14 l S -Q -BT -/F15 10.9091 Tf 267.048 474.634 Td [(Multi-lev)28(el)-377(h)27(ybrid)-377(preconditioner)-377(\050additiv)28(e)-377(on)]TJ 0 -13.549 Td [(the)-390(same)-391(lev)28(el)-391(and)-390(m)28(ultiplicativ)28(e)-391(through)-390(the)]TJ 0 -13.55 Td [(lev)28(els\051,)-458(with)-432(pre-)-433(and)-433(p)-28(ost-smo)-27(othing.)-743(Num-)]TJ 0 -13.549 Td [(b)-28(er)-458(of)-459(lev)28(els:)-695(2.)-821(Smo)-28(other:)-695(RAS)-458(with)-459(o)28(v)28(er-)]TJ 0 -13.549 Td [(lap)-399(1)-400(and)-399(ILU\0500\051)-400(on)-400(th)1(e)-400(lo)-28(cal)-399(blo)-28(c)28(ks.)-643(Aggre-)]TJ 0 -13.549 Td [(gation:)-559(decoupled)-391(smo)-28(othed)-390(aggregation)-391(with)]TJ 0 -13.549 Td [(threshold)]TJ/F22 10.9091 Tf 48.308 0 Td [(\022)]TJ/F15 10.9091 Tf 9.018 0 Td [(=)-329(0.)-538(Coarsest)-364(matrix:)-507(distributed)]TJ -57.326 -13.549 Td [(among)-344(the)-344(pro)-27(ce)-1(ssors.)-476(Coarsest-lev)28(el)-344(solv)28(er:)-466(4)]TJ 0 -13.55 Td [(sw)28(eeps)-387(of)-386(the)-386(blo)-28(c)28(k-Jacobi)-387(solv)28(er,)-400(with)-386(LU)-386(or)]TJ 0 -13.549 Td [(ILU)-239(factorization)-240(of)-239(the)-240(blo)-28(c)28(ks)-240(\050UM)1(FP)83(A)28(CK)-240(for)]TJ 0 -13.549 Td [(the)-329(double)-330(p)1(re)-1(cision)-329(v)28(ersions)-329(and)-330(Sup)-27(erLU)-330(for)]TJ 0 -13.549 Td [(the)-382(single)-382(precision)-382(ones,)-395(if)-382(the)-382(pac)28(k)55(ages)-382(ha)28(v)28(e)]TJ 0 -13.549 Td [(b)-28(een)-333(installed;)-333(ILU\0500\051,)-334(otherwise\051.)]TJ -ET -q -1 0 0 1 494.128 307.979 cm -[]0 d 0 J 0.398 w 0 0 m 0 176.14 l S -Q -q -1 0 0 1 105.524 307.779 cm -[]0 d 0 J 0.398 w 0 0 m 388.604 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 123.31 277.09 Td [(T)83(able)-333(1:)-444(Preconditioner)-334(t)28(yp)-28(es,)-333(corresp)-28(onding)-333(strings)-333(and)-334(d)1(e)-1(f)1(ault)-334(c)28(hoices.)]TJ -0 g 0 G -0 g 0 G -/F17 11.9552 Tf -29.71 -40.13 Td [(5.1)-1125(Examples)]TJ/F15 10.9091 Tf 0 -20.595 Td [(The)-340(co)-28(de)-340(rep)-28(orted)-340(i)1(n)-340(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-340(2)]TJ -0 g 0 G - [-340(sho)27(ws)-340(ho)28(w)-340(to)-340(set)-340(and)-340(apply)-340(t)1(he)-340(default)-340(m)27(ulti)1(-)-1(lev)28(el)-340(pre-)]TJ 0 -13.549 Td [(conditioner)-258(a)28(v)56(ailable)-258(in)-257(the)-258(real)-258(dou)1(ble)-258(precision)-258(v)28(ersion)-257(of)-258(MLD2P4)-258(\050see)-257(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-258(1)]TJ -0 g 0 G - [(\051.)-419(This)]TJ 0 -13.549 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 -13.55 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 -13.549 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 g 0 G -0 g 0 G -ET - -endstream -endobj -383 0 obj -<< -/Length 6858 ->> -stream -0 g 0 G -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 -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 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)28(y;)-412(t)1(he)-386(statemen)28(ts)-385(con-)]TJ 0 -13.549 Td [(cerning)-265(the)-264(deallo)-28(cation)-265(of)-264(the)-265(PSBLAS)-264(data)-265(structure)-265(are)-264(neglec)-1(ted)-264(to)-28(o.)-422(Th)1(e)-265(complete)]TJ 0 -13.549 Td [(co)-28(de)-306(can)-307(b)-27(e)-307(found)-306(in)-307(the)-306(example)-307(program)-306(\014le)]TJ/F44 10.9091 Tf 223.484 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 -332.301 -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 -0 0 1 rg 0 0 1 RG - [-390(3.5)]TJ -0 g 0 G - [(\051.)-617(F)83(or)-390(details)-391(on)-391(the)-390(use)-391(of)]TJ -101.625 -13.549 Td [(the)-333(PSBLAS)-334(rou)1(tines,)-334(see)-333(the)-334(PSBLAS)-333(User's)-333(Guide)-334([)]TJ -1 0 0 rg 1 0 0 RG - [(15)]TJ -0 g 0 G - [(])1(.)]TJ 16.936 -13.55 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 -16.936 -13.549 Td [(single)-450(precision)-451(and)-450(the)-451(complex,)-479(single)-451(and)-450(double)-451(precision,)-479(v)28(e)-1(r)1(s)-1(ion)1(s)-451(are)-450(obtained)]TJ 0 -13.549 Td [(with)-352(straigh)27(tfor)1(w)27(ard)-352(mo)-28(di\014cations)-352(of)-353(the)-352(previous)-353(example)-352(\050see)-353(Section)]TJ -0 0 1 rg 0 0 1 RG - [-352(6)]TJ -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)-27(onding)-503(F)83(ortran)-502(95)-503(co)-28(des)-502(are)-503(a)28(v)55(ailable)-502(in)]TJ/F44 10.9091 Tf 0 -13.549 Td [(examples/fileread/)]TJ/F15 10.9091 Tf 103.09 0 Td [(.)]TJ -86.154 -13.55 Td [(Di\013eren)28(t)-270(v)28(ersions)-269(of)-270(m)28(ulti-lev)28(el)-270(precondition)1(e)-1(r)1(s)-270(can)-269(b)-28(e)-270(obtain)1(e)-1(d)-269(b)28(y)-270(c)28(hanging)-269(the)-270(d)1(e)-1(-)]TJ -16.936 -13.549 Td [(fault)-273(v)56(alues)-273(of)-272(the)-273(preconditioner)-273(parameters.)-424(The)-273(co)-28(d)1(e)-273(rep)-28(orted)-273(in)-272(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-273(3)]TJ -0 g 0 G - [-273(sho)28(ws)-273(ho)28(w)]TJ 0 -13.549 Td [(to)-281(s)-1(et)-281(a)-282(three-lev)28(el)-281(h)27(ybr)1(id)-282(Sc)28(h)28(w)27(arz)-281(preconditioner,)-292(whic)28(h)-281(use)-1(s)-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(bl)1(o)-28(c)27(ks)-264(as)-265(p)-28(ost-smo)-28(other,)-279(has)-265(a)-265(coarsest)-265(matrix)-265(replicated)-264(on)-265(the)-265(pro)-28(cessors,)]TJ 0 -13.549 Td [(and)-250(solv)28(es)-251(the)-250(coarsest-lev)28(el)-251(system)-250(with)-250(the)-250(LU)-250(factorization)-251(f)1(rom)-251(UMFP)84(A)28(C)-1(K)-250([)]TJ -1 0 0 rg 1 0 0 RG - [(9)]TJ -0 g 0 G - [(].)-416(The)]TJ 0 -13.55 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 182.181 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 68.727 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 112.039 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 63 0 Td [(.)-497(Note)-350(that)-351(the)-351(t)28(yp)-28(e)-350(of)-351(m)28(ultilev)28(el)-351(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(onl)1(y\051)-280(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 68.848 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 68.727 0 Td [(.)]TJ -120.639 -13.549 Td [(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-301(4)]TJ -0 g 0 G - [-301(sho)28(ws)-301(ho)28(w)-301(to)-301(set)-301(a)-300(three-lev)27(el)-301(ad)1(ditiv)27(e)-300(Sc)27(h)28(w)28(arz)-301(preconditioner,)-307(whic)28(h)-301(uses)]TJ -16.936 -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)28(ks)-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)-339(the)-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 196.865 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 67.39 0 Td [(is)-403(u)1(s)-1(ed)-402(only)-402(to)-403(set)-402(non-default)]TJ -264.255 -13.549 Td [(v)56(alues)-271(of)-271(the)-270(paramete)-1(r)1(s)-271(\050see)-271(T)83(ables)]TJ -0 0 1 rg 0 0 1 RG - [-270(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(5)]TJ -0 g 0 G - [(\051.)-424(In)-271(b)-27(oth)-271(cases,)-283(the)-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)-268(for)-269(the)-269(default)-268(m)27(ulti-lev)28(el)-269(precondi)1(tioner.)]TJ 0 -13.549 Td [(The)-368(co)-28(de)-368(fragmen)28(ts)-368(sho)28(wn)-368(in)-368(in)-368(Figures)]TJ -0 0 1 rg 0 0 1 RG - [-368(3)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(4)]TJ -0 g 0 G - [-368(are)-368(included)-368(in)-368(the)-368(example)-368(program)-368(\014le)]TJ/F44 10.9091 Tf 0 -13.55 Td [(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 112.453 0 Td [(to)-28(o.)]TJ -95.517 -13.549 Td [(Finally)83(,)-295(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-286(5)]TJ -0 g 0 G - [-286(sho)28(ws)-286(the)-286(setup)-286(of)-286(a)-285(one-le)-1(v)28(el)-286(additiv)28(e)-286(Sc)28(h)28(w)28(arz)-286(preconditioner,)-295(i.e.)]TJ -16.936 -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 45.817 0 Td [(.)]TJ -28.881 -13.549 Td [(F)83(or)-452(all)-452(the)-452(previous)-452(preconditi)1(oners)-1(,)-481(example)-452(programs)-452(where)-452(the)-452(sparse)-452(matrix)]TJ -16.936 -13.55 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(ailab)1(le)-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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -391 0 obj -<< -/Length 3439 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(5)]TJ -0 g 0 G - [-378(Getting)-378(St)67(ar)67(ted)]TJ/F15 10.9091 Tf 401.542 0 Td [(19)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -/F44 9.9626 Tf -370.457 -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 -10.461 -11.956 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(sparse)-525(matrix)]TJ 10.461 -11.955 Td [(type\050psb_dspmat_type\051)-525(::)-525(A)]TJ -10.461 -11.955 Td [(!)-525(sparse)-525(matrix)-525(descriptor)]TJ 10.461 -11.955 Td [(type\050psb_desc_type\051)-1575(::)-525(desc_A)]TJ -10.461 -11.956 Td [(!)-525(preconditioner)]TJ 10.461 -11.955 Td [(type\050mld_dprec_type\051)-1050(::)-525(P)]TJ -10.461 -11.955 Td [(!)-525(right-hand)-525(side)-525(and)-525(solution)-525(vectors)]TJ 10.461 -11.955 Td [(type\050psb_d_vect_type\051)-525(::)-525(b,)-525(x)]TJ -10.461 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.956 Td [(!)-525(initialize)-525(the)-525(parallel)-525(environment)]TJ 10.461 -11.955 Td [(call)-525(psb_init\050ictxt\051)]TJ 0 -11.955 Td [(call)-525(psb_info\050ictxt,iam,np\051)]TJ -10.461 -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(pre-)-525(and)-525(post-smoother)-525(and)-525(4)-525(block-Jacobi)-525(sweeps)]TJ 0 -11.955 Td [(!)-525(\050with)-525(UMFPACK)-525(LU)-525(on)-525(the)-525(blocks\051)-525(as)-525(distributed)-525(coarse-level)]TJ 0 -11.955 Td [(!)-525(solver.)]TJ 10.461 -11.955 Td [(call)-525(mld_precinit\050P,'ML',info\051)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(build)-525(the)-525(preconditioner)]TJ 10.461 -11.956 Td [(call)-525(mld_precbld\050A,desc_A,P,info\051)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(set)-525(the)-525(solver)-525(parameters)-525(and)-525(the)-525(initial)-525(guess)]TJ 10.461 -11.955 Td [(...)-525(...)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(solve)-525(Ax=b)-525(with)-525(preconditioned)-525(BiCGSTAB)]TJ 10.461 -11.956 Td [(call)-525(psb_krylov\050'BICGSTAB',A,P,b,x,tol,desc_A,info\051)]TJ 0 -11.955 Td [(...)-525(...)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(deallocate)-525(the)-525(preconditioner)]TJ 10.461 -11.955 Td [(call)-525(mld_precfree\050P,info\051)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.956 Td [(!)-525(deallocate)-525(other)-525(data)-525(structures)]TJ 10.461 -11.955 Td [(...)-525(...)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(exit)-525(the)-525(parallel)-525(environment)]TJ 10.461 -11.955 Td [(call)-525(psb_exit\050ictxt\051)]TJ 0 -11.956 Td [(stop)]TJ -0 g 0 G -/F15 10.9091 Tf -23.026 -20.748 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 -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -ET - -endstream -endobj -396 0 obj -<< -/Length 3054 ->> -stream -0 g 0 G -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 -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -/F44 9.9626 Tf -182.641 -59.668 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 10.46 -11.955 Td [(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.955 Td [(call_mld_precset\050P,'SMOOTHER_TYPE','BJAC',info\051)]TJ 0 -11.955 Td [(call_mld_precset\050P,'SMOOTHER_POS,'POST'w,info\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,'COARSE_MAT','REPL',info\051)]TJ 0 -11.956 Td [(call)-525(mld_precset\050P,'COARSE_SOLVE','UMF',info\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ -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(S)1(c)27(h)28(w)28(arz)-334(p)1(rec)-1(on)1(ditioner.)]TJ -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 -/F44 9.9626 Tf -34.98 -90.324 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 10.46 -11.955 Td [(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,'ML_TYPE','ADD',info\051)]TJ 0 -11.956 Td [(call_mld_precset\050P,'SMOOTHER_POS','TWOSIDE',info\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,'COARSE_SWEEPS',5,info\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ -0 g 0 G -/F15 10.9091 Tf 28.328 -18.535 Td [(Figure)-333(4:)-445(Setup)-333(of)-333(an)-334(add)1(itiv)27(e)-333(three-lev)28(el)-334(Sc)28(h)28(w)28(arz)-334(precondi)1(tioner.)]TJ -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 -/F44 9.9626 Tf -28.328 -90.323 Td [(...)-525(...)]TJ 0 -11.956 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 10.46 -11.955 Td [(call)-525(mld_precinit\050P,'AS',info\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,'SUB_OVR',2,info\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ -0 g 0 G -/F15 10.9091 Tf 56.222 -18.535 Td [(Figure)-333(5:)-445(Setup)-333(of)-333(a)-334(one-lev)28(el)-333(Sc)28(h)27(w)28(arz)-333(preconditioner.)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -ET - -endstream -endobj -402 0 obj -<< -/Length 5985 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(21)]TJ -0 g 0 G -/F17 14.3462 Tf -401.542 -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(te)-1(rf)1(ac)-1(e)-396(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 45.818 0 Td [(,)]TJ/F44 10.9091 Tf 6.095 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 63 0 Td [(,)]TJ/F44 10.9091 Tf 6.095 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 71.65 0 Td [(encapsulate)-268(all)-268(the)-268(fun)1(c)-1(tion)1(-)]TJ -279.078 -13.549 Td [(alities)-323(for)-322(the)-323(setup)-323(and)-322(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 198.572 0 Td [(mld_precfree)]TJ/F15 10.9091 Tf 71.919 0 Td [(deallo)-28(cates)-292(the)-293(preconditioner)]TJ -270.491 -13.55 Td [(data)-387(s)-1(tr)1(ucture,)-401(while)]TJ/F44 10.9091 Tf 105.073 0 Td [(mld_precdescr)]TJ/F15 10.9091 Tf 78.681 0 Td [(prin)28(ts)-388(a)-387(description)-388(of)-387(the)-387(preconditioner)-388(setup)]TJ -183.754 -13.549 Td [(b)28(y)-334(t)1(he)-334(user.)]TJ 16.937 -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(erl)1(oade)-1(d)-222(with)-222(resp)-28(ect)-222(to)-222(the)-222(real/complex)]TJ -16.937 -13.549 Td [(case)-371(and)-371(th)1(e)-371(single/double)-371(precision;)-389(argumen)27(t)1(s)-371(with)-371(appropriate)-371(d)1(ata)-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 -0 g 0 G -/F25 10.9091 Tf 16.364 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 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 82.798 0 Td [(psb_)]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 25.835 0 Td [(x)]TJ/F15 10.9091 Tf 10.998 0 Td [(=)]TJ/F44 10.9091 Tf 13.109 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 13.108 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 10.422 0 Td [(=)]TJ/F44 10.9091 Tf 12.532 0 Td [(c)]TJ/F15 10.9091 Tf 9.774 0 Td [(for)-371(complex)-371(single)-371(precision,)]TJ/F18 10.9091 Tf 140.11 0 Td [(x)]TJ/F15 10.9091 Tf 10.422 0 Td [(=)]TJ/F44 10.9091 Tf 12.532 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 -0 g 0 G -/F25 10.9091 Tf -10.909 -22.515 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 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 241.776 0 Td [(mld_)]TJ/F18 10.9091 Tf 22.908 0 Td [(x)]TJ/F44 10.9091 Tf 6.375 0 Td [(prec_type)]TJ/F15 10.9091 Tf 51.544 0 Td [(,)-338(with)]TJ/F18 10.9091 Tf 31.606 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 5.727 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 6.667 0 Td [(c)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F44 10.9091 Tf 6.667 0 Td [(z)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-333(according)-334(to)-333(the)-333(sparse)-334(matrix)-333(data)-333(structure;)]TJ -0 g 0 G -/F25 10.9091 Tf -41.424 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-321(arra)28(ys)-321(con)27(tain)1(ing)-321(the)-322(v)28(ectors)]TJ/F22 10.9091 Tf 159.847 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 11.606 0 Td [(in)28(v)28(olv)27(ed)-321(in)-321(the)-321(preconditioner)-321(appli)1(c)-1(a-)]TJ -201.713 -13.549 Td [(tion)]TJ/F22 10.9091 Tf 21.781 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 8.672 0 Td [(m)28(ust)-275(b)-27(e)-275(of)-274(t)28(yp)-28(e)]TJ/F44 10.9091 Tf 76.276 0 Td [(psb_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F44 10.9091 Tf 6.374 0 Td [(vect_type)]TJ/F15 10.9091 Tf 54.538 0 Td [(with)]TJ/F18 10.9091 Tf 24.205 0 Td [(x)]TJ/F15 10.9091 Tf 9.367 0 Td [(=)]TJ/F44 10.9091 Tf 11.478 0 Td [(s)]TJ/F15 10.9091 Tf 5.728 0 Td [(,)]TJ/F44 10.9091 Tf 6.152 0 Td [(d)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F44 10.9091 Tf 6.152 0 Td [(c)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F44 10.9091 Tf 6.152 0 Td [(z)]TJ/F15 10.9091 Tf 5.728 0 Td [(,)-286(in)-274(a)-275(manner)]TJ -322.707 -13.549 Td [(completely)-333(analogous)-334(to)-333(the)-333(sparse)-334(matrix)-333(t)28(yp)-28(e;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(real)-450(parameters)-450(de\014ning)-450(the)-450(preconditioner)-450(m)28(ust)-450(b)-28(e)-450(d)1(e)-1(clared)-449(ac)-1(cord)1(ing)-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(\050se)-1(e)-245(Section)]TJ -0 0 1 rg 0 0 1 RG - [-245(6.2)]TJ -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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -408 0 obj -<< -/Length 3097 ->> -stream -0 g 0 G -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 -0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.1)-1125(Subroutine)-375(mld)]TJ -ET -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 -Q -BT -/F17 11.9552 Tf 213.457 704.136 Td [(precinit)]TJ -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(in)1(itializes)-269(the)-268(preconditioner)-268(data)-268(structure,)-281(acc)-1(or)1(ding)-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(th)1(e)-334(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 11.588 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 [(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)-27(e)-1(ci\014ed)-333(in)-333(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-333(1)]TJ -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 -0 0 1 rg 0 0 1 RG - [-333(7)]TJ -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 [(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)-27(e)-1(r)-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 22.908 0 Td [(,)-438(then)]TJ/F44 10.9091 Tf 33.579 0 Td [(nlev)]TJ/F15 10.9091 Tf 22.909 0 Td [(=2)-417(is)-418(assumed.)-697(Oth)1(e)-1(r)1(wis)-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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -418 0 obj -<< -/Length 6579 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(23)]TJ -0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.2)-1125(Subroutine)-375(mld)]TJ -ET -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 -Q -BT -/F17 11.9552 Tf 220.657 704.136 Td [(precset)]TJ -0 g 0 G -0 g 0 G -/F44 10.9091 Tf -15.33 -20.594 Td [(call)-525(mld_precset\050p,what,val,info\051)]TJ/F15 10.9091 Tf -111.727 -24.354 Td [(This)-389(routine)-388(sets)-389(the)-389(parameters)-388(de\014ning)-389(the)-388(prec)-1(on)1(ditioner.)-611(More)-388(precisely)83(,)-403(th)1(e)-389(pa-)]TJ 0 -13.549 Td [(rameter)-333(iden)27(ti\014)1(e)-1(d)-333(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)55(al)1(ue)-334(con)28(tained)-333(in)]TJ/F44 10.9091 Tf 163.213 0 Td [(val)]TJ/F15 10.9091 Tf 17.181 0 Td [(.)]TJ -293.396 -13.549 Td [(The)-306(routine)-306(ma)28(y)-306(also)-307(b)-27(e)-306(in)27(v)28(ok)28(ed)-306(as)-306(a)-306(metho)-28(d)-306(of)-306(the)-306(preconditioner)-306(ob)-56(ject)-306(as)-306(in)-306(the)]TJ -16.937 -13.55 Td [(follo)28(wing:)]TJ -0 g 0 G -0 g 0 G -/F44 10.9091 Tf 111.727 -21.556 Td [(call)-525(p%set\050what,val,info)-525([,ilev]\051)]TJ/F15 10.9091 Tf -111.727 -21.557 Td [(In)-373(this)-373(case)-373(it)-373(is)-373(also)-373(p)-27(os)-1(sibl)1(e)-373(to)-373(sp)-28(ecify)-373(an)-373(optional)]TJ/F44 10.9091 Tf 254.572 0 Td [(ilev)]TJ/F15 10.9091 Tf 26.977 0 Td [(argumen)28(t)-373(that)-373(restricts)-373(the)]TJ -281.549 -13.549 Td [(e\013ect)-334(of)-333(the)-333(call)-333(to)-334(the)-333(sp)-28(eci\014ed)-333(lev)28(e)-1(l)1(.)]TJ 16.937 -13.549 Td [(Finally)84(,)-277(if)-261(the)-262(user)-262(has)-262(dev)28(elop)-28(ed)-262(a)-262(new)-262(t)28(yp)-28(e)-261(of)-262(smo)-28(other)-262(and/or)-262(solv)28(er)-262(b)28(y)-262(extending)]TJ -16.937 -13.549 Td [(one)-283(of)-284(the)-283(base)-284(M)1(LD2P4)-284(t)28(yp)-28(es,)-293(and)-283(has)-284(declared)-283(a)-284(v)56(ariable)-283(of)-284(the)-283(new)-283(t)27(yp)-27(e)-284(in)-283(the)-283(m)-1(ai)1(n)]TJ 0 -13.55 Td [(program,)-401(it)-388(is)-387(p)-28(ossible)-388(to)-387(pass)-388(the)-388(n)1(e)-1(w)-387(smo)-28(other/solv)28(er)-388(v)56(ariable)-388(to)-387(the)-388(setup)-388(rou)1(tine)]TJ 0 -13.549 Td [(as)-333(follo)27(ws:)]TJ -0 g 0 G -0 g 0 G -/F44 10.9091 Tf 111.727 -21.557 Td [(call)-525(p%set\050smoother,info)-525([,ilev]\051)]TJ 5.727 -13.549 Td [(call)-525(p%set\050solver,info)-525([,ilev]\051)]TJ/F15 10.9091 Tf -117.454 -21.556 Td [(In)-375(this)-376(w)28(a)28(y)83(,)-386(the)-375(v)55(ariable)-375(will)-376(act)-375(as)-376(a)]TJ/F18 10.9091 Tf 184.403 0 Td [(mold)]TJ/F15 10.9091 Tf 28.084 0 Td [(to)-375(whic)27(h)-375(the)-376(p)1(rec)-1(on)1(ditioner)-376(will)-375(conform,)]TJ -212.487 -13.55 Td [(ev)28(en)-413(though)-412(the)-412(MLD2P4)-412(library)-413(is)-412(not)-412(mo)-28(di\014ed,)-432(and)-412(th)28(us)-413(has)-412(no)-412(direct)-413(kno)28(wledge)]TJ 0 -13.549 Td [(ab)-28(out)-333(the)-333(new)-334(t)28(yp)-28(e.)]TJ/F17 11.9552 Tf 0 -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 11.589 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 -13.549 Td [(what)-2114(integer,)-525(intent\050in\051)]TJ/F18 10.9091 Tf 158.424 0 Td [(or)]TJ/F44 10.9091 Tf 14.987 0 Td [(character\050len=*\051)]TJ/F15 10.9091 Tf 91.635 0 Td [(.)]TJ -219.075 -13.55 Td [(The)-366(parameter)-367(to)-366(b)-28(e)-366(set.)-543(It)-367(can)-366(b)-28(e)-366(sp)-28(eci\014ed)-366(b)28(y)-367(a)-366(prede\014ned)-366(constan)28(t,)]TJ 0 -13.549 Td [(or)-333(through)-333(its)-334(name;)-333(the)-333(s)-1(tr)1(ing)-334(is)-333(case-insensitiv)28(e.)-445(See)-333(also)-334(T)84(ables)]TJ -0 0 1 rg 0 0 1 RG - [-334(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(5)]TJ -0 g 0 G - [(.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(val)-2639(integer)]TJ/F18 10.9091 Tf 105.137 0 Td [(or)]TJ/F44 10.9091 Tf 30.425 0 Td [(character\050len=*\051)]TJ/F18 10.9091 Tf 110.71 0 Td [(or)]TJ/F44 10.9091 Tf 30.425 0 Td [(real\050psb_spk_\051)]TJ/F18 10.9091 Tf 99.256 0 Td [(or)]TJ/F44 10.9091 Tf -329.982 -13.549 Td [(real\050psb_dpk_\051)]TJ/F15 10.9091 Tf 80.181 0 Td [(,)]TJ/F44 10.9091 Tf 6.667 0 Td [(intent\050in\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(.)]TJ -144.12 -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(e)-1(d)-305(v)55(alu)1(e)-1(s)-305(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 -0 0 1 rg 0 0 1 RG - [-392(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(5)]TJ -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 24.546 0 Td [(character\050len=*\051)]TJ/F15 10.9091 Tf 91.635 0 Td [(,)-333(it)-334(is)-333(also)-333(treated)-334(as)-333(case)-333(inse)-1(n)1(s)-1(i)1(tiv)27(e.)]TJ/F44 10.9091 Tf -162.152 -13.549 Td [(smoother)-14(class\050mld_x_base_smoother_type\051)]TJ/F15 10.9091 Tf 45.971 -13.549 Td [(The)-333(user-de\014ned)-334(new)-333(smo)-28(other)-333(to)-333(b)-28(e)-334(emplo)28(y)28(ed)-333(in)-334(the)-333(preconditioner.)]TJ/F44 10.9091 Tf -45.971 -13.549 Td [(solver)-1064(class\050mld_x_base_solver_type\051)]TJ/F15 10.9091 Tf 45.971 -13.549 Td [(The)-333(user-de\014ned)-334(new)-333(solv)28(er)-334(to)-333(b)-28(e)-333(emplo)28(y)28(ed)-334(in)-333(the)-333(preconditioner.)]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 -0 0 1 rg 0 0 1 RG - [-333(7)]TJ -0 g 0 G - [-333(for)-334(details.)]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)-28(e)-382(obtained)-383(b)28(y)-383(a)-383(suitable)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -309 0 obj -<< -/Type /ObjStm -/N 100 -/First 899 -/Length 12714 ->> -stream -300 0 301 146 302 302 307 465 51 519 304 572 317 756 311 922 312 1073 313 1235 -314 1386 315 1537 319 1692 310 1746 323 1803 324 1857 325 1911 316 1964 331 2173 329 2331 -326 2477 327 2633 328 2790 333 2945 334 2999 335 3056 336 3113 330 3170 350 3354 337 3552 -338 3706 339 3849 340 3999 341 4146 342 4291 343 4435 344 4581 345 4732 352 4884 55 4938 -353 4991 354 5045 355 5099 356 5153 357 5207 358 5261 349 5315 368 5434 366 5608 346 5754 -347 5905 348 6056 362 6203 363 6349 370 6494 359 6548 59 6604 367 6656 382 6788 364 7002 -365 7153 372 7307 373 7453 374 7599 375 7749 376 7894 377 8039 378 8184 379 8330 380 8476 -384 8621 381 8675 390 8768 388 8902 392 9048 371 9102 389 9159 395 9252 397 9366 385 9420 -386 9477 387 9533 394 9590 401 9683 399 9825 398 9971 403 10122 63 10176 400 10229 407 10400 -404 10542 405 10687 409 10834 67 10888 406 10941 417 11060 415 11234 410 11380 411 11525 412 11670 -% 300 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [266.719 306.671 274.166 318.361] -/A << /S /GoTo /D (figure.1) >> ->> -% 301 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [476.537 188.614 483.984 197.636] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 302 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [488.085 188.614 500.987 197.636] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 307 0 obj -<< -/D [305 0 R /XYZ 92.6 752.957 null] ->> -% 51 0 obj -<< -/D [305 0 R /XYZ 93.6 236.589 null] ->> -% 304 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F18 171 0 R /F22 173 0 R /F26 276 0 R /F20 277 0 R /F23 275 0 R /F28 279 0 R /F25 174 0 R /F17 108 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 317 0 obj -<< -/Type /Page -/Contents 318 0 R -/Resources 316 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 308 0 R -/Annots [ 311 0 R 312 0 R 313 0 R 314 0 R 315 0 R ] ->> -% 311 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [146.365 303.928 153.812 312.951] -/A << /S /GoTo /D (cite.apnum_07) >> ->> -% 312 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [233.95 303.928 246.851 312.951] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 313 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [203.767 120.525 211.214 129.547] -/A << /S /GoTo /D (cite.aaecc_07) >> ->> -% 314 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [215.888 120.525 223.336 129.547] -/A << /S /GoTo /D (cite.apnum_07) >> ->> -% 315 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [228.01 120.525 240.911 129.547] -/A << /S /GoTo /D (cite.TUMINARO_TONG) >> ->> -% 319 0 obj -<< -/D [317 0 R /XYZ 85.4 752.957 null] ->> -% 310 0 obj -<< -/D [317 0 R /XYZ 154.731 438.097 null] ->> -% 323 0 obj -<< -/D [317 0 R /XYZ 86.4 392.526 null] ->> -% 324 0 obj -<< -/D [317 0 R /XYZ 86.4 375.457 null] ->> -% 325 0 obj -<< -/D [317 0 R /XYZ 86.4 352.82 null] ->> -% 316 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F22 173 0 R /F7 320 0 R /F43 155 0 R /F10 321 0 R /F13 322 0 R /F25 174 0 R /F23 275 0 R /F18 171 0 R /F28 279 0 R /F20 277 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 331 0 obj -<< -/Type /Page -/Contents 332 0 R -/Resources 330 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 308 0 R -/Annots [ 329 0 R 326 0 R 327 0 R 328 0 R ] ->> -% 329 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.4) >> ->> -% 326 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [458.571 581.593 466.018 590.616] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 327 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [471.783 581.593 484.685 590.616] -/A << /S /GoTo /D (cite.StubenGMD69_99) >> ->> -% 328 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [95.634 505.478 103.081 514.501] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 333 0 obj -<< -/D [331 0 R /XYZ 92.6 752.957 null] ->> -% 334 0 obj -<< -/D [331 0 R /XYZ 208.419 686.318 null] ->> -% 335 0 obj -<< -/D [331 0 R /XYZ 275.766 634.196 null] ->> -% 336 0 obj -<< -/D [331 0 R /XYZ 258.969 558.081 null] ->> -% 330 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F22 173 0 R /F23 275 0 R /F18 171 0 R /F25 174 0 R /F26 276 0 R /F24 278 0 R /F28 279 0 R /F20 277 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 350 0 obj -<< -/Type /Page -/Contents 351 0 R -/Resources 349 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 308 0 R -/Annots [ 337 0 R 338 0 R 339 0 R 340 0 R 341 0 R 342 0 R 343 0 R 344 0 R 345 0 R ] ->> -% 337 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [422.391 665.239 435.292 674.261] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 338 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [437.306 511.73 444.753 523.42] -/A << /S /GoTo /D (table.1) >> ->> -% 339 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [376.238 394.65 392.17 406.642] -/A << /S /GoTo /D (subsection.5.1) >> ->> -% 340 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [150.858 367.854 158.305 379.544] -/A << /S /GoTo /D (section.6) >> ->> -% 341 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [197.282 367.854 204.729 379.544] -/A << /S /GoTo /D (table.2) >> ->> -% 342 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [206.373 367.854 213.82 379.544] -/A << /S /GoTo /D (table.5) >> ->> -% 343 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [394.762 199.699 402.21 211.388] -/A << /S /GoTo /D (section.6) >> ->> -% 344 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [323.04 186.149 338.972 197.839] -/A << /S /GoTo /D (subsection.5.1) >> ->> -% 345 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [327.343 117.797 343.275 130.699] -/A << /S /GoTo /D (subsection.5.1) >> ->> -% 352 0 obj -<< -/D [350 0 R /XYZ 85.4 752.957 null] ->> -% 55 0 obj -<< -/D [350 0 R /XYZ 86.4 715.095 null] ->> -% 353 0 obj -<< -/D [350 0 R /XYZ 86.4 647.246 null] ->> -% 354 0 obj -<< -/D [350 0 R /XYZ 86.4 571.115 null] ->> -% 355 0 obj -<< -/D [350 0 R /XYZ 86.4 467.887 null] ->> -% 356 0 obj -<< -/D [350 0 R /XYZ 86.4 364.658 null] ->> -% 357 0 obj -<< -/D [350 0 R /XYZ 86.4 328.873 null] ->> -% 358 0 obj -<< -/D [350 0 R /XYZ 86.4 265.989 null] ->> -% 349 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F17 108 0 R /F18 171 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 368 0 obj -<< -/Type /Page -/Contents 369 0 R -/Resources 367 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 308 0 R -/Annots [ 366 0 R 346 0 R 347 0 R 348 0 R 362 0 R 363 0 R ] ->> -% 366 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.5) >> ->> -% 346 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [235.521 635.394 242.968 644.417] -/A << /S /GoTo /D (cite.aaecc_07) >> ->> -% 347 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [246.442 635.394 253.889 644.417] -/A << /S /GoTo /D (cite.apnum_07) >> ->> -% 348 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [252.277 592.019 259.724 604.921] -/A << /S /GoTo /D (section.6) >> ->> -% 362 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [231.694 213.248 239.141 224.937] -/A << /S /GoTo /D (figure.2) >> ->> -% 363 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [466.482 199.093 473.929 211.994] -/A << /S /GoTo /D (table.1) >> ->> -% 370 0 obj -<< -/D [368 0 R /XYZ 92.6 752.957 null] ->> -% 359 0 obj -<< -/D [368 0 R /XYZ 166.644 290.64 null] ->> -% 59 0 obj -<< -/D [368 0 R /XYZ 93.6 248.18 null] ->> -% 367 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F43 155 0 R /F44 200 0 R /F22 173 0 R /F17 108 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 382 0 obj -<< -/Type /Page -/Contents 383 0 R -/Resources 381 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 308 0 R -/Annots [ 364 0 R 365 0 R 372 0 R 373 0 R 374 0 R 375 0 R 376 0 R 377 0 R 378 0 R 379 0 R 380 0 R ] ->> -% 364 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [351.028 659.765 366.96 672.667] -/A << /S /GoTo /D (subsection.3.5) >> ->> -% 365 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [345.177 648.943 358.078 657.966] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 372 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [433.406 605.568 440.853 618.47] -/A << /S /GoTo /D (section.6) >> ->> -% 373 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [439.662 551.978 447.109 563.667] -/A << /S /GoTo /D (figure.3) >> ->> -% 374 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [463.005 513.451 470.452 522.474] -/A << /S /GoTo /D (cite.UMFPACK) >> ->> -% 375 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [136.41 443.584 143.857 455.274] -/A << /S /GoTo /D (figure.4) >> ->> -% 376 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [257.668 388.781 265.115 401.683] -/A << /S /GoTo /D (table.2) >> ->> -% 377 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [266.759 388.781 274.206 401.683] -/A << /S /GoTo /D (table.5) >> ->> -% 378 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [283.296 362.289 290.743 373.978] -/A << /S /GoTo /D (figure.3) >> ->> -% 379 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [292.387 362.289 299.834 373.978] -/A << /S /GoTo /D (figure.4) >> ->> -% 380 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [175.076 335.191 182.523 346.88] -/A << /S /GoTo /D (figure.5) >> ->> -% 384 0 obj -<< -/D [382 0 R /XYZ 85.4 752.957 null] ->> -% 381 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 390 0 obj -<< -/Type /Page -/Contents 391 0 R -/Resources 389 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 393 0 R -/Annots [ 388 0 R ] ->> -% 388 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.5) >> ->> -% 392 0 obj -<< -/D [390 0 R /XYZ 92.6 752.957 null] ->> -% 371 0 obj -<< -/D [390 0 R /XYZ 149.417 116.004 null] ->> -% 389 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 395 0 obj -<< -/Type /Page -/Contents 396 0 R -/Resources 394 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 393 0 R ->> -% 397 0 obj -<< -/D [395 0 R /XYZ 85.4 752.957 null] ->> -% 385 0 obj -<< -/D [395 0 R /XYZ 189.762 555.797 null] ->> -% 386 0 obj -<< -/D [395 0 R /XYZ 183.11 339.342 null] ->> -% 387 0 obj -<< -/D [395 0 R /XYZ 211.004 182.662 null] ->> -% 394 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 401 0 obj -<< -/Type /Page -/Contents 402 0 R -/Resources 400 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 393 0 R -/Annots [ 399 0 R 398 0 R ] ->> -% 399 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 398 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [483.843 382.76 499.775 395.662] -/A << /S /GoTo /D (subsection.6.2) >> ->> -% 403 0 obj -<< -/D [401 0 R /XYZ 92.6 752.957 null] ->> -% 63 0 obj -<< -/D [401 0 R /XYZ 93.6 715.095 null] ->> -% 400 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F17 108 0 R /F44 200 0 R /F25 174 0 R /F18 171 0 R /F22 173 0 R /F26 276 0 R /F20 277 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 407 0 obj -<< -/Type /Page -/Contents 408 0 R -/Resources 406 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 393 0 R -/Annots [ 404 0 R 405 0 R ] ->> -% 404 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [443.652 504.679 451.099 518.312] -/A << /S /GoTo /D (table.1) >> ->> -% 405 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 464.032 402.493 477.665] -/A << /S /GoTo /D (section.7) >> ->> -% 409 0 obj -<< -/D [407 0 R /XYZ 85.4 752.957 null] ->> -% 67 0 obj -<< -/D [407 0 R /XYZ 86.4 715.095 null] ->> -% 406 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F17 108 0 R /F44 200 0 R /F18 171 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 417 0 obj -<< -/Type /Page -/Contents 418 0 R -/Resources 416 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 393 0 R -/Annots [ 415 0 R 410 0 R 411 0 R 412 0 R 413 0 R 414 0 R ] ->> -% 415 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 410 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [479.944 284.111 487.391 297.744] -/A << /S /GoTo /D (table.2) >> ->> -% 411 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [489.035 284.111 496.482 297.744] -/A << /S /GoTo /D (table.5) >> ->> -% 412 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [376.234 231.858 383.681 243.547] -/A << /S /GoTo /D (table.2) >> ->> - -endstream -endobj -426 0 obj -<< -/Length 4105 ->> -stream -0 g 0 G -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 -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 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 -0 g 0 G - 13.333 -22.515 Td [(1.)]TJ -0 g 0 G - [-500(the)-333(t)27(yp)-27(e)-334(of)-333(m)28(ulti-lev)28(el)-334(preconditioner;)]TJ -0 g 0 G - 0 -22.516 Td [(2.)]TJ -0 g 0 G - [-500(the)-333(one-lev)27(el)-333(preconditioner)-333(used)-333(as)-334(smo)-28(other;)]TJ -0 g 0 G - 0 -22.516 Td [(3.)]TJ -0 g 0 G - [-500(the)-333(aggregation)-334(algorith)1(m;)]TJ -0 g 0 G - 0 -22.515 Td [(4.)]TJ -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 -0 0 1 rg 0 0 1 RG - [-296(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(5)]TJ -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)-470(to)-469(Section)]TJ -0 0 1 rg 0 0 1 RG - [-470(4)]TJ -0 g 0 G - [(.)-853(The)-470(smo)-27(other)-470(and)-470(solv)28(er)-469(ob)-56(jects)-470(are)-469(arranged)-470(in)-469(a)-470(hierarc)28(hical)]TJ 0 -13.549 Td [(manner;)-519(when)-457(sp)-28(ecifying)-457(a)-457(smo)-28(other)-457(ob)-55(ject,)-488(its)-457(parameters)-457(including)-457(the)-457(con)27(tained)]TJ 0 -13.549 Td [(solv)28(er)-277(are)-277(set)-277(to)-277(default)-277(v)56(alues,)-288(and)-277(when)-277(a)-277(solv)28(er)-277(ob)-55(ject)-277(is)-277(sp)-28(eci\014ed)-277(its)-277(defaults)-277(ar)1(e)-277(also)]TJ 0 -13.55 Td [(set,)-300(o)28(v)28(erriding)-291(in)-292(b)-28(oth)-291(cases)-291(an)27(y)-291(previous)-291(settings)-292(ev)28(en)-291(if)-292(explicitly)-291(sp)-28(eci\014ed.)-430(Therefore)]TJ 0 -13.549 Td [(if)-383(the)-383(user)-383(sets)-383(a)-382(new)-383(smo)-28(other,)-395(and)-383(wishes)-383(to)-383(use)-383(a)-383(solv)28(er)-383(di\013eren)28(t)-383(from)-383(the)-383(default)]TJ 0 -13.549 Td [(one,)-307(the)-300(call)-300(to)-300(set)-300(the)-300(solv)28(er)-300(m)27(ust)-300(come)]TJ/F18 10.9091 Tf 193.685 0 Td [(after)]TJ/F15 10.9091 Tf 26.611 0 Td [(the)-300(call)-300(to)-300(set)-300(the)-300(smo)-28(other.)-433(Com)-1(p)1(le)-1(t)1(e)-1(ly)]TJ -220.296 -13.549 Td [(new)-354(smo)-27(other)-354(and/or)-353(solv)27(er)-353(class)-354(deriv)28(ed)-353(from)-354(the)-354(b)1(as)-1(e)-353(ob)-56(jects)-353(in)-354(the)-353(library)-354(ma)28(y)-353(b)-28(e)]TJ 0 -13.549 Td [(used)-419(without)-419(recompiling)-419(the)-420(librar)1(y)-420(itself.)-702(Once)-419(the)-419(new)-419(smo)-28(other/solv)28(er)-420(class)-419(has)]TJ 0 -13.55 Td [(b)-28(een)-422(dev)28(elop)-28(ed,)-444(the)-423(u)1(s)-1(er)-422(can)-422(declare)-422(a)-422(v)55(ariable)-422(of)-422(that)-422(new)-422(t)27(yp)-27(e)-423(in)-422(the)-422(application,)]TJ 0 -13.549 Td [(and)-358(pass)-358(th)1(at)-358(v)55(ariable)-357(to)-358(the)]TJ/F44 10.9091 Tf 143.268 0 Td [(p%set\050solver,info\051)]TJ/F15 10.9091 Tf 106.993 0 Td [(call;)-370(the)-358(new)-358(solv)28(er)-358(ob)-55(ject)-358(is)-358(then)]TJ -250.261 -13.549 Td [(dynamically)-333(included)-333(in)-334(the)-333(preconditioner)-333(structure.)]TJ 16.936 -13.549 Td [(The)]TJ/F44 10.9091 Tf 24.161 0 Td [(what,val)]TJ/F15 10.9091 Tf 51.19 0 Td [(pairs)-492(des)-1(crib)-27(ed)-493(here)-492(are)-493(those)-492(of)-493(the)-492(prede\014ned)-493(smo)-27(other/solv)27(er)]TJ -92.287 -13.549 Td [(ob)-55(jec)-1(ts;)-333(newly)-333(dev)28(elop)-28(ed)-333(s)-1(olv)28(ers)-333(ma)28(y)-334(de\014ne)-333(new)-333(pairs)-334(according)-333(to)-333(their)-333(nee)-1(d)1(s)-1(.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -435 0 obj -<< -/Length 4494 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(25)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -q -0 1 -1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 0 87.078 cm -[]0 d 0 J 0.398 w 0 0 m 599.807 0 l S -Q -q -1 0 0 1 0 73.329 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -1 0 0 1 -299.826 -121.521 cm -BT -/F44 10.9091 Tf 305.803 198.915 Td [(what)]TJ -ET -q -1 0 0 1 453.513 194.85 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 459.491 198.915 Td [(d)22(a)67(t)66(a)-377(type)]TJ -ET -q -1 0 0 1 557.104 194.85 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F44 10.9091 Tf 563.081 198.915 Td [(val)]TJ -ET -q -1 0 0 1 625.752 194.85 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 631.729 198.915 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 689.252 194.85 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 695.229 198.915 Td [(comments)]TJ -ET -q -1 0 0 1 899.632 194.85 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 194.651 cm -[]0 d 0 J 0.398 w 0 0 m 599.807 0 l S -Q -q -1 0 0 1 299.826 153.804 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 305.803 184.967 Td [(mld_ml_type_)]TJ 0 -13.549 Td [(ML_TYPE)]TJ -ET -q -1 0 0 1 453.513 153.804 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 459.491 184.967 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 557.104 153.804 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 563.081 184.967 Td [('ADD')]TJ 0 -13.549 Td [('MULT')]TJ -ET -q -1 0 0 1 625.752 153.804 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 631.729 184.967 Td [('MULT')]TJ -ET -q -1 0 0 1 689.252 153.804 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 695.229 184.967 Td [(Basic)-449(m)28(ulti-lev)28(e)-1(l)-448(framew)27(ork:)-675(additiv)28(e)-449(or)]TJ 0 -13.549 Td [(m)28(ultiplicativ)28(e)-587(amon)1(g)-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 -ET -q -1 0 0 1 899.632 153.804 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 299.826 153.605 cm -[]0 d 0 J 0.398 w 0 0 m 599.807 0 l S -Q -q -1 0 0 1 299.826 112.758 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 305.803 143.921 Td [(mld_smoother_type_)]TJ 0 -13.549 Td [(SMOOTHER_TYPE)]TJ -ET -q -1 0 0 1 453.513 112.758 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 459.491 143.921 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 557.104 112.758 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 563.081 143.921 Td [('DIAG')]TJ 0 -13.549 Td [('BJAC')]TJ 0 -13.549 Td [('AS')]TJ -ET -q -1 0 0 1 625.752 112.758 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 631.729 143.921 Td [('AS')]TJ -ET -q -1 0 0 1 689.252 112.758 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 695.229 143.921 Td [(Basic)-434(p)1(rede\014ned)-434(one-lev)28(el)-433(preconditioner)]TJ 0 -13.549 Td [(\050i.e.)-534(sm)-1(o)-27(other\051:)-847(diagonal,)-584(blo)-28(c)28(k)-535(Jacobi,)]TJ 0 -13.549 Td [(AS.)]TJ -ET -q -1 0 0 1 899.632 112.758 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 299.826 112.559 cm -[]0 d 0 J 0.398 w 0 0 m 599.807 0 l S -Q -q -1 0 0 1 299.826 71.712 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 305.803 102.875 Td [(mld_smoother_pos_)]TJ 0 -13.549 Td [(SMOOTHER_POS)]TJ -ET -q -1 0 0 1 453.513 71.712 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 459.491 102.875 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 557.104 71.712 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 563.081 102.875 Td [('PRE')]TJ 0 -13.549 Td [('POST')]TJ 0 -13.549 Td [('TWOSIDE')]TJ -ET -q -1 0 0 1 625.752 71.712 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 631.729 102.875 Td [('TWOSIDE')]TJ -ET -q -1 0 0 1 689.252 71.712 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 695.229 102.875 Td [(\134P)28(osition")-234(of)-233(the)-233(smo)-28(other:)-394(pre-sm)-1(o)-27(other,)]TJ 0 -13.549 Td [(p)-28(ost-smo)-28(other,)-333(pre-)-333(and)-334(p)-27(ost-smo)-28(other.)]TJ -ET -q -1 0 0 1 899.632 71.712 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 299.826 71.513 cm -[]0 d 0 J 0.398 w 0 0 m 599.807 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 432.658 40.824 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 -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -440 0 obj -<< -/Length 10037 ->> -stream -0 g 0 G -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 -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -q -0 -1 1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 14.002 196.767 cm -[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S -Q -q -1 0 0 1 14.002 183.018 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -1 0 0 1 -292.625 -715.095 cm -BT -/F44 10.9091 Tf 312.605 902.178 Td [(what)]TJ -ET -q -1 0 0 1 417.795 898.113 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 423.773 902.178 Td [(d)22(a)67(t)67(a)-378(type)]TJ -ET -q -1 0 0 1 536.768 898.113 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F44 10.9091 Tf 542.746 902.178 Td [(val)]TJ -ET -q -1 0 0 1 639.432 898.113 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 645.41 902.178 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 718.51 898.113 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 724.488 902.178 Td [(comments)]TJ -ET -q -1 0 0 1 872.198 898.113 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 306.627 897.914 cm -[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S -Q -q -1 0 0 1 306.627 870.616 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 312.605 888.23 Td [(mld_sub_ovr_)]TJ 0 -13.549 Td [(SUB_OVR)]TJ -ET -q -1 0 0 1 417.795 870.616 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 423.773 888.23 Td [(integer)]TJ -ET -q -1 0 0 1 536.768 870.616 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 542.746 888.23 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 -ET -q -1 0 0 1 639.432 870.616 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 645.41 888.23 Td [(1)]TJ -ET -q -1 0 0 1 718.51 870.616 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 724.488 888.23 Td [(Num)28(b)-28(er)-333(of)-334(o)28(v)28(erlap)-333(la)28(y)27(ers.)]TJ -ET -q -1 0 0 1 872.198 870.616 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 306.627 870.417 cm -[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S -Q -q -1 0 0 1 306.627 816.021 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F44 10.9091 Tf 312.605 860.733 Td [(mld_sub_restr_)]TJ 0 -13.549 Td [(SUB_RESTR)]TJ -ET -q -1 0 0 1 417.795 816.021 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F44 10.9091 Tf 423.773 860.733 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 536.768 816.021 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F44 10.9091 Tf 542.746 860.733 Td [('HALO')]TJ 0 -13.549 Td [('NONE')]TJ -ET -q -1 0 0 1 639.432 816.021 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F44 10.9091 Tf 645.41 860.733 Td [('HALO')]TJ -ET -q -1 0 0 1 718.51 816.021 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F15 10.9091 Tf 724.488 860.733 Td [(T)28(yp)-28(e)-501(of)-501(restriction)-501(op)-28(erator:)]TJ/F44 10.9091 Tf 0 -13.549 Td [('HALO')]TJ/F15 10.9091 Tf 42.331 0 Td [(for)-731(taking)-730(in)27(to)-730(ac-)]TJ -42.331 -13.549 Td [(coun)28(t)-354(the)-354(o)28(v)28(erlap,)]TJ/F44 10.9091 Tf 90.45 0 Td [('NONE')]TJ/F15 10.9091 Tf 38.222 0 Td [(for)]TJ -128.672 -13.549 Td [(neglecting)-333(it.)]TJ -ET -q -1 0 0 1 872.198 816.021 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -q -1 0 0 1 306.627 815.822 cm -[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S -Q -q -1 0 0 1 306.627 761.426 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F44 10.9091 Tf 312.605 806.138 Td [(mld_sub_prol_)]TJ 0 -13.549 Td [(SUB_PROL)]TJ -ET -q -1 0 0 1 417.795 761.426 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F44 10.9091 Tf 423.773 806.138 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 536.768 761.426 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F44 10.9091 Tf 542.746 806.138 Td [('SUM')]TJ 0 -13.549 Td [('NONE')]TJ -ET -q -1 0 0 1 639.432 761.426 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F44 10.9091 Tf 645.41 806.138 Td [('NONE')]TJ -ET -q -1 0 0 1 718.51 761.426 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F15 10.9091 Tf 724.488 806.138 Td [(T)28(yp)-28(e)-560(of)-561(prolon)1(gation)-561(op)-27(e)-1(r)1(a-)]TJ 0 -13.549 Td [(tor:)]TJ/F44 10.9091 Tf 21.445 0 Td [('SUM')]TJ/F15 10.9091 Tf 31.465 0 Td [(for)-259(adding)-260(th)1(e)-260(con-)]TJ -52.91 -13.549 Td [(tributions)-622(from)-623(t)1(he)-623(o)28(v)28(erlap,)]TJ/F44 10.9091 Tf 0 -13.55 Td [('NONE')]TJ/F15 10.9091 Tf 37.999 0 Td [(for)-333(neglecting)-334(them.)]TJ -ET -q -1 0 0 1 872.198 761.426 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -q -1 0 0 1 306.627 761.226 cm -[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S -Q -q -1 0 0 1 306.627 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F44 10.9091 Tf 312.605 751.543 Td [(mld_sub_solve_)]TJ 0 -13.549 Td [(SUB_SOLVE)]TJ -ET -q -1 0 0 1 417.795 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F44 10.9091 Tf 423.773 751.543 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 536.768 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F44 10.9091 Tf 542.746 751.543 Td [('ILU')]TJ 0 -13.549 Td [('MILU')]TJ 0 -13.55 Td [('ILUT')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ -ET -q -1 0 0 1 639.432 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F44 10.9091 Tf 645.41 751.543 Td [('ILU')]TJ -ET -q -1 0 0 1 718.51 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F15 10.9091 Tf 724.488 751.543 Td [(Prede\014ned)-1775(lo)-28(cal)-1775(solv)28(er:)]TJ 0 -13.549 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-693(MILU\050)]TJ/F22 10.9091 Tf 48.012 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-693(ILU\050)]TJ/F22 10.9091 Tf 38.012 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051,)]TJ -134.459 -13.55 Td [(LU)-931(from)-932(UMFP)83(A)28(CK,)-932(LU)]TJ 0 -13.549 Td [(from)-460(Sup)-28(erLU)-460(\050plus)-461(tr)1(iangu-)]TJ 0 -13.549 Td [(lar)-333(solv)28(e)-1(\051.)]TJ -ET -q -1 0 0 1 872.198 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -q -1 0 0 1 306.627 693.082 cm -[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S -Q -q -1 0 0 1 306.627 665.784 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 312.605 683.398 Td [(mld_sub_fillin_)]TJ 0 -13.549 Td [(SUB_FILLIN)]TJ -ET -q -1 0 0 1 417.795 665.784 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 423.773 683.398 Td [(integer)]TJ -ET -q -1 0 0 1 536.768 665.784 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 542.746 683.398 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 -ET -q -1 0 0 1 639.432 665.784 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 645.41 683.398 Td [(0)]TJ -ET -q -1 0 0 1 718.51 665.784 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 724.488 683.398 Td [(Fill-in)-550(lev)27(el)]TJ/F22 10.9091 Tf 62.164 0 Td [(p)]TJ/F15 10.9091 Tf 11.495 0 Td [(of)-551(th)1(e)-551(incom-)]TJ -73.659 -13.549 Td [(plete)-333(LU)-334(factorizations.)]TJ -ET -q -1 0 0 1 872.198 665.784 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 306.627 665.585 cm -[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S -Q -q -1 0 0 1 306.627 638.287 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 312.605 655.901 Td [(mld_sub_iluthrs_)]TJ 0 -13.549 Td [(SUB_ILUTHRS)]TJ -ET -q -1 0 0 1 417.795 638.287 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 423.773 655.901 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ -ET -q -1 0 0 1 473.15 656.101 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 476.496 655.901 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ -ET -q -1 0 0 1 536.768 638.287 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 542.746 655.901 Td [(An)28(y)-333(re)-1(al)-333(n)28(um.)]TJ/F25 10.9091 Tf 72.152 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ -ET -q -1 0 0 1 639.432 638.287 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 645.41 655.901 Td [(0)]TJ -ET -q -1 0 0 1 718.51 638.287 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 724.488 655.901 Td [(Drop)-1063(tol)1(e)-1(r)1(ance)]TJ/F22 10.9091 Tf 90.366 0 Td [(t)]TJ/F15 10.9091 Tf 15.532 0 Td [(in)-1063(t)1(he)]TJ -105.898 -13.549 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-333(factorization.)]TJ -ET -q -1 0 0 1 872.198 638.287 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 306.627 638.088 cm -[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S -Q -q -1 0 0 1 306.627 556.594 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F44 10.9091 Tf 312.605 628.405 Td [(mld_sub_ren_)]TJ 0 -13.55 Td [(SUB_REN)]TJ -ET -q -1 0 0 1 417.795 556.594 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F44 10.9091 Tf 423.773 628.405 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 536.768 556.594 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F44 10.9091 Tf 542.746 628.405 Td [('RENUM)]TJ -ET -q -1 0 0 1 577.796 628.604 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F44 10.9091 Tf 581.233 628.405 Td [(NONE')]TJ -38.487 -13.55 Td [('RENUM)]TJ -ET -q -1 0 0 1 577.796 615.055 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F44 10.9091 Tf 581.233 614.855 Td [(GLOBAL')]TJ -ET -q -1 0 0 1 639.432 556.594 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F44 10.9091 Tf 645.41 628.405 Td [('RENUM)]TJ -ET -q -1 0 0 1 680.46 628.604 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F44 10.9091 Tf 683.897 628.405 Td [(NONE')]TJ -ET -q -1 0 0 1 718.51 556.594 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F15 10.9091 Tf 724.488 628.405 Td [(Ro)28(w)-257(and)-256(column)-256(reordering)-256(of)]TJ 0 -13.55 Td [(the)-423(lo)-28(cal)-422(s)-1(u)1(bmatrice)-1(s:)-623(no)-423(re-)]TJ 0 -13.549 Td [(ordering,)-248(reordering)-227(according)]TJ 0 -13.549 Td [(to)-253(the)-254(global)-253(n)28(um)27(b)-27(ering)-254(of)-253(the)]TJ 0 -13.549 Td [(ro)28(ws)-229(and)-229(columns)-229(of)-229(the)-229(whole)]TJ 0 -13.549 Td [(matrix.)]TJ -ET -q -1 0 0 1 872.198 556.594 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -q -1 0 0 1 306.627 556.395 cm -[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 405.352 525.705 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 -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -446 0 obj -<< -/Length 13521 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(27)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -q -0 1 -1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 0 250.664 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -q -1 0 0 1 0 236.916 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -1 0 0 1 -299.826 -121.521 cm -BT -/F44 10.9091 Tf 305.803 362.501 Td [(what)]TJ -ET -q -1 0 0 1 453.513 358.437 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 459.491 362.501 Td [(d)22(a)67(t)66(a)-377(type)]TJ -ET -q -1 0 0 1 572.487 358.437 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F44 10.9091 Tf 578.464 362.501 Td [(val)]TJ -ET -q -1 0 0 1 652.473 358.437 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 658.451 362.501 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 732.46 358.437 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 738.437 362.501 Td [(comments)]TJ -ET -q -1 0 0 1 914.493 358.437 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 358.237 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -q -1 0 0 1 299.826 263.194 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F44 10.9091 Tf 305.803 348.554 Td [(mld_coarse_aggr_size_)]TJ 0 -13.549 Td [(COARSE_AGGR_SIZE)]TJ -ET -q -1 0 0 1 453.513 263.194 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F44 10.9091 Tf 459.491 348.554 Td [(integer)]TJ -ET -q -1 0 0 1 572.487 263.194 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F15 10.9091 Tf 578.464 348.554 Td [(A)-2120(p)-27(ositiv)28(e)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)]TJ -ET -q -1 0 0 1 652.473 263.194 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F15 10.9091 Tf 658.451 348.554 Td [(0,)-1792(meaning)]TJ 0 -13.549 Td [(that)-726(the)-727(size)]TJ 0 -13.55 Td [(is)-1296(\014xed)-1296(at)]TJ/F44 10.9091 Tf 0 -13.549 Td [(precinit)]TJ/F15 10.9091 Tf 0 -13.549 Td [(time)]TJ -ET -q -1 0 0 1 732.46 263.194 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F15 10.9091 Tf 738.437 348.554 Td [(Coarse)-614(size)-615(threshold.)-1287(Disregard)]TJ 0 -13.549 Td [(the)-360(original)-360(sp)-28(eci\014cation)-360(of)-360(n)28(um)27(b)-27(er)]TJ 0 -13.55 Td [(of)-427(lev)28(els)-427(in)]TJ/F44 10.9091 Tf 57.369 0 Td [(precinit)]TJ/F15 10.9091 Tf 50.476 0 Td [(and)-427(con)28(tin)28(ue)]TJ -107.845 -13.549 Td [(aggregation)-500(un)28(til)-501(either)-500(the)-501(global)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)-575(of)-575(v)56(ariables)-575(is)-575(b)-27(elo)27(w)-574(this)]TJ 0 -13.549 Td [(threshold,)-526(or)-487(the)-487(aggregation)-488(d)1(o)-28(es)]TJ 0 -13.549 Td [(not)-333(reduce)-334(the)-333(size)-333(an)27(y)-333(longer.)]TJ -ET -q -1 0 0 1 914.493 263.194 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -q -1 0 0 1 299.826 262.995 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -q -1 0 0 1 299.826 222.148 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 305.803 253.311 Td [(mld_aggr_alg_)]TJ 0 -13.549 Td [(AGGR_ALG)]TJ -ET -q -1 0 0 1 453.513 222.148 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 459.491 253.311 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 572.487 222.148 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 578.464 253.311 Td [('DEC')]TJ -ET -q -1 0 0 1 652.473 222.148 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 658.451 253.311 Td [('DEC')]TJ -ET -q -1 0 0 1 732.46 222.148 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 738.437 253.311 Td [(Aggregation)-478(algorithm.)-879(Curren)28(tly)83(,)]TJ 0 -13.549 Td [(only)-569(the)-569(decoupled)-569(aggregation)-569(is)]TJ 0 -13.55 Td [(a)28(v)55(ailable.)]TJ -ET -q -1 0 0 1 914.493 222.148 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 299.826 221.948 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -q -1 0 0 1 299.826 181.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 305.803 212.265 Td [(mld_aggr_kind_)]TJ 0 -13.549 Td [(AGGR_KIND)]TJ -ET -q -1 0 0 1 453.513 181.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 459.491 212.265 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 572.487 181.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 578.464 212.265 Td [('SMOOTHED')]TJ 0 -13.549 Td [('NONSMOOTHED')]TJ -ET -q -1 0 0 1 652.473 181.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 658.451 212.265 Td [('SMOOTHED')]TJ -ET -q -1 0 0 1 732.46 181.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 738.437 212.265 Td [(T)28(yp)-28(e)-736(of)-736(aggregation:)-1249(smo)-28(othed,)]TJ 0 -13.549 Td [(nonsmo)-28(othed)-464(\050i.e.)-464(using)-465(th)1(e)-465(ten)28(ta-)]TJ 0 -13.55 Td [(tiv)28(e)-334(pr)1(olongator\051.)]TJ -ET -q -1 0 0 1 914.493 181.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 299.826 180.902 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -q -1 0 0 1 299.826 153.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 305.803 171.219 Td [(mld_aggr_thresh_)]TJ 0 -13.549 Td [(AGGR_THRESH)]TJ -ET -q -1 0 0 1 453.513 153.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 459.491 171.219 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ -ET -q -1 0 0 1 508.868 171.418 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 512.214 171.219 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ -ET -q -1 0 0 1 572.487 153.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 578.464 171.219 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 -ET -q -1 0 0 1 652.473 153.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 658.451 171.219 Td [(0.05)]TJ -ET -q -1 0 0 1 732.46 153.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 738.437 171.219 Td [(Threshold)]TJ/F22 10.9091 Tf 50.816 0 Td [(\022)]TJ/F15 10.9091 Tf 8.27 0 Td [(in)-261(the)-261(aggregation)-261(algo-)]TJ -59.086 -13.549 Td [(rithm.)]TJ -ET -q -1 0 0 1 914.493 153.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 299.826 153.406 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -q -1 0 0 1 299.826 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 305.803 143.722 Td [(mld_aggr_scale_)]TJ 0 -13.549 Td [(AGGR_SCALE)]TJ -ET -q -1 0 0 1 453.513 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F44 10.9091 Tf 459.491 143.722 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ -ET -q -1 0 0 1 508.868 143.921 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 512.214 143.722 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ -ET -q -1 0 0 1 572.487 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 578.464 143.722 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 -ET -q -1 0 0 1 652.473 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 658.451 143.722 Td [(1.0)]TJ -ET -q -1 0 0 1 732.46 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 738.437 143.722 Td [(Scale)-266(factor)-266(applied)-266(to)-265(the)-266(threshold)]TJ 0 -13.549 Td [(going)-248(from)-249(lev)28(el)]TJ/F22 10.9091 Tf 76.95 0 Td [(il)-20(ev)]TJ/F15 10.9091 Tf 20.697 0 Td [(to)-248(lev)27(el)]TJ/F22 10.9091 Tf 36.33 0 Td [(il)-20(ev)]TJ/F15 10.9091 Tf 18.56 0 Td [(+)-52(1.)]TJ -ET -q -1 0 0 1 914.493 126.108 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 299.826 125.909 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -q -1 0 0 1 299.826 57.963 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F44 10.9091 Tf 305.803 116.225 Td [(mld_aggr_omega_alg_)]TJ 0 -13.549 Td [(AGGR_OMEGA_ALG)]TJ -ET -q -1 0 0 1 453.513 57.963 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F44 10.9091 Tf 459.491 116.225 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 572.487 57.963 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F44 10.9091 Tf 578.464 116.225 Td [('EIG)]TJ -ET -q -1 0 0 1 602.06 116.424 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F44 10.9091 Tf 605.497 116.225 Td [(EST')]TJ -27.033 -13.549 Td [('USER)]TJ -ET -q -1 0 0 1 607.787 102.875 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F44 10.9091 Tf 611.224 102.676 Td [(CHOICE')]TJ -ET -q -1 0 0 1 652.473 57.963 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F44 10.9091 Tf 658.451 116.225 Td [('EIG)]TJ -ET -q -1 0 0 1 682.047 116.424 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F44 10.9091 Tf 685.483 116.225 Td [(EST')]TJ -ET -q -1 0 0 1 732.46 57.963 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F15 10.9091 Tf 738.437 116.225 Td [(Ho)28(w)-508(the)-507(damping)-508(parameter)]TJ/F22 10.9091 Tf 148.269 0 Td [(!)]TJ/F15 10.9091 Tf 12.719 0 Td [(in)]TJ -160.988 -13.549 Td [(the)-269(smo)-28(othed)-269(aggregation)-269(should)-269(b)-28(e)]TJ 0 -13.549 Td [(computed:)-435(either)-315(via)-314(an)-315(estimate)-314(of)]TJ 0 -13.55 Td [(the)-362(sp)-28(ectral)-361(radius)-362(of)]TJ/F22 10.9091 Tf 106.272 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 [(,)-369(or)-362(ex-)]TJ -135.108 -13.549 Td [(plicily)-333(sp)-28(eci\014ed)-333(b)27(y)-333(the)-333(user.)]TJ -ET -q -1 0 0 1 914.493 57.963 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -q -1 0 0 1 299.826 57.764 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -q -1 0 0 1 299.826 16.917 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 305.803 48.081 Td [(mld_aggr_eig_)]TJ 0 -13.55 Td [(AGGR_EIG)]TJ -ET -q -1 0 0 1 453.513 16.917 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 459.491 48.081 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 572.487 16.917 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 578.464 48.081 Td [('A)]TJ -ET -q -1 0 0 1 590.606 48.28 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F44 10.9091 Tf 594.042 48.081 Td [(NORMI')]TJ -ET -q -1 0 0 1 652.473 16.917 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 658.451 48.081 Td [('A)]TJ -ET -q -1 0 0 1 670.592 48.28 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F44 10.9091 Tf 674.029 48.081 Td [(NORMI')]TJ -ET -q -1 0 0 1 732.46 16.917 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 738.437 48.081 Td [(Ho)28(w)-319(to)-320(estimate)-319(the)-319(sp)-28(ectral)-319(radius)]TJ 0 -13.55 Td [(of)]TJ/F22 10.9091 Tf 12.94 0 Td [(D)]TJ/F26 7.9701 Tf 9.334 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 [(.)-586(Curren)28(tly)-381(only)-380(the)-381(in\014n-)]TJ -41.775 -13.549 Td [(it)28(y)-334(n)1(orm)-334(estimate)-333(is)-334(a)28(v)56(ailable.)]TJ -ET -q -1 0 0 1 914.493 16.917 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 299.826 16.718 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -q -1 0 0 1 299.826 -91.875 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F44 10.9091 Tf 305.803 7.034 Td [(mld_aggr_omega_val_)]TJ 0 -13.549 Td [(AGGR_OMEGA_VAL)]TJ -ET -q -1 0 0 1 453.513 -91.875 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F44 10.9091 Tf 459.491 7.034 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ -ET -q -1 0 0 1 508.868 7.234 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 512.214 7.034 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ -ET -q -1 0 0 1 572.487 -91.875 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F15 10.9091 Tf 578.464 7.034 Td [(An)28(y)-486(nonnega-)]TJ 0 -13.549 Td [(tiv)28(e)-334(real)-333(n)28(um.)]TJ -ET -q -1 0 0 1 652.473 -91.875 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F15 10.9091 Tf 658.451 7.034 Td [(4)]TJ/F22 10.9091 Tf 5.454 0 Td [(=)]TJ/F15 10.9091 Tf 5.455 0 Td [(\0503)]TJ/F22 10.9091 Tf 9.697 0 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\051)]TJ -ET -q -1 0 0 1 732.46 -91.875 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F15 10.9091 Tf 738.437 7.034 Td [(Damping)-1068(parameter)]TJ/F22 10.9091 Tf 115.343 0 Td [(!)]TJ/F15 10.9091 Tf 18.837 0 Td [(in)-1068(the)]TJ -134.18 -13.549 Td [(smo)-28(othed)-915(aggr)1(e)-1(gation)-914(algorithm.)]TJ 0 -13.549 Td [(It)-804(m)28(ust)-804(b)-28(e)-803(s)-1(et)-803(b)27(y)-803(the)-804(user)-804(if)]TJ/F44 10.9091 Tf 0 -13.549 Td [(USER_CHOICE)]TJ/F15 10.9091 Tf 75.101 0 Td [(w)28(as)-1110(sp)-28(eci\014ed)-1110(for)]TJ/F44 10.9091 Tf -75.101 -13.549 Td [(mld_aggr_omega_alg_)]TJ/F15 10.9091 Tf 108.817 0 Td [(,)-1218(otherwise)]TJ -108.817 -13.55 Td [(it)-354(is)-354(computed)-354(b)28(y)-354(the)-354(library)83(,)-359(using)]TJ 0 -13.549 Td [(the)-303(selected)-303(estimate)-304(of)-303(the)-303(sp)-28(ectral)]TJ 0 -13.549 Td [(radius)]TJ/F22 10.9091 Tf 32.818 0 Td [(\032)]TJ/F15 10.9091 Tf 5.64 0 Td [(\050)]TJ/F22 10.9091 Tf 4.243 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 [(\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 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(.)]TJ -ET -q -1 0 0 1 914.493 -91.875 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -q -1 0 0 1 299.826 -92.074 cm -[]0 d 0 J 0.398 w 0 0 m 614.668 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 459.779 -122.763 Td [(T)83(able)-333(4:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(aggregation)-333(algorithm.)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -451 0 obj -<< -/Length 10694 ->> -stream -0 g 0 G -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 -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -q -0 -1 1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 26.449 250.963 cm -[]0 d 0 J 0.398 w 0 0 m 540.678 0 l S -Q -q -1 0 0 1 26.449 237.215 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -1 0 0 1 -292.625 -715.095 cm -BT -/F44 10.9091 Tf 325.051 956.375 Td [(what)]TJ -ET -q -1 0 0 1 430.241 952.31 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 436.219 956.375 Td [(d)22(a)67(t)66(a)-377(type)]TJ -ET -q -1 0 0 1 549.215 952.31 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F44 10.9091 Tf 555.192 956.375 Td [(val)]TJ -ET -q -1 0 0 1 651.879 952.31 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 657.856 956.375 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 706.064 952.31 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F41 10.9091 Tf 712.041 956.375 Td [(comments)]TJ -ET -q -1 0 0 1 859.751 952.31 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 319.074 952.111 cm -[]0 d 0 J 0.398 w 0 0 m 540.678 0 l S -Q -q -1 0 0 1 319.074 911.264 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 325.051 942.427 Td [(mld_coarse_mat_)]TJ 0 -13.549 Td [(COARSE_MAT)]TJ -ET -q -1 0 0 1 430.241 911.264 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 436.219 942.427 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 549.215 911.264 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 555.192 942.427 Td [('DISTR')]TJ 0 -13.549 Td [('REPL')]TJ -ET -q -1 0 0 1 651.879 911.264 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 657.856 942.427 Td [('DISTR')]TJ -ET -q -1 0 0 1 706.064 911.264 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 712.041 942.427 Td [(Coarsest)-498(matrix:)-775(distributed)]TJ 0 -13.549 Td [(among)-276(the)-276(pro)-27(cess)-1(or)1(s)-276(or)-276(repli-)]TJ 0 -13.549 Td [(cated)-333(on)-334(eac)28(h)-333(of)-334(them.)]TJ -ET -q -1 0 0 1 859.751 911.264 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 319.074 911.065 cm -[]0 d 0 J 0.398 w 0 0 m 540.678 0 l S -Q -q -1 0 0 1 319.074 775.373 cm -[]0 d 0 J 0.398 w 0 0 m 0 135.492 l S -Q -BT -/F44 10.9091 Tf 325.051 901.381 Td [(mld_coarse_solve_)]TJ 0 -27.098 Td [(COARSE_SOLVE)]TJ -ET -q -1 0 0 1 430.241 775.373 cm -[]0 d 0 J 0.398 w 0 0 m 0 135.492 l S -Q -BT -/F44 10.9091 Tf 436.219 901.381 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 549.215 775.373 cm -[]0 d 0 J 0.398 w 0 0 m 0 135.492 l S -Q -BT -/F44 10.9091 Tf 555.192 901.381 Td [('BJAC')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ 0 -13.55 Td [('SLUDIST')]TJ -ET -q -1 0 0 1 651.879 775.373 cm -[]0 d 0 J 0.398 w 0 0 m 0 135.492 l S -Q -BT -/F44 10.9091 Tf 657.856 901.381 Td [('BJAC')]TJ -ET -q -1 0 0 1 706.064 775.373 cm -[]0 d 0 J 0.398 w 0 0 m 0 135.492 l S -Q -BT -/F15 10.9091 Tf 712.041 901.381 Td [(Solv)28(er)-659(used)-659(at)-660(the)-659(coarsest)]TJ 0 -13.549 Td [(lev)28(el:)-929(blo)-27(c)27(k)-575(Jacobi,)-636(sequen-)]TJ 0 -13.549 Td [(tial)-909(LU)-908(from)-908(UMFP)83(A)28(CK,)]TJ 0 -13.55 Td [(sequen)28(tial)-355(LU)-355(from)-355(S)1(up)-28(erLU,)]TJ 0 -13.549 Td [(distributed)-1119(LU)-1118(from)-1119(Su-)]TJ 0 -13.549 Td [(p)-28(erLU)]TJ -ET -q -1 0 0 1 743.181 833.834 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 746.454 833.635 Td [(Dist.)]TJ/F44 10.9091 Tf 55.775 0 Td [('SLUDIST')]TJ/F15 10.9091 Tf -90.188 -13.549 Td [(requires)-599(the)-599(c)-1(oar)1(s)-1(est)-599(matrix)]TJ 0 -13.549 Td [(to)-274(b)-28(e)-274(distributed,)-286(while)]TJ/F44 10.9091 Tf 113.097 0 Td [('UMF')]TJ/F15 10.9091 Tf -113.097 -13.55 Td [(and)]TJ/F44 10.9091 Tf 24.426 0 Td [('SLU')]TJ/F15 10.9091 Tf 35.483 0 Td [(require)-628(it)-628(to)-628(b)-27(e)]TJ -59.909 -13.549 Td [(replicated.)]TJ -ET -q -1 0 0 1 859.751 775.373 cm -[]0 d 0 J 0.398 w 0 0 m 0 135.492 l S -Q -q -1 0 0 1 319.074 775.174 cm -[]0 d 0 J 0.398 w 0 0 m 540.678 0 l S -Q -q -1 0 0 1 319.074 666.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F44 10.9091 Tf 325.051 765.49 Td [(mld_coarse_subsolve_)]TJ 0 -27.098 Td [(COARSE_SUBSOLVE)]TJ -ET -q -1 0 0 1 430.241 666.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F44 10.9091 Tf 436.219 765.49 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 549.215 666.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F44 10.9091 Tf 555.192 765.49 Td [('ILU')]TJ 0 -13.549 Td [('MILU')]TJ 0 -13.549 Td [('ILUT')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ -ET -q -1 0 0 1 651.879 666.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F15 10.9091 Tf 657.856 765.49 Td [(See)-333(note)]TJ -ET -q -1 0 0 1 706.064 666.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -BT -/F15 10.9091 Tf 712.041 765.49 Td [(Solv)28(er)-343(for)-342(the)-343(d)1(iagonal)-343(blo)-28(c)28(ks)]TJ 0 -13.549 Td [(of)-456(the)-455(coarse)-456(matrix,)-486(in)-456(case)]TJ 0 -13.549 Td [(the)-304(blo)-28(c)28(k)-304(Jacobi)-304(solv)28(er)-304(is)-304(c)28(ho-)]TJ 0 -13.549 Td [(sen)-727(as)-727(coarsest-lev)27(el)-727(solv)28(er:)]TJ 0 -13.549 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-693(MILU\050)]TJ/F22 10.9091 Tf 48.012 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-693(ILU\050)]TJ/F22 10.9091 Tf 38.011 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.277 0 Td [(\051,)]TJ -134.46 -13.55 Td [(LU)-931(from)-932(UMFP)83(A)28(CK,)-932(LU)]TJ 0 -13.549 Td [(from)-497(Sup)-28(erLU,)-497(plus)-498(triangu-)]TJ 0 -13.549 Td [(lar)-333(solv)27(e.)]TJ -ET -q -1 0 0 1 859.751 666.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S -Q -q -1 0 0 1 319.074 666.382 cm -[]0 d 0 J 0.398 w 0 0 m 540.678 0 l S -Q -q -1 0 0 1 319.074 625.535 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 325.051 656.698 Td [(mld_coarse_sweeps_)]TJ 0 -27.098 Td [(COARSE_SWEEPS)]TJ -ET -q -1 0 0 1 430.241 625.535 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 436.219 656.698 Td [(integer)]TJ -ET -q -1 0 0 1 549.215 625.535 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 555.192 656.698 Td [(An)28(y)-334(in)28(t.)-333(n)28(um.)]TJ/F22 10.9091 Tf 70.607 0 Td [(>)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ -ET -q -1 0 0 1 651.879 625.535 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 657.856 656.698 Td [(4)]TJ -ET -q -1 0 0 1 706.064 625.535 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 712.041 656.698 Td [(Num)28(b)-28(er)-1536(of)-1537(Blo)-27(c)27(k-Jacobi)]TJ 0 -13.549 Td [(sw)28(eeps)-486(when)-486('BJA)28(C')-485(is)-486(used)]TJ 0 -13.549 Td [(as)-333(coarse)-1(st-lev)28(el)-333(solv)28(er.)]TJ -ET -q -1 0 0 1 859.751 625.535 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 319.074 625.336 cm -[]0 d 0 J 0.398 w 0 0 m 540.678 0 l S -Q -q -1 0 0 1 319.074 584.489 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 325.051 615.652 Td [(mld_coarse_fillin_)]TJ 0 -27.098 Td [(COARSE_FILLIN)]TJ -ET -q -1 0 0 1 430.241 584.489 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 436.219 615.652 Td [(integer)]TJ -ET -q -1 0 0 1 549.215 584.489 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 555.192 615.652 Td [(An)28(y)-334(in)28(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 70.607 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ -ET -q -1 0 0 1 651.879 584.489 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 657.856 615.652 Td [(0)]TJ -ET -q -1 0 0 1 706.064 584.489 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 712.041 615.652 Td [(Fill-in)-550(le)-1(v)28(el)]TJ/F22 10.9091 Tf 62.165 0 Td [(p)]TJ/F15 10.9091 Tf 11.494 0 Td [(of)-551(the)-550(incom-)]TJ -73.659 -13.549 Td [(plete)-333(LU)-334(factorizations.)]TJ -ET -q -1 0 0 1 859.751 584.489 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 319.074 584.29 cm -[]0 d 0 J 0.398 w 0 0 m 540.678 0 l S -Q -q -1 0 0 1 319.074 543.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 325.051 574.606 Td [(mld_coarse_iluthrs_)]TJ 0 -27.098 Td [(COARSE_ILUTHRS)]TJ -ET -q -1 0 0 1 430.241 543.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F44 10.9091 Tf 436.219 574.606 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ -ET -q -1 0 0 1 485.597 574.806 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 488.942 574.606 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ -ET -q -1 0 0 1 549.215 543.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 555.192 574.606 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 -ET -q -1 0 0 1 651.879 543.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 657.856 574.606 Td [(0)]TJ -ET -q -1 0 0 1 706.064 543.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 712.041 574.606 Td [(Drop)-1063(tolerance)]TJ/F22 10.9091 Tf 90.367 0 Td [(t)]TJ/F15 10.9091 Tf 15.531 0 Td [(in)-1063(the)]TJ -105.898 -13.549 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.277 0 Td [(\051)-333(factorization.)]TJ -ET -q -1 0 0 1 859.751 543.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 319.074 543.244 cm -[]0 d 0 J 0.398 w 0 0 m 540.678 0 l S -Q -q -1 0 0 1 319.074 529.495 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F43 10.9091 Tf 325.051 533.56 Td [(Note:)]TJ/F15 10.9091 Tf 35.053 0 Td [(defaults)-333(for)]TJ/F44 10.9091 Tf 57.667 0 Td [(m)]TJ/F15 10.9091 Tf 5.727 0 Td [(ld)]TJ -ET -q -1 0 0 1 433.244 533.759 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 436.516 533.56 Td [(coarse)]TJ -ET -q -1 0 0 1 466.353 533.759 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 469.625 533.56 Td [(subsolv)28(e)]TJ -ET -q -1 0 0 1 509.795 533.759 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 516.704 533.56 Td [(are)-333(c)27(hosen)-333(as)]TJ -ET -q -1 0 0 1 859.751 529.495 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 319.074 515.946 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 325.051 520.011 Td [(single)-333(precision)-334(v)28(ersion:)-444('SLU')-334(if)-333(installed,)-333('ILU')-333(otherwise)]TJ -ET -q -1 0 0 1 859.751 515.946 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 319.074 502.397 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 325.051 506.462 Td [(double)-333(precision)-334(v)28(ersion:)-444('UMF')-333(if)-334(installed,)-333(else)-333('SLU')-334(if)-333(installed,)-333('ILU')-333(otherwise)]TJ -ET -q -1 0 0 1 859.751 502.397 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 319.074 502.198 cm -[]0 d 0 J 0.398 w 0 0 m 540.678 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 403.64 471.509 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 -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -459 0 obj -<< -/Length 3122 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(29)]TJ -0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.3)-1125(Subroutine)-375(mld)]TJ -ET -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 -Q -BT -/F17 11.9552 Tf 220.657 704.136 Td [(precbld)]TJ -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 rg 1 0 0 RG - [(15)]TJ -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 rg 1 0 0 RG - [(15)]TJ -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 -0 0 1 rg 0 0 1 RG - [-333(7)]TJ -0 g 0 G - [-333(for)-334(details.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -464 0 obj -<< -/Length 9096 ->> -stream -0 g 0 G -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 -0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.4)-1125(Subroutine)-375(mld)]TJ -ET -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 -Q -BT -/F17 11.9552 Tf 213.457 704.136 Td [(precaply)]TJ -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 [(psb_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 -ET -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 -Q -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 -ET -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 -Q -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 -ET -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 -Q -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 -ET -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 -Q -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 -0 0 1 rg 0 0 1 RG - [-333(7)]TJ -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 -ET -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 -Q -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 -ET -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 -Q -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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -470 0 obj -<< -/Length 1564 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(31)]TJ -0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.5)-1125(Subroutine)-375(mld)]TJ -ET -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 -Q -BT -/F17 11.9552 Tf 220.657 704.136 Td [(precfree)]TJ -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 -0 0 1 rg 0 0 1 RG - [-307(7)]TJ -0 g 0 G - [-308(for)-308(details.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -476 0 obj -<< -/Length 2271 ->> -stream -0 g 0 G -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 -0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.6)-1125(Subroutine)-375(mld)]TJ -ET -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 -Q -BT -/F17 11.9552 Tf 213.457 704.136 Td [(precdescr)]TJ -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 -0 0 1 rg 0 0 1 RG - [-333(7)]TJ -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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -482 0 obj -<< -/Length 1804 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F41 10.9091 Tf 93.6 740.002 Td [(7)]TJ -0 g 0 G - [-378(Err)22(o)1(r)-378(handling)]TJ/F15 10.9091 Tf 401.542 0 Td [(33)]TJ -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 rg 1 0 0 RG - [(15)]TJ -0 g 0 G - [(].)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -486 0 obj -<< -/Length 4007 ->> -stream -0 g 0 G -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 -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 -0 g 0 G -0 g 0 G -/F44 9.9626 Tf 141.219 -44.832 Td [(MLD2P4)-1050(version)-525(2.0)]TJ -130.759 -11.955 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(3.3\051)]TJ -57.534 -23.91 Td [(\050C\051)-525(Copyright)-525(2008,)-525(2010,)-525(2012,)-525(2015)]TJ 104.607 -23.911 Td [(Salvatore)-525(Filippone)-1050(University)-525(of)-525(Rome)-525(Tor)-525(Vergata)]TJ 0 -11.955 Td [(Alfredo)-525(Buttari)-3150(CNRS-IRIT,)-525(Toulouse)]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 -35.866 Td [(Redistribution)-525(and)-525(use)-525(in)-525(source)-525(and)-525(binary)-525(forms,)-525(with)-525(or)-525(without)]TJ 0 -11.955 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 10.461 -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 -11.956 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 -11.955 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 -11.956 Td [(software)-525(without)-525(specific)-525(written)-525(permission.)]TJ -26.152 -23.91 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 -11.956 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 -11.955 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 -11.956 Td [(POSSIBILITY)-525(OF)-525(SUCH)-525(DAMAGE.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -490 0 obj -<< -/Length 6685 ->> -stream -0 g 0 G -BT -/F41 10.9091 Tf 93.6 740.002 Td [(References)]TJ/F15 10.9091 Tf 401.542 0 Td [(35)]TJ -0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(References)]TJ -0 g 0 G -/F15 10.9091 Tf 5.455 -24.352 Td [([1])]TJ -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 -0 g 0 G - -51.563 -21.189 Td [([2])]TJ -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 -0 g 0 G - -16.969 -21.189 Td [([3])]TJ -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 -0 g 0 G - -16.969 -21.189 Td [([4])]TJ -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 -0 g 0 G - -16.969 -21.189 Td [([5])]TJ -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 -0 g 0 G - -16.969 -21.19 Td [([6])]TJ -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 -0 g 0 G - -16.969 -21.189 Td [([7])]TJ -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 -0 g 0 G - -16.969 -21.189 Td [([8])]TJ -0 g 0 G - [-500(P)83(.)-352(D'Am)28(bra,)-357(D.)-352(di)-352(Sera\014no,)-356(S.)-352(Filipp)-28(one,)]TJ/F18 10.9091 Tf 219.527 0 Td [(MLD2P4:)-495(a)-375(Package)-375(of)-375(Par)51(al)-51(lel)-375(Multi-)]TJ -202.558 -13.549 Td [(level)-312(A)26(lgebr)51(aic)-312(Domain)-312(De)51(c)51(omp)51(osition)-312(Pr)51(e)51(c)51(onditioners)-312(in)-312(F)77(ortr)51(an)-312(95)]TJ/F15 10.9091 Tf 324.852 0 Td [(,)-294(A)28(CM)-283(T)83(rans.)]TJ -324.852 -13.549 Td [(Math.)-333(Soft)28(w.,)-334(37\0503\051,)-333(2010.)]TJ -0 g 0 G - -16.969 -21.19 Td [([9])]TJ -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(C)1(o)-1(l)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 -0 g 0 G - -383.998 -21.189 Td [([10])]TJ -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 22.424 -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 -13.55 Td [(Applications,)-333(20,)-334(3,)-333(1999,)-333(720{755.)]TJ -0 g 0 G - -22.424 -21.189 Td [([11])]TJ -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(Mat)1(hem)-1(atical)-444(Sof)1(t)27(w)28(are,)-472(16,)]TJ -135.936 -13.549 Td [(1990,)-333(1{17.)]TJ -0 g 0 G - -22.424 -21.19 Td [([12])]TJ -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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -494 0 obj -<< -/Length 7080 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(36)]TJ/F41 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [([13])]TJ -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 179.47 0 Td [(,)-391(Lapac)28(k)]TJ -348.639 -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 -0 g 0 G - -22.424 -21.125 Td [([14])]TJ -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 -0 g 0 G - -128.805 -21.126 Td [([15])]TJ -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-3.0)-1158(User's)-1159(Guide.)-1158(A)-1157(R)51(efer)51(enc)51(e)]TJ -163.658 -13.549 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(2012,)-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 -0 g 0 G - -211.422 -21.125 Td [([16])]TJ -0 g 0 G - [-500(Salv)56(atore)-444(Filipp)-27(one)-444(and)-443(Alfredo)-443(Buttari.)]TJ/F18 10.9091 Tf 226.395 0 Td [(Obje)51(ct-Oriente)51(d)-459(T)77(e)51(chniques)-459(for)-459(Sp)52(arse)]TJ -203.971 -13.549 Td [(Matrix)-277(Computations)-276(in)-277(F)77(ortr)51(an)-277(2003.)]TJ/F15 10.9091 Tf 183.774 0 Td [(A)28(CM)-245(T)83(rans.)-245(on)-245(Math)-246(S)1(oft)27(w)28(are,)-263(38\0504\051,)-263(2012.)]TJ -0 g 0 G - -206.198 -21.126 Td [([17])]TJ -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 -13.549 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 -0 g 0 G - -22.424 -21.125 Td [([18])]TJ -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 -13.549 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 -13.55 Td [(Press,)-333(1998.)]TJ -0 g 0 G - -22.424 -21.125 Td [([19])]TJ -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 -13.549 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 -0 g 0 G - -22.424 -21.125 Td [([20])]TJ -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 -ET -q -1 0 0 1 276.516 393.869 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 279.861 393.669 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 -13.549 Td [(ical)-333(Soft)28(w)27(are,)-333(29,)-333(2,)-334(2003,)-333(110{140.)]TJ -0 g 0 G - -22.424 -21.125 Td [([21])]TJ -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 -0 g 0 G - -269.95 -21.125 Td [([22])]TJ -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 -13.55 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 -0 g 0 G - -22.424 -21.125 Td [([23])]TJ -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 -0 g 0 G - -201.78 -21.125 Td [([24])]TJ -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 -13.55 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 -0 g 0 G - -22.424 -21.125 Td [([25])]TJ -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 -13.549 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 -0 g 0 G - -22.424 -21.126 Td [([26])]TJ -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 -13.549 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 -0 g 0 G -0 g 0 G -ET - -endstream -endobj -420 0 obj -<< -/Type /ObjStm -/N 100 -/First 881 -/Length 9834 ->> -stream -413 0 414 145 419 291 71 345 416 398 425 517 421 667 422 810 423 954 427 1101 -428 1155 429 1209 430 1263 431 1317 424 1371 434 1477 432 1611 436 1757 360 1811 433 1869 -439 1962 441 2076 442 2130 438 2189 445 2321 443 2455 447 2601 448 2655 444 2713 450 2871 -452 2985 361 3039 449 3098 458 3243 456 3401 453 3547 454 3701 455 3855 460 4002 75 4056 -457 4109 463 4228 461 4362 465 4508 79 4562 462 4615 469 4786 467 4928 466 5074 471 5221 -83 5275 468 5328 475 5447 473 5581 477 5728 87 5782 474 5835 481 5954 479 6096 478 6242 -483 6396 91 6450 480 6503 485 6609 487 6723 95 6777 484 6830 489 6936 491 7050 99 7104 -178 7157 285 7211 286 7265 287 7319 296 7373 256 7427 257 7481 288 7535 217 7589 225 7643 -213 7697 214 7751 488 7805 493 7924 495 8038 496 8092 297 8146 182 8200 181 8254 180 8308 -216 8361 215 8415 226 8469 289 8523 176 8577 183 8631 283 8685 284 8739 179 8793 492 8847 -% 413 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [385.325 231.858 392.772 243.547] -/A << /S /GoTo /D (table.5) >> ->> -% 414 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [402.247 135.07 409.694 148.703] -/A << /S /GoTo /D (section.7) >> ->> -% 419 0 obj -<< -/D [417 0 R /XYZ 92.6 752.957 null] ->> -% 71 0 obj -<< -/D [417 0 R /XYZ 93.6 715.095 null] ->> -% 416 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F17 108 0 R /F44 200 0 R /F18 171 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 425 0 obj -<< -/Type /Page -/Contents 426 0 R -/Resources 424 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 393 0 R -/Annots [ 421 0 R 422 0 R 423 0 R ] ->> -% 421 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [159.7 561.343 167.147 573.032] -/A << /S /GoTo /D (table.2) >> ->> -% 422 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [168.79 561.343 176.238 573.032] -/A << /S /GoTo /D (table.5) >> ->> -% 423 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [166.591 547.793 174.038 559.483] -/A << /S /GoTo /D (section.4) >> ->> -% 427 0 obj -<< -/D [425 0 R /XYZ 85.4 752.957 null] ->> -% 428 0 obj -<< -/D [425 0 R /XYZ 86.4 683.983 null] ->> -% 429 0 obj -<< -/D [425 0 R /XYZ 86.4 661.467 null] ->> -% 430 0 obj -<< -/D [425 0 R /XYZ 86.4 638.952 null] ->> -% 431 0 obj -<< -/D [425 0 R /XYZ 86.4 616.436 null] ->> -% 424 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F18 171 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 434 0 obj -<< -/Type /Page -/Contents 435 0 R -/Resources 433 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R -/Annots [ 432 0 R ] ->> -% 432 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 436 0 obj -<< -/D [434 0 R /XYZ 92.6 752.957 null] ->> -% 360 0 obj -<< -/D [434 0 R /XYZ 366.766 4378.384 null] ->> -% 433 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 439 0 obj -<< -/Type /Page -/Contents 440 0 R -/Resources 438 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R ->> -% 441 0 obj -<< -/D [439 0 R /XYZ 85.4 752.957 null] ->> -% 442 0 obj -<< -/D [439 0 R /XYZ -3963.913 559.035 null] ->> -% 438 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F44 200 0 R /F25 174 0 R /F22 173 0 R /F18 171 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 445 0 obj -<< -/Type /Page -/Contents 446 0 R -/Resources 444 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R -/Annots [ 443 0 R ] ->> -% 443 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 447 0 obj -<< -/D [445 0 R /XYZ 92.6 752.957 null] ->> -% 448 0 obj -<< -/D [445 0 R /XYZ 530.237 4405.505 null] ->> -% 444 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F44 200 0 R /F18 171 0 R /F25 174 0 R /F22 173 0 R /F26 276 0 R /F20 277 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 450 0 obj -<< -/Type /Page -/Contents 451 0 R -/Resources 449 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 437 0 R ->> -% 452 0 obj -<< -/D [450 0 R /XYZ 85.4 752.957 null] ->> -% 361 0 obj -<< -/D [450 0 R /XYZ -4018.109 560.748 null] ->> -% 449 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F44 200 0 R /F22 173 0 R /F25 174 0 R /F18 171 0 R /F43 155 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 458 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 453 0 R 454 0 R 455 0 R ] ->> -% 456 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 453 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [364.686 535.842 377.588 544.865] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 454 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [199.125 495.195 212.027 504.218] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 455 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [402.247 409.835 409.694 423.468] -/A << /S /GoTo /D (section.7) >> ->> -% 460 0 obj -<< -/D [458 0 R /XYZ 92.6 752.957 null] ->> -% 75 0 obj -<< -/D [458 0 R /XYZ 93.6 715.095 null] ->> -% 457 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F17 108 0 R /F44 200 0 R /F18 171 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 463 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 ] ->> -% 461 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 314.99 402.493 328.624] -/A << /S /GoTo /D (section.7) >> ->> -% 465 0 obj -<< -/D [463 0 R /XYZ 85.4 752.957 null] ->> -% 79 0 obj -<< -/D [463 0 R /XYZ 86.4 715.095 null] ->> -% 462 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F17 108 0 R /F44 200 0 R /F22 173 0 R /F26 276 0 R /F20 277 0 R /F18 171 0 R /F23 275 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 469 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 ] ->> -% 467 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 466 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [399.894 531.778 407.341 545.411] -/A << /S /GoTo /D (section.7) >> ->> -% 471 0 obj -<< -/D [469 0 R /XYZ 92.6 752.957 null] ->> -% 83 0 obj -<< -/D [469 0 R /XYZ 93.6 715.095 null] ->> -% 468 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F17 108 0 R /F44 200 0 R /F18 171 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 475 0 obj -<< -/Type /Page -/Contents 476 0 R -/Resources 474 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 472 0 R -/Annots [ 473 0 R ] ->> -% 473 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 504.679 402.493 518.312] -/A << /S /GoTo /D (section.7) >> ->> -% 477 0 obj -<< -/D [475 0 R /XYZ 85.4 752.957 null] ->> -% 87 0 obj -<< -/D [475 0 R /XYZ 86.4 715.095 null] ->> -% 474 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F17 108 0 R /F44 200 0 R /F18 171 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 481 0 obj -<< -/Type /Page -/Contents 482 0 R -/Resources 480 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 472 0 R -/Annots [ 479 0 R 478 0 R ] ->> -% 479 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.7) >> ->> -% 478 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [314.074 583.943 326.976 592.966] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 483 0 obj -<< -/D [481 0 R /XYZ 92.6 752.957 null] ->> -% 91 0 obj -<< -/D [481 0 R /XYZ 93.6 715.095 null] ->> -% 480 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F17 108 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 485 0 obj -<< -/Type /Page -/Contents 486 0 R -/Resources 484 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 472 0 R ->> -% 487 0 obj -<< -/D [485 0 R /XYZ 85.4 752.957 null] ->> -% 95 0 obj -<< -/D [485 0 R /XYZ 86.4 715.095 null] ->> -% 484 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F17 108 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 489 0 obj -<< -/Type /Page -/Contents 490 0 R -/Resources 488 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 472 0 R ->> -% 491 0 obj -<< -/D [489 0 R /XYZ 92.6 752.957 null] ->> -% 99 0 obj -<< -/D [489 0 R /XYZ 93.6 722.069 null] ->> -% 178 0 obj -<< -/D [489 0 R /XYZ 93.6 697.153 null] ->> -% 285 0 obj -<< -/D [489 0 R /XYZ 93.6 660.294 null] ->> -% 286 0 obj -<< -/D [489 0 R /XYZ 93.6 598.457 null] ->> -% 287 0 obj -<< -/D [489 0 R /XYZ 93.6 538.741 null] ->> -% 296 0 obj -<< -/D [489 0 R /XYZ 93.6 488.332 null] ->> -% 256 0 obj -<< -/D [489 0 R /XYZ 93.6 442.166 null] ->> -% 257 0 obj -<< -/D [489 0 R /XYZ 93.6 393.878 null] ->> -% 288 0 obj -<< -/D [489 0 R /XYZ 93.6 357.018 null] ->> -% 217 0 obj -<< -/D [489 0 R /XYZ 93.6 308.124 null] ->> -% 225 0 obj -<< -/D [489 0 R /XYZ 93.6 259.837 null] ->> -% 213 0 obj -<< -/D [489 0 R /XYZ 93.6 212.155 null] ->> -% 214 0 obj -<< -/D [489 0 R /XYZ 93.6 163.867 null] ->> -% 488 0 obj -<< -/Font << /F41 121 0 R /F15 120 0 R /F17 108 0 R /F18 171 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 493 0 obj -<< -/Type /Page -/Contents 494 0 R -/Resources 492 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 472 0 R ->> -% 495 0 obj -<< -/D [493 0 R /XYZ 85.4 752.957 null] ->> -% 496 0 obj -<< -/D [493 0 R /XYZ 86.4 715.095 null] ->> -% 297 0 obj -<< -/D [493 0 R /XYZ 86.4 670.523 null] ->> -% 182 0 obj -<< -/D [493 0 R /XYZ 86.4 636.454 null] ->> -% 181 0 obj -<< -/D [493 0 R /XYZ 86.4 587.928 null] ->> -% 180 0 obj -<< -/D [493 0 R /XYZ 86.4 552.95 null] ->> -% 216 0 obj -<< -/D [493 0 R /XYZ 86.4 505.333 null] ->> -% 215 0 obj -<< -/D [493 0 R /XYZ 86.4 457.109 null] ->> -% 226 0 obj -<< -/D [493 0 R /XYZ 86.4 408.885 null] ->> -% 289 0 obj -<< -/D [493 0 R /XYZ 86.4 360.662 null] ->> -% 176 0 obj -<< -/D [493 0 R /XYZ 86.4 338.931 null] ->> -% 183 0 obj -<< -/D [493 0 R /XYZ 86.4 293.434 null] ->> -% 283 0 obj -<< -/D [493 0 R /XYZ 86.4 256.639 null] ->> -% 284 0 obj -<< -/D [493 0 R /XYZ 86.4 210.536 null] ->> -% 179 0 obj -<< -/D [493 0 R /XYZ 86.4 160.191 null] ->> -% 492 0 obj -<< -/Font << /F15 120 0 R /F41 121 0 R /F18 171 0 R /F44 200 0 R >> -/ProcSet [ /PDF /Text ] ->> - -endstream -endobj -516 0 obj -<< -/Length1 2110 -/Length2 16860 -/Length3 0 -/Length 18970 ->> -stream -%!PS-AdobeFont-1.0: CMBX10 003.002 -%%Title: CMBX10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMBX10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMBX10 known{/CMBX10 findfont dup/UniqueID known{dup -/UniqueID get 5000768 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /JVXWMJ+CMBX10 def -/FontBBox {-56 -250 1164 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMBX10.) readonly def -/FullName (CMBX10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end 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 78 /N 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 58 /colon 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 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 -readonly def -currentdict end -currentfile eexec -oc;jAw-=%W)-{ru)rAE(@{빴Q|_R -ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ -}3{Z2zݬT2s$Z&{BJ{=מ7ڄĒKV"~Pr-=L$wcrlVcN &'{%Gf#ɨ_i#SXd+U*|:1m=⾝~6/aGLf#NOS}ERs{[.-jj|tm\: x8PbPh[_9t237,I2B8J0msUWQdX!??Q4eRH ]ӊ.p_?8:o:UuDZ[m^/a4l4ȒtL<~&WwLa9gPqhQΠjv)]sqR"ЯDž#eZKPHrF"tw;*l5 FF BW1S!2*`8:XlUI?[wc &Z`ѩް sdHeF'*s ЁTd9Baऋ[a$g1f\0 7aR^(Lj#!mw2#nr$|TL]{X`4.Gw|P2BgܴwbkF Nfj;d?#l"+6g{* ,SQ2&'n\`]Q:ݹ6ln0b9m],/ڨ\Y$6[+UE#ƸMO( ϲ.DL\*@z3'&Е62%+(k`D/k(ɒkpt`^Bձ\H~Y_˒c%~(! -Jvs}9qw{6sΓM &Q-p'&M&7tZ\r|5M5"*<ΕD,Lfj+ʾɝ"x0h#u[@}"փ -dIE* , j]v.tx kEYl}d.-eJ C=KD jnI"yX D|&k>ixbu?ѱ ,VszAc  G 7H`Ď'Ķ)r -ҎG֯Z~C -U. EC3}henħE!C[xxnCq##Ti.iW/i*?K`ɞ}g;ο@>Hmn91-[ tj7 3Myz,?Z@RPBi>vVF\Ahko8*NIQv94z4m n8)Db]ٞ>=e3Q-'0y#JW 0݈7\t53=μغ|[R>5Ir xhhy!kVSȮ7I ThaToɁ( WdsUI=]әM|dJ\YRGy4d(N{"l\ ]kȮ8V -A==r V^*mx(e=\ʰ!Bb8йX ֙Mاi -p)r ~1 ׏<;d,^6f,PpΨ|kR87>i e ^NҢ@h`[BF,L%mUBe*$nox3K V$[[fU;4Qjggo !%Uh(ԝ 2ן, O[Ј_\?Wt<ȅ/; "Rm®)E\rW1 ђoy։)B̊\@gJ?m Eqqٔ84^Da97 㤸{ɧZ!_`-rlُ*qٺ؊t LCg -:nbJ Lqrj5^9NRVJ7en%ϰYƕut4ƸF΋ėvQj6%c#~ O e҉'aS1e F u s^i"yw,~ C~Rƒ`,j"+ȬKk Q5IjEbT)">wv|$.4*@s? -ipb\r 9AZx; -~c/Hϫ+%Bm-7 S2*Eoq;ջ/6[ LoT F>=8$d�otu[QEU!\ސswE6W׍ Q8 < %xl& -~Bh=F"2\],ӱ@re(lF*ŊY7ٍ` pS?%i|ˋt|[b<7M=7snѪw24ׅd/bD~[)g43G&/pN%;t :p }wM/{ Ϭ0.bj!Z@< zyl)" KUmoҙ2c})z:<ۄF oŃGLyT7;$^>,Y.Fܔ%Gj,&U&S0Sg\+h8.!ɧ?4}+dC֡;GľZ#AeqE>RL K@$|DW/PN^Е3*0KƷ)}JMg"$58_gCs2C7,K՞?λ)效4 1#oIXcP~1 a^46Ӕ)jOa a ^oy^&9ߗǫ%<mLLN9y a)U)D.?9f4R2X w#_RzZu)q{ 3hSߛPDŒx)8%֗Q]9 rf!:wn; @AK ?gNq48)ďT cݨRSK:k4S};3<ʵ< SU^΋opf"5@A bq]W*VOMt,Sg__]0-GXz+G|f_r]EGaqۜgm ]Mnv(D/LbdR;G??aJVTy^ۭgm~`Z2Ј|{AJcQR qnd(ۜyoD`TJCHzRaPהxƜC@Mp<[0?e;ZT+R[kgϧa"q^b *r|::VNBOUzHbaGDH$6$4tLJb -INIC֜qa.K,ƭ >Cy -l7'mf &o1:i҅u meNπ@1; BB}Z(P3>f`mwyج]}L0qoJ 4VCBBLx1s_(\2ZZ. -G?eu8 3p8Dq,ƾ&[3M st/ϪT ;C;]DDu0 դQ[=zʥP*KCUqk#?k )M GRWI "RY7Wư0+@γTNT?aJxy~8up| ?5$[)sNd<#UM(8 bEQHt.f6֡U ǟ*xϟOiא`r/\coωS:#D=@KA2 gLHmO٘b9PoǕ -ڄOiI8RUSy2+n!%_Ǐ&X݈*zjA3?U*}b.y=-^ Kc5fJŞGQ"zZ -6>ur+lW>ntq/˖. hں̲ G C -@?TW\3'1xZNK;Ɨn!A\2r/L۪*Q$s2ӊ;hJy}E-M=>A9Js3BK=h-[c<ݟ H^t|ݺf?Dѯ2V{D# '26:G GRğ\*A_SFE8JټTص y_][wC|$+[۱dY׳ e -KL'2Ҙgk\DDyk?* <3dީ&Яnb#x_{)u n!Jq?~_w#v.59X -2*ey Td\露܂14үE-Xj+AgjJbF0`ُjJdD=!\}9mbsV.(7=Ƣ"{q}>*S\o|z#-HZޱb+Pk3M h2b4e:eqle~y+i*M`,Ȯ[Ǒ@''.MWV2ߒBPEmjPoخI䢺^ҏ'=w^$,sE)m&(YE>LvYΠXك!%8l9Dcǰס(릪bă+;٘1tLJ#'Ⳟdg~_l&N<(;F?17Zq?{S:\,H\G}/8oDE`yYj(0\Wδty%שAKWREfFtB,+ 9_x\Q`ٮU'3Qw3MJa}$šr0,7#Bk"o @#Mxh&w!,()WD|.no<2|`9mޚ(!ވ'PO#F_H,m5rL<|,3 I* -kRy  !S}*aL>J-{6t"Ka qjז3M0*NK|BD6tњ[};}{C)GG֎Ms -b&--c(:rHTZC&i)Vh7?%‘нRX;7Y.R>Q;٪ u+:SB'))߆qy] ί- : '3톢z! RMZgaYDž"_aoS^V"'\B>3_]UBuaNM)ۺ SaSw -`K$2F^@va1$C -j7uaO]^|Zozf Yo'3vꤒ[K䪰Zq 0&AQ^6HUƓ;a-Fr!ޟA=Ow*9`őa?WWnF#'X:1;dT4DrEO(zՁi +d8:<oAc$l}IP=No! BĹl'k_{n.2=&v58%qvf(cri\ +7;T3tj ]O >9>i)94oVg㢚bGNՔ"ՎDP>4kN 8MˤkD.8\0Ehgy\NW~&k:TEZ0Wݟ,Hߕe -]ߝm<7:3~"@ &hZ{~;/G=nS %-ۄ\[o@m}W̓gO<0-$ G~>ګnDj1F9(x^"3YI9=aH Cik)"4A(gg['o45@!r5- 4y;-"5`G&&厂%75vk3XvOi r]v{=1,xUhnr;d=#ugFP$} m,;̨ ZFn?vK(JV!WƊ4L90g3"|u=Ag>t OL&Ém1d WV y6)U'NÄУ,Lg4{4p*YύM?& uU\ϖf%Jie* -l`D3Jߙ݊1ܿ?=E JG@ņ<#Ψ|sfȄ(j[Nѐ'9Flu}hǀH+rԵSOy{~ӱtm]Fl^][,f]M3X#?p4~2} X{nNHFICʔnqT?"$7^Dr YP{3+lOD 2[7P{e:>VfIJe#19A̾6#˞4~Z{eU>+U`0}h:#G/nuҸ Gګ_ٌ?-W -{cq rjL"fPq;EL)! -x8rD*fѼvXA\>(T\I$=J|Nz+2V1T﯀H64xRt?q_<edބ3F`R=XsdHln-GbtZ.VlcU< xDaYdM䵮}gݏ\o[wk[j?WqqCSUREE4!B*N Jp$T43d4M/?Q w]{/:e{c -Ewf^/cP(0<Cf fy|&S!l8wHWl$ -DĞ/g;f" 9ӟ@9 &Uz{L`v@s91k$[?mf Km%5Xzxc_XmW&mʲuO,y"&D7fg!gA=a LeIȟ!Rk;ԝ}Ol_5d;4Ϣp:k?q8&qF^w Ʌv2oWK4<`pCOLEt=xSJ%ˢ13VOðY  8dOηYտpK2Xke?qv+sW3꠱ce)ƷWލEXχ+^HWؤs$ԇt\pk}o>D{0krd‘]~lɩ} $ʶjuȯiM,/1Fb?MqCCe=ͬ_^*XL+F@ 1̅ʭ Ӵa򊒚 +O2ET xݞj]4tnXaSRlNd˓v46|GT -(Tcqur-} v zjԧKyPErģw)"uoikWiΰt3"Dz̡P[%?3-RԦEgzC dn!K#doD ObJj?o](n @ZcĂĤfKЏi}-g64OQHD^7z r&l9sklk`ehܑq@&-HqNUĶ3eqx'+˚Ǫ㏶`~ꃛ L̰e^ߒAIM؈*K_"/ШlIHG4 d*@ -DrU3i1[tOuea-FTSM=&02cRɲ5VT6,Mx@m^ ɠٶ}URZ(03eN@qLj^~&+PǼOEݸHB8(UaL6G=rq>RV(5pOCn&0.buEt%E{g|)!%IxldEp[4B q3RRhO -6+|@0[d&ԉ4;PB!V+ּ=ـr wa)*:.Zӏ:?+qk3'͉-#7O~`REPNenȅKX[ -wj -rJ7nPoJZܫ'8vwV>w: ->EFttaybZǞ/7⿹Zǖ /?>$a'+mm򰵼X Ѣ+BҔcVE ZwHۼjy7)n05ϙ̐ -z,8}^.*$hS7.Z?38) _{}  &{hwX6*Z]>+)D#7Wz,IO,V&n:Ǻz~F3Gkӎ%ᔬXc A=xط}ʲ3=!} t|3ÐPdwhTeS_$РēhS}8FBm'9vdjNYJdu*g)x3&okW=;D@Zgv{c`3c5`F!'`%,/\148R=S*g5Ÿ| ݸXjLyme*&N~0 -P+?k1_( .El=M0Ί*=0g(@F-ovw䖿oM6abw;w~8n&!8&{@߼iS҉!L\boxbZ1v -zr ÆO.UBA" -^y\ &gJi$`E:68#ڢ8 ?W)d5žm$ hjﳝ'z0Z5/ltSAѳ\sN]4kyfJ%qi+wMps1/>%\׀@Kg;wߗyk~W9U]L~Lj4+% VD=}yD f+ہ* w)aHXvǷex+8cIp` %Ax7$^۹1EMNx4SףOw;Ń8{Kpv<M0,=Th -m43ƬL;n0Eio%nw14|*$6G-FBV.vc₟ -DgXf"82E -'dF*X9=[%w72^OPS]"=t:a0ȸ'm,ǟ}d `^z]0Gǯ`g2OυOp]zY -zx'YW? ui6,D7H87wݳ$3uO #ir)X݀wPPp7g -`lt.Iuۉ?5[?3wvw2r0 [4]-mUYq]kXX؊=GvipaYaBU~8XXX"sݸv7=lV 0H^C8m^ybr;8^؉(je^ds褘j ---puӬ2x#'*o}l)UInMEH @N3JaRd~˷5 !ǩa m>(saf<aS }tWPv1-wvϞ ӿV>O?N{" 1 }_hƧQ |Y>!gs\8`pp9?s}(CiFO 4x9CQf@%ЅxM,`cyy6mԈVɭUnl <,k:cgXg)lgKcv{a[jV\@^ AF6!=v#9TvUg. 8{9s/ 4x#BzzΡV$S._BJ3BMMIJN8p03Laݑ7ab/A(Ф#PW/f?Ԓ,}M/~RD -D R&OF>Jx6e ^ɗZt}ohХ{7袡mw J?>Gge2}^gj$[.éh'@)or- `lE?z=Y|ְ7Hs=jKIf=aC23;2#VfSߑ,cEQ -!̍+'[iC.I~7I_|oEұ[" Ssfi5CNj+;!]P!h9Xw]e,7u.&w`Dž.t..⧝$:tE$v;F\8ˌP(/\鯁*%Z4BFDP3.\BttՂ~y1'I1Zj}7eN&xћS=i !kui#;h`2eDM|??q[ED5۷pcp -vLɽ ;ӛ`i2.K9RSiݮS5KL -nmC˸-?-hF!e2EF}B wN$%%*틂ե -S81 -пTsJhy1uOGL܌n﮻>&2ɭ3M:Bd= >?vFhTy\0i;ѿ]/EU=Ƅ݉)+oLI1"_t8X_]bڽ/ʱT˦c$hLs 㲫HISniTY}$gOB~\"1LH@̮r(7.ȁyhFrtp"i۷Y)F4E4SRaoJ1-z+#p7GBeughqz^}<&(`p_K"sTz\--ŞZ;R38JHj2J7{]z)&J Z|PE>Ɣ.`e=S] ǬJ O\'73xx[xrۧXim@(v`x"Sb3W,d1}$0ݨ#~^aO,uf6&m: T8߆YZ8̥DqV\_Z+f8vr~n2/G~ )c:_mUE}(Z[ xUǯa6 -gHt,Kt>"NLo@huq) s> -stream -%!PS-AdobeFont-1.0: CMBX12 003.002 -%%Title: CMBX12 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMBX12. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMBX12 known{/CMBX12 findfont dup/UniqueID known{dup -/UniqueID get 5000769 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /VZSPNB+CMBX12 def -/FontBBox {-53 -251 1139 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMBX12.) readonly def -/FullName (CMBX12) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end 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 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 -currentdict end -currentfile eexec -oc;jAw-=%W)-{ru)rAE(@{빴Q|_R -ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ -}3{Z2zݬT2s$Z&{BJ{Jf^ַ>aq4!<_CцcQ%BlS71_ -sQzԜr?ktP2Òl(?69~'@2bt[{ax 7}Gn[TY>T#a1h!;`WƮk>Kj̱JzNc?^<@ qTud[eюj:JnK#2S[ŝBb?̬Mo7aa'gP:δѩ҈ dBd|IH^wMe#DD13W.J.6׮r(N #>Zjhɵ+Uw -$\WN.C(V\N¸3A?l_sMP yfSyֿb`9upPȐNur)L=uhՂD١Pԋ^} --zU*3~HwzQ:.cxv(P}F>48zeU+Jk <>,H~^U>~~)9G-_+ԇ2miΝ1r>Z?ώ8PZm#meDPњ69v=hE_X(yN(9d5p7LZC~ld1:/ g!, -}Q+93V{ QlG 7!;yq+ JA vj/rڜZP)4f+OpX_t~ 5[RZ$ҹ=#e@K*WEt_-J bΣZdh>xNpsGLOh>o련J;J+\m -J6km9"N `D[ h6w{Ac<=ޮv}PC*|sAחfK+1!Sn~#_*]\i!Jiq˘mJ K fy*S}iGV6wa$mv<zZQ^L0NRq!*7uLO=b~_J CI?<5 T zs}uL`M؀"7K 8yO {|v`).D3K$ ,3sÝDRT c2쑃%yD\MS9HQ՝rfG^\55#v[Yϴ)KS^~nMX,8&7a d$ݕ ^t/WyϿ4QK{)=WDd>oeZpٕi-e@PLb|#p"6KLPXzbZc})%LKfO2ݮ (NԴU-eru RyTkl>'H 9т-)u -u+ld4zcLsTJ[:v?WNM* NiLffF/? ̔o_a! Bt]z\ޔR/r4MFwe5']ZPp׶r?PaL'- -c3G}T'ڡn#^>Ҡ'-ހFwMOTDsJQ{ T޾2VNsҎ%Bh$,>oK"Hϯ 2BU7'J(Ǜc1PIݐ.lQjF%jP -1zb2ɮWM+mKf,"/3~į;7/7=o-R%nJB@n6A0hRF9T {(&$߅:hMj %FVڈGv?`S::JepR̶9y?O_4:╱bEV]1Vb,"KoF0dba̟f4G^̬k({: -]-eJbc?hs+΢_sS,atyir%F3gދ&M}ۨ3Dkh`\rud>;iA_ -oF_љckNԋn`v)2ۙ$# 6{⮶\FvUW l -%x[gj6~C "^klCy%)%nWFO/My~ZqiI$CT*x])it4ZV]m剁VO)gi -%-JUƠ[fTX7/.cU,h78M4 z9:̳jmrvP# >bx_Løğ y5R@/{fQC}d~r!4ѐfPo퀿M+^',6_/W{h/њjS}Jz sնj ޳~zL{qA\Rh$):zNSJLyj^Ĕǒ)T~KZAP0JP~(>~9&åv^")X5=hN҂aNز%1v1gv?467H!NjO4پb夹tFy&{wQ[+ZJq -+@ mn,jMnEfI m RGUY8šNK:]ĤB!N?J'A.k{c㣆+/lB~z- NWWcr酉?V,d\$;tTR%M8DLsY{D#4 D{a\j;$ndʟ'KE 'p a_C1daEE4"<[ɬ}77%غk/2Ik'wblZqq@`C,6|U[2ǩ{{_W{l[(Eㅐ&K!.0t)f7lnMwX< | w2#:|м6ޡ4Hkr~IEmvb,[xY@rL'3:`A7C~X+_显R#GAVt]Dd ! 0*uzbrYN%gUX&h͈6OW2^zG iNΫyf_S">.g`B6G -BdXXE}텅eW_llQ6ioF<3ԙZN%Q^w݃{&E:k= BI| -~ڛfKikx zm 3ٳ~mk -R-rHsډZ嬪.]]Mmјrx{%u_p[ -5~`31>pajdoT&]J[[@ǿ&#F8i ^9<we+-lBdv>B2p["jaƯesk40?`oёL^e OagJQIs[lyZ&CXO3¼UjtYVmE!ؓ jyfn(Rv64꾙o^vXrG\PidDFO"pMx -zM"t@-:C.R<L?l)Ld*v9l$٨{K4u;Mv=gE)]"[w 3URzןI$TuD!Zu*׭XeDx`:uV3)5Sw&unL 4d@6lWk:zkP\صyE*(YE"$]?{oNCdѓ ᒦ^V8 r#sfi鳖N{N?a$zQ>3>Ė18ЊwFBKZpRcG 4')Try mQL򕥶d4erz#nD:HۚFZG.]ï|\S`s]C' iOԫL/mX -~I[;24D# :r} OM@4\g{%oƙ\DNz h:VqUkw)iȀ ߭,vI] V4f̐)1 e.s9Zt/=k-+C%hv!c\)yǶ@WN(+4P5a%~+M@W}%Bn0;Tȧqs,~QN NziD,.|>_"Xߑӛ;BKL!X, FYnQ5xJcIj0؝ Lo\$qn{|ehy7 !=~f|^){,gM49R.s:Am, y8Oq3V:nзK5.d:Bn8rƵgZ&m-:? -5HvIMrpȗ\E뢆t^6=gSO R~ _}>S"uȦΎup\/orc`8L{ o0~%ԃKrqޛ+ -!X rlb$Z?@[OzBMLx0ijqkG-5J\񳪮ftcȾlSP``#K_G mvW6^0Gy5lBo~Pu_4<̆1xvȶa66hlF:,6L$ -cK𳔁%Ցξ!W|y^@2ZTs*H2b3&#e{kp#BY$DZQ^%9Ac8xLs ؘE}/s$UѰGKt#4LjW Jv";D-k)B NG;f-g'sﲶ<%{a7x ahmI-yl[ՇCrJ6XӁ nV ޭ#9L^$hbWq2%w^֋֢\$&"/q(5Wn&^R3 -&rGuq8{V Rd><:EM]w$5O!ȔnjO)қφ:{Q*O[vu)> cϹi `Xd8)b,V-!0~8Q y"2%hT\ Q[?ζ-p =yrs84Fp}J!>z߹I#>XrU߂V2f -AπLDX#eC֠%|\_ac8WɺRAB$M+jʃhp*iώso!X2Id% ç}݃g𒍗§xE2{4 ;N@~HT1s'tJ9;ߛy%U/%|\~h,NI -ޠ5wR.M{jZf4`4]p}5ɊgdŝĿTB -4T+8Odډ/p'qR.ՐD-s3<- niүV|gL/6oZ2f_DnNSR׫VJi~*b+C͎G䕤gyj-нL icȨlz_'#fe95B㤝]WՓ~G$7"2CHtz+#TY+R8ft^1EvMp@AY_sIEؚ[GtZؑ?uȅ ]Dv;gbucrTn Nuҥϱꓚ٤J-ڀ6ZthqšNhAxt{u>9\@^ -I-qҚkaorٗ' pdI&zlޓ+w:)ve K}RQ&`^<_!ˉxO-* nWu l't䯻WRVGT~X 6D`=(OV@Kp -QcQ-FEH{RFO TɤIl? -&x9j?&:6?7z1[D)A0/h&p$Y -:)/ [[ۘTB:dXQeGӞRTxIq5 r2rוGcMEOd'Dc3[ԝ\U꤭sP`>=*MaNN"^@WH6SNZ% 6R{|5Y?U M]ptZ ~ݟt_c*T3#pXk$IlnAEco=nO$hhqff!wF!c6H ʏ5%ڳx)4'1_a탐sn  -0'p̧<\|A}Ww]C*fC5pn`=k!ÿj9AyCv~PX.FVnZ@@ŔoUAc6$E,D,k5GD ,gH@ҏzl0A;s O@C:|1+a6x}HT.ѯ`ٲ (W%\_~? ='xwWXk#r/Ee*j|JaxC7mT3V#~4ҌGrD]@v֙Qtfģ ~:tA 56?Dt-J*ñ3'kq@Y~"? - *<XD53*Ʒ -|a^Z3Xr7޵ =ߐ뱳P/*^x}G|]izaU)ujiNİ-~INJ0V 3؁񅆁Oy˜>;nj` T4h8Ȩ'XZw3N$ MeJXpz6gICW@r8Nj׵Z6q@DޚQc=ۗQ~(`6%g{rFCd#DsUgmn7n1N$_I~f'<}' 𐓏[CXE(9v9ufTLx?N䃨GE8M/i>R?.3w0Tp|&:}#6@j=< *i3i9Ra;`%ܨv2j) -֎_`sjkA:PSSk&>YyijX\NEی##ܥsFH, M]Qشj`Vl zeS%,W{@.lbڽ}9}e.ţ;}ؙ_(eDwje63*Ag =U%h~,a1#> rYu՘aL^:!{ Km9:TK3nY8(]2iA'= -$M#t?@ek(QJuUIe*3ϸ*Q{|j^ǯSG']2gx0lI򯶚寁.6e\`~&F/lYX`paܔ~sFui_&UO9˵njd -+V>^ W/0S0>ElGQ0? _`Yk=a3)qk̩vp2X8M|NS{g:(x-\3w!R ~:t@mA$Jش^2G-!uJfz[3D̸08&kx<,V,۳k"FݓlY"ng C:&Xm~mEh2t3t @jTh. sUrSH+]R>7,@Jͬ/Ż,`aQqܔ͖am´zjej'dK+GH+ b} /Mi m:M] YѰj\--Q$6EE7TZwGo?I()reϽ_^@:ыI!?+yj3:&k$ؠt'elwL̤RrI69lS4 qʔ[(7۝!6?ƇkG @'hRKZ(@w?iGr/hƨPDF5Mk1cHOza`au:~:Vn*a1Q߾j`jMNb塦 .Խh̠ItX,hv7gI{IG-{-JJ(KXE+q^^T~$#"jvɍUc:}Ub"nz}Cۺݵ\0R1qO/ -4^Ęw>:/D8YQ…YٖM7BBZAO*XlA5DzL]EbS`2ȣ*g.[0hn} v[0 b]3ajr~`hS!Qw"FOM2VmdSgoϧoDsM9d*1j{(i7Uݒm*pRb䪡Aex>{},Hcɷ2HGɎ{@rIr.Ǹwϖ>LM#ck?)RRkTprw22%4?ǥV ؤ@v^abJmY[?ydRY &O~GuP/r)݋hm UF,Xq(؉g3u1t"( r3Lc9Cc&kbfD&E q_zb0~lg2nqJd|΁)0+e5)(Rfb)INRhZ0y);RS --=\wc<gA@:=[ߖ $b.Nx qJfGuveݫK֢oGvt=0&L'WL FfRr^D_Ccn'HDACQƐ&* iQGm<;Ld5Ez_fwq$C~t4@۽gERcڞ2k߁'t^@ I:|;4) **ʿ,^\r}^LDIگqAB )VK9Id+lI_9b]g-,bŽ2Xq"K;R&tVi6#Ùko1ng1,US]| b>x1F,@U|T \2OɹpfŴ<fvWSX:e0p#">`6PpY - 'V#,hM{v#Qt(Ҕ6R 'ÜŝC4P.zdة|?i N1}jK(Xhb -QE%ޙT@_ǻa>.kF e,BݰAJ z{xvW=8xxաΆ0S%}2~Z>7(*៉L:[ :$uG-Cpi -1cʗSeG&.F$4 Y) PIJ/K( y"DaQr8HT*51tt Y[fAj7?ŨX{`ڝ9f,oyY^X_J:b#9mJ `!Ɣka[u qC薰֤s>줒K4ИF[ۣBId;]C3_@.t6PajlGe`׃eguON%na *ָfF X]U@*V`W^#Rk`@-Gh -4]uϴ*#G31cѣt5pt0bYTƲ(Q */u>aDnO - zdQ|nzB:uŠ3/gr4ʞo?DW鏕7e +32M4h+֮4mvF[lH!pyy W J,uboVq:?)Nd"N9ܡ:#*ocSvP4<y`Se}gN8`hּ7hqoH\m.SE1ݠ Y %Ww⏁2eɸXNYNCN=_kSdT &>{&М~#Gq5v/5q>y*x5JAOTCQ0x.%wWlMm L&  -endstream -endobj -520 0 obj -<< -/Length1 2086 -/Length2 14482 -/Length3 0 -/Length 16568 ->> -stream -%!PS-AdobeFont-1.0: CMCSC10 003.002 -%%Title: CMCSC10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMCSC10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMCSC10 known{/CMCSC10 findfont dup/UniqueID known{dup -/UniqueID get 5087402 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /WARYBH+CMCSC10 def -/FontBBox {14 -250 1077 750 }readonly def -/PaintType 0 def -/FontInfo 10 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMCSC10.) readonly def -/FullName (CMCSC10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -/ascent 750 def -end 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 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 -currentdict end -currentfile eexec -oc;jAw-<X2-Τ^tE_SKF1F^jNBq{y4-Fgbԓ{"WB:rP ?dgS%|'ؓw&F7JNL9VRtbT5'm\N"K< -wJv$tE;D4Vܢv{bG@dŪ,|e( *VV:\?)Eeߘʴa.zbQ*%EJhFZy,٬dw8w:GI z:X4(nAN;H0hAoi.a)8Ma4@-ߦ~)zavгjFFw]:LE_;ǡͩc<(Vz5?<{STd#׍ZaЩkcZJj14S/cYt1db,0 j4ڕ؆Cy-%XWN2wQRyCOEbMv_c[dxt #; 8@ϋE ·z"T]ptX_+kK+sےWǖIMWXR觼*;R taW`4b_ԿP/`|v4e4UVh8R'|e$E&)% H2N]pGֺm}#{t$ zء=[|;!Ψa-D3 Vz޼ڈL4ؽ~旤(L(:k"HPw5WvX !I66w/lgj a+U:4_EC;V|ǤdjBՖֻdK[=f 'YuW,`6L -P:'jM]?gzj һM/NQ)d>|tUUnXaIuyt|Qߍ?]!H&kOpl(@NNgt3[<ѹ dI>эr%T!ɋ$f2quwuR*e6`* NmByfv.u+"| ?.X"l'~]/r]]/p `дp`J+"}*֗H4% Vb$wփR -CrUhU<[iI0@m*8_f/3M -*Lc6Ľ}nղ$SEUK _oц" -_!ЏXAcǪ݉9q8͂kEB,JclQ UcsCE:)iAH Rp$_C-GqBaB/")G bߌ. >'9-΋7Ξ_0='@e^ndKMN<._PeSM3ƶo9Z12CO+;Af_@b}Tb'N>,Q -w_3lS)]>?k, /;ٴu[ /FXJ4r+k {b% _C!wn"^+7mxG2Qo -:!SfJfYv㙥a("`\ﷆI,3SU|TkSYjbG>a^pb8= ng&ZD ꏱ y~iOĨG Hqv1࣎K"&]äs͎g4MEo8AX]D2bөA$L[K/c+w -z׍!i]"^!)٘ذ2EsoGr6>$_ʹ2/@] h 疁lg0boSQH>HHI0X/i!`_PL1슒O>e$+)_WzѓV,zdcUN3RZSx@4Q#s{,؍>dKasO w`5{e u!o4}qhJ_90Ypvfte9-ha0y 9-\,Ӈ@H.چN&,gb:NA,BQx!t>"Z *қ#upuNBk.8=NDТ9goU׭gmaŁo Cnge!klHt.澳GtJ+6$CNa@q"FN\gݴ/i@r/ߩb?UXn뽏, -@TMRwseh׸k>"IH.^I+HgS}ޅxY+[vEyD)%l 䑤^CI+~d/{ҾU ]W1QP(C"Q5n״Lm`&aئj ɛ\}ixsU;bT N5ٖ+ʩ{>M|cF+B|S%do 5*"svmNi5q -moϝjv"|L! 7Z2扶RTVU";%?q -d?cqIBNElC<6nn0 TJĨF,}TAqA޳Q5G6c]BzBb95r\>/LPB%SUh|^(dJ/:@iκN[6G/;22VH4g؊c>(uR$e:3v})/pkѤr<ą"kLs[I@ye;t . .eR3H5IB]E.La - ==a+r]{u&9[< 6[87 M2=\f݀7\ބ pw8StAR_ 2 -YQqJϪ@8B$`A|) G:T]S{F -x6@yơd{ "뷬*Va{T&Y1UA,R'TXcZv x5 -{a#B2OL>67pU2#;;\=W/b&<} .'DQ^0v^)0ؓIlڱ3ÌB"xտbZQαY7\ʭNFP{u{gw .o`fp>xٝ$jV!Q %,`=q<(1>lߠ\a("`8Xh lv}C{ ΞPaZ芪)|<ϖ/I{6AkmjCQR:!Y 3|14X`4 x`"Tݘ&K,LQ E!uz+07YKRmz#UdXa`/[#T,ZHhZОM[OxY{BfCvܳTdYl 3'Ǥ+ggCi[lv֩;;1lzs5~5"z)qPOXLl; =nwId⬇@Ô^QjNG\|g\]#QgJ]]G6O.=%ѮҠ65לIpn'$:bm½Ӊꇩw~ :ƶדd#~lFt<ŢԘ}ww_i*hƢc)\*G0@_~\1;k0;f(d* rvݺnAcÌd S2n-0U@$BLi- W˙ܖֱߧc1_يxm̦(k&rHp-"Ύb2mFt~4p3Vvi (f\$:&|Yzo00YA.GA9k+YFo>]l-~ _8C5"KUDȧԣDv6WV -— vy9~عRnA>x^ƻ: mW@"И(v1)g~#K 7kh%wj9rD rN:ÄDpSVNAuKe%Cg %Ce&v z84E#z^vEՈ0,jLPK̘񠳾unq)}M̎_|P!̹2-:N8=[0(LN8ġ53ũA;MQ9D|?ˆ)0#5s!j JpUЇfU\U=zDb!r --hP)x>53"3.D5!Nt?4Ww؉Ԧi Z,/Rd>Ŵᣘfztۥ' W5`':sEMĀsƔa'*WD:r~ l,~:@$E[kó V 5 핤>Ò'.#90̹HGft%lqDT]zE Q)ύ -;3ZXIĮub4KPtʇY["0;›J>ge-sZQ4I.+V* 'l[vPFL̑V!Њ.9})A -$aXh:'hPFO}"YπcEB]SZXJǥʩ$dIvWS*qI i<:&?<}\@rZ=+[<3뺽J:SJ\UV3Ҭ1@L]Ȃd2t&#,O_p5̖iPp ͒Ĕ*AʝrWv?ky+?coJ9| ɸ#˕vw;pItMHj箐-C9O|֕R)U)ȏvwL'W@/ -eת޷R:-U&Pխ :ÿn^y7/;=8"Vn^(0c5x-fO-)b`s~T?%_b@S4ap%-m#H@iw-(8 -B'׆X:쯿5婄?o\/yT5e~sGP~:dn<Ǩ* x,1&s=—RF㫝Wj9iW2m]7g{5,H9V#u[DdrO7+^??Hu{c9!klY4w0$1 ӑ%vU:%t1%6Zm$Ra8lk.~~yS$g}7CpSz뱤Ps$4a>[@Ą4$İ"ٔ]In8MrL, ëS/X]t16!CH֞7_ӗ^4c5[T&*vX!)&Um>f1DSɡtrD y RCvNU%3V2*+zn[߁+QG - -՘zM|.K=e`~+Gb?` "&{1[DshO@k~#R].UIn-?ʬCnAbrYG7˨%ekja-?3gB78VyT.|}*{wmX%}ψ!h0Žw2J'tgyҌtn%)/6^pF '1{  #5B$%¦6gv)۲Rf_ud^d_@v =BPID3Tأ;QP${(eu C  -e~OfIID]` Zv`MbJlDj[<='t 6:uSys4bFX2Ϭ#߻uX#\Yޤ1YXfXƏ ljˇoޘ^:L ~{,W)Cd3y؈+^ՒA?ڮT'hY3ncr'ˡe~~`Nq -0à>tؾ}25 lm{j|QfGFg3f94fN_/$LE쇀4 ')x=ڻBER͛[BgP屧pfDQs"RG.?- r=^ Xf](cjΒDf&pt`fp/JxvĽa4T,ݸ+=96,#-df3rp[(#p D--FUY?7IM-@St*av~,K'/m@PG`vAj6a%.u}Hq`ٜ]L_ -hc"} տ``W_ǿv_aE)28L!`=G/{eˉI6*U]VN;Y)H7⻨l5-[ oE_,=?٦޸^dh|@aR2Y9SfvS60J7( -n XEȚj2Aq)|ZR!^&~xTΈU/CO {XOlDiV*w1I罌Qp`(g$:DGWK"dr/R#)9Wo8N,EߢEgY40_] :`u)z=:6)ċ-zV4ڀ1;[^5ѕLq/ڶ!DfW!oj#ß2<gOemNV1NAM#˟ŪAs5 ׌J8sLd;g7cRcxh͈v^^tC}Ǻfb+[ 4;|c7`VAj"~dz{ڕA U8߷{5˜ -/UÈsBǸ~jZ 9&"䪩[M{6kV!n1=_]jRÐ}ƽQa.],9{ȿQ[k ?DC~f[t`Vm)AP0;<|VaFe4:B> H`'nI 8[#bG; -KHv|aZ&IU-UYJ&~FX^vz.8iCrX}b0FݦH)/A<ީjE9&ܶƈBrܸƷO:*qMpCAϤ-sZy^vMSL.Fg׎R$\ʪ>ߜaF6*}0-'2aN3zRac m?~ 0"7]%F(qY# -mnoY^sg7%1`4jEPr6pfo_TwV1>ʱB1Q%\ӞXǭߐ=7rRgp[tSQikEmKOai6 c7ӹc9qi8ʗ=;;)ZOwnNCV:Z4JTWv0R&n g#~"@ nxc)aSc+Ee10'"((Uَ2GWm$dQoZ׷eSk0~ͷ V$ێ=NVMg9ccd~]1#ٝC5z_dSKcQܔ -!u 2)t J\.)1ݢL\e6<;`B{+qGЏ.H&%"TyRVZZsC)%Wg*I]G=!w_0a:9 'J6ɘA%SF9?yp>yF9Qt+*m U,w5"hmK,iyxOx\үqAKtTTΜqY"+0shuX';DS+H\mz;Ci-d.H337rW$n}IO: CE4@0z|&Ub^YC Cz^* n ~rYwX귿͌.5;8+pڡK̓/,mԜigΖ4@FBcdChTts'SFj\}qj l K׊u8~_E|^}%`]ب.7uka'Ov%9/YjX2K\.Q&~a}qٴJ8/M]Ǣ(z$#AiNjuTwQ ɷnc3n]{Yk3c.bqlng u4.y+v>ynB;6֤[ @>Gj;K*=RT[s-<(NhW-3t`H]3_bU{)yJ}ˣ08joŮ(+uۡ)U '|܎w( 漄5uo>pfπ֨QG"Ҋ.S fKG:P).tH/냱S#\N̨}0*,6+^iM/l^mRE:λ{llݗKF m[|0/d>k,Ǭ F?}K_ɀ5-isGA2i*9o}b_Q fz3w+yY!GU TE0n]ڜGx)-0F*rT]3UHƌtבs맟\'H2f!@Yy&u==s -HJNK_psSv%B_p/%$1r#v@B`"(CPcDJI^P*ܕQ"<k cY}32x'mn9UU>D: VX:%+-RVpVȉ݇sE]~+9=/Qss~:o2TEy;h&fx3?+8q?k -ќt4Obė ao :Y@wdSI&-BGI&@=LJz -f歕0' H p޻D -ܫUxqD蕸Kp$y-~^q><E!,GZ 'i-7RoaDí84Ma?957YDXNX6ns߱j()K/M8raa"IVVO9Asy>DTXaÃng;*NQϢ5=uUsQ.l*!(Pīl~%G H.4JvZłX@wNc=pJ ;> HHl\b V>ӏ/ dm~()oo|\GPb֮ǽs>|? :-uv=Cw-zgH\%v(TX <8qiWy^O'U !gޢؐ&7gδlM\p.e.YSA<S>iNИ ,Z~gyS!WW#!: <8 zi+ڇ߂q<ױ'q LҒ&̑hȁA%o'W<<ָ.O&XfQoK *o վ"Sغ-so ,*xE+EU^[4Ka -2}&[$f *Ґ ѭV`Ag#K(Y_>Z_\f^S ojtPUރγiEPCswNSz܇$K4 )P#z1xTZR \?0 IQEi<ׂ2Yqv;@ҁ.'PQG= / -hNP`z< a'q U+~. :5,ߘ$LF2kLLSwVetũk/s1ߧ~,J=j8JpIajo.[r,YN@:m*C8#5f8ʯl rQgcC,N T[!Њ}뫀DUwwSu3rH vT +66 a,v{,/TbyEC& ֣toq)A5RR1DucݣXF:-t[řLgڦ4'ϼՋ*YdhY4"לoci/Af3TŒos?Ɯmv1,J\R=pV082K5]MZD&b I"%oST l%9:R%^%<ÙyH@Εe'sͩ%_T6j<+'pa4-}mQ-Rk)&pN>Rw6?V Ⱥ*/Eg޷xJ=d -?]<ˇʡsYCG@U#iCZ<4ʾaE'&1_ʫ+ | *xY˱3KDyf%=-\3V`.̢,(ob6e -0TF p=s@KJd >-g7Qٳ(f昂* ->/NC*J4\\?3՟,?p2VJʝSW} |b,1}b-^/gɤ)uF4sHu#8{ļ,z٪\J÷ .4?ao *gA*#^+YwWyF(T[yvP -Qc$Q lϩgoj#͡!ȃJ0Cw{&'H4D -f-R'"SGCed|ȇ5K 1, Vҡ6@h({ 5˟ޝ -endstream -endobj -522 0 obj -<< -/Length1 1565 -/Length2 7176 -/Length3 0 -/Length 8741 ->> -stream -%!PS-AdobeFont-1.0: CMEX10 003.002 -%%Title: CMEX10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMEX10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMEX10 known{/CMEX10 findfont dup/UniqueID known{dup -/UniqueID get 5092766 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /QZSJAN+CMEX10 def -/FontBBox {-24 -2960 1454 772 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMEX10.) readonly def -/FullName (CMEX10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end 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 80 /summationtext put -readonly def -currentdict end -currentfile eexec -oc;jAw-=%W)-{ru)rAE(@{빴Q|_R -ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ -}3{Z2zݬT2s$Z&{BJ{ޣ!fpG?[Ttku'5O P 1[.BBBo0 VoG;wCMdK&\YT{#v m E57G~ߡ +3[ť73ŝ:&uN]B Je v(7JIFO/kZ)Ckz*7Xuvw نg&֋U+DWAԳPx;%]r@G~fJ48{vFM"~wvԇ1I mJXk k51D[Wopl^(;w\FIzHy$$r ./xj83>z>9Nќv-v)TTD*IL}qbx>u}&:=l]o:Eiۧ[A^ [/ER;R;"6(ũK?C!>;gh) Ga 9nQ<@(<|+)}Pˇ2&dqmc#IhFeI-S n|{cfyv40]vO?݋ZωN#I'\9wÅPp`i(2NzfAʑ[?}7N)-t)^EI(^ܒM[ ҽTf[z{ rC2YcCŤŬfvnTgTBg^fOW 3Kgiuؓe>Nוq1S.֢+0ȉ<]vmZ =WVhY&R{!2ܼ'Nr6ɱbk_ک'@13{MKݐ__GaTAbʊ0ZB{䤡 d2J> 7RK7׏T;Ȱ+[4B*q4~;7D 5W?S&3[L^'{P)V̴~B,10Z]TC2e;=@7n6 -|,E+ʻ%_B κ7() xK6qQl: `qyi_O7MK!5(sfgHQ1N9!;8 @ߙ:Ϭ&-(D00fkC[x'=xWH i~ -swOVꮈiJL%{yݘF": -1[[ nse]-D.ct&_C$I]Dؘƫ'DGSQ$ҀpՄ6<~"Dg՞1o/+8>YX+갭҅:fXM(~t~xc+`Hcv"+!gl;%kι #v" %MA6ֆN{%]D`;>I뼳g!CSiØofglu:o3yUݢ\a;'f@ᛙv⬊Zj NB].yiW3 5{$";Y]`!i1{Zn|VS,v6.am$|%>)TCk"3o@*RU,6<#44`xDo:Et{M6#:]wޞCA'j]=K4EA=:MOa+VX[b,ma*69Z]ʤ|`?tvFwr2)/-Ov5@y9 ]#x~{! ˣz{TD]7d{WtMpiځ(+\, pZ]8âwcl_E΀G#ӱ¶ꭚ=]Y7*rQ !WQӄrgdM9n*P b3Bxe @1RhOj\Bycwzj eH? U~pE.kIc4g<BZ\B5hrEd^wŠim ;2 "? -]`_Z 8P\w)9%9dS6X?}+LYJ^y@1 (h{Uem,F/d"H7?j V}2 -l -Olb(FY8G߱4. eS]<b@{ɤA.S f>oLơ6/翔OHeAᤇ#:j -7 6Y^Rvr?NVIz1x^PA~KutS`ZGR`Tg3H4'eKR `܁k+j|7oHNPqJg4{"NJ.Go[yv.IS+9jULd+fu˥~mQfsGMb)RY2>y2d=Ue8@*<*?!.y]PhNЫ1qrYgMR/ -_X仾ru'Apue+`Y>q WXG6dZ e T_j^-'[nnyOZ:O?U3z;Fra}/_ -D'o!OQ'ʱL@ .!Ux~eRj=U=ΥDqKߒ&u9qD<: Lb.3c%x]׉; aRy Z:Սl^nz!/rUզ4)hOMMd 14/Xsa0"A묵erᶒlBNr8ݰY~ry9h?chٞ!c -Y猅Oc}q5\(y!^(L 153jvzh9鷔7ZCY即O:,!UC$*h[G%4O#+y6">RR-:#XL%YDd,[FTꠤgXcб:o9LJ\{h%v9'tUBQŕ&Fpԥ,8W뗶FF-QEWDEz5s#.TD1R0݊:$}+r*WޮUb\]Evs|?LkoOiFx(8z1d8w .b"%K^i59C|]J4ptjŊÑCȇ -ĭGe/" # @!aMbE0U?\ bYӽImʗ.`x+2qZ:j㱦tWMK;8ƦA s&q\oqVjQ %i3k$n'=E#* -WVV IPQ8>i 4bm miʾ.P`W0'20vwl.]elЂ!Yz"FkR͙,`k%Iuban\Rڇud :t?YS/WXlO]{j -f_p|=ZO(+`H -5 ~7dh֫]V1Ԅ2D(W[/tG -W ( zK֍3Z!>LWaF;w0cA܂LcEa; *DG5HX&sw*;s(#PBپ hoOt%J u.:ۃ &essE3a̕*Pv*k]5D6?x3{%ЯEiVjӨPNx[ ЩnP1#WvA8޿6dzLtGb5Pw,.#gF:4:uBV@aO2zn! `pgTwaG7= bzsФY@}0{9B6$ʗԧЋ>n4=#|h~ޕ4R_= 5igCwi$ܵc/ 7hJ0) 4W7ERAtp&k{c b7G}G+l7mT"O^.ҩ˞32t;Qʤz&3Bxove}y=h$7ZnuؚMtMoaVcs\ -hpcbw͎$e0Y\}>&ܾ&(E @ar>;Fc,^wH0ؽ{|J - s,|lI˺$XzWdԻ~H%Ky},r Cɇ\ Կ}^Hi%;*VG;gc.w *l2G?6\jdvL yBgC]:~>0P2`7G"86bWNDM$h_*q(Ӟ `41*+4S!Slp}BQ+0M}mC+tj7}y`pp,ү6?RƘ--Dqw.yR>2O  lɭQȹGRZP#,A);V&y>D՚6.Nqr(M hm`J*)breSM$5[aS!m'l}ϏDA OE8>Mn|etfh=u?q")S>cFFltܭ$Y݌݆wIh\c'eH)麭vIe7*K7l:"9aUQ~7xE2Y `!VS.9tjIۿa"6 : .h&'m?'_[vDgH%o12SXY+0sD! (kWu)Đ%^ђ퍓|/!IP5+B#*M~)ayE{~ay>2jk[#z C†qZK2%Nn" -0IBj`%ϸ2Hεx١W@iIr l,yxh'&ʾFI!lÊskvJP4Ty -}z:ȵT_zd,e9t3-o, -xfK71/e  -endstream -endobj -524 0 obj -<< -/Length1 1960 -/Length2 13492 -/Length3 0 -/Length 15452 ->> -stream -%!PS-AdobeFont-1.0: CMMI10 003.002 -%%Title: CMMI10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMMI10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup -/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /SQUASS+CMMI10 def -/FontBBox {-32 -250 1048 750 }readonly def -/PaintType 0 def -/FontInfo 10 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI10.) readonly def -/FullName (CMMI10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -/ascent 750 def -end 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 -currentdict end -currentfile eexec -oc;jAw-<X2-Τ^tE_SKF1F^jNBq{y4-Fgbԓ{"WB:rP ?dgS%|'ؓw&F7JNL9VRtbT5'm\N"K< -wJv$tE;D4Vܢv{bG@dū)Nh]!(7h`f1zpBrd۞>sVÙiHޭkJKyuKI[Ƅ(,M=}%vf'E+)}f$l(W2[8hT>9X33 viU/Y{z4B&qnz|1/ɴcCzwm|x]Lmo}zm5o: 꿊."ĈdNo3 -vz N -pzP;Vҿg6Ǣ >,>OJ4mA0R3ֹ*{+9iuMO@h}-( Qȃ钏A)ӱ =.93g=[_bo_BVƂW"䶝aoZFsO)%d2wNH>D}۝Y1jZg1bJa|`hb)wYc[&0jX7yg -hS&}p-f^ a_ -l4zVnR_e@*z|Wi.9)ǙBSs3Ϗk,^bz˹a ˅4_B1+W2poDx>fH[]TEjRȊ~/+  l8zXܒpH!V܁d!;d4T5:,v#cK*;+zXz k Qw>aqb61IK&?e=f?ToRw: -e -/ y}tX"7qtf}є)8SRXyԍ/Cmo0%}pd{h4>^wD@eQdaidY^@?p i3;BŹAe "Kc_ - ->To=*y#p$Ua5Q2Z3:wXEk!XLǑU MlTHnyeUsAܜo3|] ]zN&GU1@./9;IFz$U/Klf6xq y -w}HH/*%bkYyoxжjxS\y)n?VJ+ka[zffI*[f=M3)%qO(\-Z!J -H)rQQ5TbL}/>5k=QwO75#:,U_LP?NCSMi > 3*j#WÝD8$|!F̊L;_ -dQJI$Y(mRqJ[~f9,6_1~w S,?1? Ayl(LtU m@*T9EWOg-ږHpaH"\z/EjV{11̃TVL5yWK|z|ڶtjBdV=z3TJ~[3`vpnrU MVW.Y-t虘鰭2z񑄥 -Kxq3å_t|W%0=E@.2^r:(H>ePݳ;ס}mW-MAzs`sb}s@_s/FOE«lh\G`ba8$(^U3qC"vj?Aӷ5.s:];H2?lcP!e-t1//ǑbK @3\SN:8'gU?)Rb%o>6 ~) O -Xw5/"|k(e$/JG 0Mo#hpT%-R(>* Ҩ25h|I.5u`QPւ)`QQǶ(45^ބM߯o5G*`?RFM Àgpfn51dK[L -yq B$@'6!W -ΐEI6,IT$yهHpiVch]l&ߡF:O$#Ȋ!D:%)aMx"_L?d*:02]7x(4p P8*.v5sb<]LQ0*K+@>e.-oӏCƀl\~R+$voDgya|n)>1_|hvD5"Pt#'徹.GESJW˕̪N AZr!o"XF-)$^Y|i RA5=OgCna8z*2e6]Ԃpc'S\I |,qnL %HTz88Wqs.op ^nCz\M@ς+<.(]wvڐ($hyB[٣'&k~Q 7ۣ%R*>t[ a\ -^{*yi|rdI'8 v#8sP67 is5ajABl нaxQB)߄<2\eg8kvƥa83m!f-ނÑp -WlV&! Uȡ 1vi)ܜ˨W}PZ>,1M4D|x`}~Rs51VÒjNUA0W$@~>k!BxϿE*XQo?X}ˠz$͍zƻ+WƾH ڋAF1|\3PGݡ<Хf))oU#PZn/{}Ӳqs豰5-=>_-R'/3loۺHuY'i?ǩ^+ kHfǴLϔ7~ -`'+,D3>W%|w22Nj$DoG֝"A'1`-OAؖgcSN"&m԰- -?]㓾A ]h97idzKI$݊`H/n(ܱm]:HrLI -^8hAvߖ`Xj ͱ3inWij#=xŅ:ʶǾ2_  8!գS~b/(|Stl/-ǘp6Vs -~[EUJz?Ug/ .y]&ʧr,NwfJ(z^GT)owb}m)~z7Aw=A -.@ -gpb(lӫMJ%xA1 Y#hP UЇ!L;(H\_#7,Z.y?v?I_U6t *{*fqiNՋ ߉man5PMD*Q^jWHj¢/M>NeKТBOd5TulufqkALiF~J8aR S -/\סFLwL8#@%߶Xm#D¶ރOh$s&0Y\j㕗+\Pɡj|PoʭJic?+z=0"ALewZ|6?ZhF;. */2l6|`㣒K:E@kxj+ڱuU 6Ezv޻#$m!fx0, -H1eHcFm:,W= Dl~Wa6uAɢk6BA濓?;<#$rZh8U 4'A<#Z'*]8jŵXvo~y)xּI2"<ٝoSu3l{EFтF5bZ[q$D Вz}B枰.8G1;62V^+%"9,Aw)* Y9&PTk:aPHG t ]>Lя:j*ދ7i:o>8Lyg8=M8UI;,*x/BEE+dRQÆ>н5E[,ʁu EF- 04eoM7CtI&U ҉c^jP)'ZуF4'Z)G^myAg_NU?M5TsvCL!gQBB,*Ć@E %;snٜƿܼ=5eax&RFNykB;TM TS2/PمkOZA䫾fTMhTiFsN'sB"\\=-ciO^BTMW假]I S̞|Xʹ ix56i?hr{ mFd㖩d2 {iuE^Pvb.Ct6?{Yv%swVv;A脏Aڋxr{}bU)at99_ 2veq/2WK`R${@qx慙hE i[!<ӯ1Wr_ڷ %A(*s;Wd -ZYݚbIew"^X p?I, -M/tA[o2J m}ƢSM1|r%z2⌌CBx#B LU! @0A -_Nrb fT^O?j^~ 6EZt7浿|dj-slY`93xVrrۅ$IiQTHj-nt(d dʏ.)8f)ӟC`vlʩ}b_k_`c &v%PDi*K\J@`y4nZH9,=Tj|$1 cjCFU)e;^AƑ8ȥAJo| -}mEp3x%++$Iolu-d̊+ %܁~qw3ua>2m<+9@Z/h B\n SpwAF[sܢQ8Q\l?ĕcd1"W2Ϣ {ULY ~ZA3ٗBؔ`Y G>Pܭ%A RɐaHDC`>N_…` v,\f$k1zT(L(6#"W.6#4G3<ϐyZ߲zyq1MW`^=$J֓,U0@Iؠ7|n۱tpA78W, VB=\#{xxpT$bgjD;P,uI؞VdXaWm wO 9tޚMY32ޚ<ɘɽXFˣW@Ck9%VjK>Y>g?xY}u)I1%-jsEj3m[. Jh%h*$9(!o:F xo=|d] -"~TT]8Xh|c+EQjO`?F;CGդD< ã=`m ifdj5avTr[i%3 0<[Ba"OޮGͭjoӟʕQ }ɯ!?:o|4EmzjAa l.Uзjfx~4PH=I:岴噜ӵw]+ 25{qs*KҢu9#K/ h}"8^pOZL#4ؽ*SzED2*En6xܭǴe7K7L3͒<3Swb%*t@9 AI`c](jqH Mq'+8?tՂIVZXu6l?yQ?N^hCJqAL$ :R{l^X7/= 7P&ëC{WYO i5 * A˺a;.[ۆKw1[]D?U,y ץYYI>A!7䩰*x2'NiM^&]"ZyT O ~-/r!6Ȭ sUt>XxӐLڈ@8%hJžh&-|m+`@uҹ? }[^[X CÒ5޹\т xڊU?/,_P-~E}+ -8X*-P]"WM_eϵ^Wj>/ySy\OhHdܭOTy1R*^&麅yo7a}e|Z` iplezV߽low!(BAXxVԛk'[PڑGд3 a-E!N[jm{&ֱY5A.%Uj}MD@1DŽda';=cG \㶗:U3}^4xaetEzfL6(pr2S ԩ`A L?Ҳ țkJP;_-Vr>﷠#w]k^{i0wڮ'#d~PA1]J"%3Mfw+|ٺn!0Ҋ~Et);p\SM3:> rqlQ\JV[[SFYqy -hJ7h'/T(*G$i^f^|JYJ״Kc8ِUԽO+ gz7h=' B~:;c?-l!$i2Be!Q{Oj1}*a[m]#CAPaf~l[?}rpq#W `l$` G֟_Zd8)('Zu}H黒f#)r Hk4]lxGy[K .} sq:0*Oxd2Nev] -:M";3hQ/+9U'@6 UTVHM[E I~`v+znXPi8%8yOC\ß f^%43xs\G'*uxt΋FvY&F5y>@4dowxBF-BFO=BMChN՚:ׯh9"V鏩<1ۭ{UW):8WZwNg^`/t!ܦl.]y͑R8p׌XS^P>k49V$Qܲ @.{>/7dNEs}v 8N_ -' <́:*52+@`TS ۣ* T5 [, eVi P#2Gf^vrI-*_?Rc}vu"GM1|/F/7+ePјkihaY-=r&ިď_ibLNjK082t~d1׿}q1$)&lo<WVϷ!S4O}ףBc9)؞NE7H$4jT1,rnc -;, vݾsјE!']/4ݹj?b\R^:YIN.H)C6Sg)" D{ykzk]1ה"r^ |Bƕ <u -endstream -endobj -526 0 obj -<< -/Length1 1417 -/Length2 6489 -/Length3 0 -/Length 7906 ->> -stream -%!PS-AdobeFont-1.0: CMMI6 003.002 -%%Title: CMMI6 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMMI6. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMMI6 known{/CMMI6 findfont dup/UniqueID known{dup -/UniqueID get 5087381 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /OFGSEC+CMMI6 def -/FontBBox {11 -250 1241 750 }readonly def -/PaintType 0 def -/FontInfo 10 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI6.) readonly def -/FullName (CMMI6) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -/ascent 750 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 67 /C put -dup 14 /delta put -dup 105 /i put -readonly def -currentdict end -currentfile eexec -oc;jAw-<X2-Τ^tE_SKF1F^jNBq{y4-Fgbԓ{"WB:rP ?dgS%|'ؓw&F7JNL9VRtbT5'm\N"K< -wJv$tE;D4Vܢv{bGCSM!R -C\#Xjh -ho35ƒ8"g{dWLtj昆G )l5 Ě46gfPQDL:J -)T,ЧqVfHeUܪGʖ#8܋.T,Ps,! tMq}K6ktwa9[~>Nlylj\̬HLcƻՐ0?o%>Luc2uUkK0ݳx ߙzΪ 0aw5Joϛ$_֙WMZh%G@L~/G2ɜdg5Nunm0! `N1=_^k9F $2@wkdDMeyc ҈&dӘ&XY6 -ߎ&L5%hEj4#U*'dɻgh#V\3m[qN<60!2>~f[-[؛Qwkps9CLFSĺqSæ#rg{#fbԧ~XDI%:`mrM/IjoƼʩyLmIе/XH2Ӽ&!)[e-~Vҳ$?$o#VCgSOGhQ|R7uu Dq-x<STmP6I+֏HS&Ab.֒#Fa6K>GS i*ıhڽy,RgdӒT;ջA{].IW"b:fXME>N_9/!O)"M nJ;89,Z ڼ ADDt'I>cI,ʃ⨄{O~WCA#BU+4B\ǡU-\^R> [֚WˑJ1͑pVycǞCz/?d-4zu$LG,<+U%5Sm}<‡O r) 'WeqؘdxN6KfG #Me~Y BkYʬ k?kwr֋Ȯj"6KFi%?=,`H -xe)TθLHe;ѽAō 4jUk{pEa';0 7qekJMg/7Cecc}$Fxd_‘d+'πa{CMx){#QÐ}qvz!܉#;$"AW+tFg9ks/NmB`)T|e9c&bW{U%UpC bGz/\~ -.vÞ@NU=x$xihE ܪ 7 мyhXåp2[ӽk~Y* McBrVϞ#x?Z>,dyA| -tW dCiعGATń}_Colim3_SҢnc]S!:LF({gPpΞd>)Us(ђW1i.x 9oqklɒK4 ͯA e6e=uzJ(bxo@L Бey -D2d-Q'>9.v!7᱈*y&{׷W9yM<8%c$ Zо:zknp6VS;c|v>])^QA|ڛhF -G,\_j6,[t`b^S9|B &umô'+-5j'TgMhDžd -QR#RI,FX'F; -6fgly;I?ȉMst.c+735Izp)ܕ7bh[ F+'Y]QU6gܶbRG}e \A 1b1i ̔vKA{gfuč[nj}cݰ6R?ZkU቙_{[ʬ\:>MZ -v˜AFG U+9[ic%YttŐ駗E?[JwNypߊo"R5`j=&Vfu0kecY+Lejڧr΂LFE`V!+O*TbҢBVGgtY's`- AZLD]4[6zRP|8h)u` i6TBzQV u~_Hv/´p%ڿOT[F\ vI5%vÛ+c5)SoK38xWo»7˜֜:Y>7G].m2Af}eGf|;~(XH_-!H-72m9B#1 -F\E6jMKZ"#K=EABO3rOZ>Fv4fwBgڤACNN4}1;hG;ʶδAqzg~. c+ڑҖ<`!IÛn.שDTFHR,Z;4n,@A2(ԁ!L \Ogma ]xX5qMAݹS 3/a\W@ - -,}4T>sDD[wzjeI.O ,35uiX=8ϻ]DZ06{Y-$=}鮾wT!2|<5x? [/[^ə)ðoޯ*ujᵙT Q=1Tw8jB5ŇduKwMޯ?h`|nIYN7v4%?k$Di3'K+ϖ-0T7"G %!~Flf Ұxh5>N rJ$@#GGF/QȒhYp y$ZjM3P3(A4`Q -{_pW'ݤz-؉:3"dϩj ?(){ iM$|]>T-<"=NN" {[;2\> -stream -%!PS-AdobeFont-1.0: CMMI7 003.002 -%%Title: CMMI7 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMMI7. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMMI7 known{/CMMI7 findfont dup/UniqueID known{dup -/UniqueID get 5087382 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /CFAIUE+CMMI7 def -/FontBBox {-1 -250 1171 750 }readonly def -/PaintType 0 def -/FontInfo 10 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI7.) readonly def -/FullName (CMMI7) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -/ascent 750 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 84 /T put -dup 101 /e put -dup 108 /l put -dup 110 /n put -dup 118 /v put -readonly def -currentdict end -currentfile eexec -oc;jAw-<X2-Τ^tE_SKF1F^jNBq{y4-Fgbԓ{"WB:rP ?dgS%|'ؓw&F7JNL9VRtbT5'm\N"K< -wJv$tE;D4Vܢv{bGBH)[)Wmu;€jA݄6p`QJ3@H0lī U=Sn1: zU2!ʯ -̹6&X!d[~gݰgZTd?}*BkӨ%>Cc-AMMغ8_/99PR lf-d] ߭EU_~f*j ~`(ks@(YH詵{>sب9ϗQ'%¤^ ϩ'qT LB%iWl;,ƤL&[͓LY!L.Ee_CrcI"#5pl$#WŮV*^-ZHh]Md&wfoZ_xOGoV%i8z`<džS{(j.KRY#u㔦nR֔LexW2N ܸm {Y2rpFSf (5b4;2}$ -Cq^`Vx_-܂ߗp\ڥf6kEW1xnnXǣj?cB۬᠘4Nw7t4-xOK|.JH%͙6.jHi>lg&w|5CW)6v}42B>Ũq%~AO.bB!dMýKK!R\-9;Q -wL%jΓ~c0Z#bprg3jN'<;Tē-XtF! -? ˢ[2}+-P L9FfVݎ44 X)+g-ٱ*m}(UYđU^> -+JFd%:=gEMuQpVp&7[9qQoIVM2]aď (|f/FrRVv^ |ĩ-pxG?'gzl,γ#ACFYm^ @.sֺ>f!]JCGuQyCWs ð&ITF̀Je&-e$Vk% vl#'6 8 H߾A7]i׈3eYx/yf] ->q^`~'}`3(1~zRjAwua8#tNʰq$ޕSOO@y{1FūÃ)^FK}J.@4z1D3$k,0Ia8pPQrCik]qB~&\PTW\}'5 Cze<(sko9!?xїE[⒞J>&"B Sc׊}5DmDUhK1M)k)P%-/l|tcT _hhk򗇿ܑCl ai&k'0 vYok9&352X8r]61*EXk d`-sW㴑`\ҋ'!Fљf8Bfمܧ()"Q%b@q+^P6Au}P:G(jH*J}a"`R_tźG{M8D*R,%-R_ϢPzQkqM)Vt8 ^ \lKt7#]뢪xNAVDPjtQAT8a BEֹ_cR2vNlFޛU'y|E3YFo`]ps - %zD 6ӬɘZ\{D-pO<Ѻ}KQ&U / ;yezFLy%LgNڝnK#꾫_:G^)S8ȼZ#Ah)<\\&ږSv%KQ' 49$ՍHD0Yyh)(;[;y,EVJO-+i&ltit$ز ,}<[$yǟک+)(xq0K׽tt"/t/Mw -e7+dW~b(6Lj?c_j -]۽Vh=-(_^:`{?BU& 9HqU2-1cdD CR5vKEiV!;qtO%7Wzj~UgYq珎SWXKL2">9$:; `k -E5 FBjl|De: -AkN4NkcOq"8&)I@ -m(=[44qqZu0P_/٧?"u텶;@ 柊"b6(N}dV&i%*%5,.Vofc.; a/p%l *u"Mh6,6ޥQ>jfRTLŧ{sj(橫2%0ł.`o{N)eugB'b!)iPOYL^peBxҴ@y,4#**PY2 ❙ȀygT>$[X{D1t?Kv {׺jޜ"4%{C{gŪPi;TM"_<.HNUFؓψĈ0NL+/lQqX -w^WwQD]~@8~("ZU5K"5DT -iur!lF,j<XQfxC㼕X: %lɻq˸n -꾸a ZSMa8"kgCLԏ -"ϓl#9BMjX3ҭڰnE`Ts[ڟN՗ej.Du 2OQajcSd#o[]"}Ñ:*y0 }D],2OQ^E:MmXS7U&倧6hf@mųue[1.Xg@kQHNVQaTb8MJ}pp++iSSj@9֙\g7ۗJ>>Z aDرԎ@zq2ԗ9{Vk2`-ʳptWYaxpl$P' _f" -Cѭ%= „JqSDqNx|3N  qkUݧUGrʾҺ^PMiVꠢIJ+K!j^3,(8fZXa;ӥc>.HxG "}(”4s[L(|S !|dP7y*QB-KڼMJPvkJ  U=;,[ ,N£ZݛJ$DAy졫iIBx&k"2 -6zb&P[t C>qD{|޺I=D=vux7:,s]k_y..N_B4>0@NLRQMI$n'P0TnYn~T)I/4\ -uwSz zDav\k_|*2m &}&rEAfCALD˰"dn².WOw@RCGt\3:Sٮjt4qߪ+.y:;_ҋe'N>)r^l[F| ;֎dwrE~Xu!7AD |xfX_,@H1RK~DB&^4ypEV}eiZo~_zKlb)~iRʊ&K/ßQnU`i_2XBWzF_a+ES <ŀ)pE(_QѮvib_Wُ!׏"~bf%+U 2}I&π dX(>lAԿ@hx$(0]DXl/p1pmʛ.3[Z: `H!"8::'mߖ?!!P,w Ŏ2%Lct kQ7W΢2XU} 4ڱlcpLzmr`c[.wH 0+IM¾nvۈV Htl%r M,{1\7< KՖRֻe7HĊNõggԊ8fn&T=sAOZn"ZyJlW[pTzBA6mwg -/{0Yb& ]V" -endstream -endobj -530 0 obj -<< -/Length1 1634 -/Length2 9793 -/Length3 0 -/Length 11427 ->> -stream -%!PS-AdobeFont-1.0: CMMI8 003.002 -%%Title: CMMI8 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMMI8. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMMI8 known{/CMMI8 findfont dup/UniqueID known{dup -/UniqueID get 5087383 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /VCFHMD+CMMI8 def -/FontBBox {-24 -250 1110 750 }readonly def -/PaintType 0 def -/FontInfo 10 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI8.) readonly def -/FullName (CMMI8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -/ascent 750 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 67 /C put -dup 69 /E put -dup 72 /H put -dup 76 /L put -dup 79 /O put -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 -dup 109 /m put -dup 110 /n put -dup 114 /r put -dup 115 /s put -readonly def -currentdict end -currentfile eexec -oc;jAw-<X2-Τ^tE_SKF1F^jNBq{y4-Fgbԓ{"WB:rP ?dgS%|'ؓw&F7JNL9VRtbT5'm\N"K< -wJv$tE;D4Vܢv{bGCSM!R -C\#Xjh -ho35ƒ8"g{dNׅs'&X83/`C37Vl"ʀbNeP@KVcR8Dh89pz㠚LF]䘼m[Yմ]Ô _hV`I1J٪*D t U#8,eG- )1C4#9նB~DIb_ 6,=;܋o,NIMj_vVo%hQi 5X<ƪl0L c0+$c:4#3R+h~y3542KmWz.g!jA|v9eqyF[q—lj -)jҙs>l2gјpT@M/{[bK1NW^tD$;Č,,BYQ53}Q7sR |4aĹ=8ש1Y ';l3#pKdo 2{P?kKuU%5@_Ba*{U-ǸG1L5UF0҄>MR 1)dqa,<ׂRBY_1;VW*]X? ?"KZj@Q8'e޻tX<k{s-ZmqqrImqt/9aNgcZFfD|lLYBjg}`㜰h$$TH-'RuVx#>ym֛&xykkxH73_؉յ^0ZS%ݖګ=jx5XWYD!<(eh6hB@2OR(!K*ܯt^";!0* -tG -l8JY| -5K9mYөn F>-?)"ȧ9V*wj gڕoL%Y~ZM : !P!l10{Ft'XꤞKEM8tˈ(Q3kZ ޛ4i_9&yslAʗ3*@xk,@|x/ʖ)Oc*DeE| fGv6\U8"ĝm1a0heAfC+55oNw^k:G \0a# }]xvRf)tsLCs_W@#赡7iOXt&{biҢYnVq̠!X[ow_ "@]J4rSE +,09DWF"C@i[ԗ @~8xtv.fU$ ^x{m`#Z,QRڶ  %Sc0G.;=8sy뿶'Z]AxwZjGOIƆ7,5o߿焘kG~D55o>@]AIm_Ҷ Jo^ɒmφo#6PUA"X꛸/B^(@n$#H褔0㴻fr,d"q+s? n~DL zC ⒎yCEJߢxүJs!(Ԙ>gs]8`;ԭV=ݏhkTJXM*8^zceхE)R !6w3''6"sɾmI`=0c%gxf2(g1Q&#pOvY@HbՈG[$њ\L5ʢ -f/6OyщT9|]O`jٳ1+W'dN(l1BD^]᣼z+L41QUq -GB ܓVA'Sq jv)4Ћ e|iſl`u/ou>_سT)^S-nw}, ZNEC Y Rez3sp$ 2RH?. p#+Ne>PrI%y@n-S4¶{֍Y[OhEi\*BxCЙ#(~#=ϑ X\yQζ5_p&R5‰SJ^ ԷrXu 㝢)Ɣ1,B7GODE k\OȧY@hn:*洊@Q?PEDS\ ؠ䟥CMhQQxMϗDv]錻ҦJ*T#"hiW_5ʙaKT$#. Ɨ Yam=fW#tj&zlIX@t߸ඔ*'>`r/XV(soGRe',q6e: 5lP&7/ -Ex*Y$ݦӢ15\>h#1F̍\`AkS?jH:+S D:]+HT5‹f\V:\g0ﮩ IҲt} -ôoDks>+D85}lS,@\.X:; }# z;d?=rXBPu 2dũģT\c!$rP-z)~·= -(a\/5:T`2Zsf5#戡!*d HE}94~k#G|wfыy懨V1 -+K=ͬbwMBuH2E>yG[ymG-( )wݞbb6o/7ˤ*&lD9*  Xx,D, -=>]D$` gN/6cVHw%3`D5ry" oigĽԕ^zss:&zwߠѰWhsS;-* -/J 9(o0|iOuSRbhbu-bjhCOX&ilH]y.K)ꌟK5oGaŵ#u~sٴ&7*>"1lkK4nCUdS.&҄Cm`L*N-g :Rр.:^1M? .ɺī0v[J4(NדOi]Hן]ޞNDzR4DDXv{^Jۢ"s0JmhQҡ}כ-%*b!Z=~}C+}T)P7[.!F{뤼̭\!bMZaCMq[%Y) CAxȅܳp]Ӧ6UzKdFӓ*=97v>QcnZrb  -,֎l܅l9s8~cfE*ݷY(^i - U t5K3F~ &!s ꁒ.ҥ; Y|YZF`КAWp)ʓU}AkdmdZHThR_1g]:at'wNMO8&}6T*.g,`@,N^'_WAq]M ݖYSpf)6qz18ކ ǺiDs %8\U %y :#+X5d|)Cozd9 ia_wL'.SBZĺJurc>DjC ODȈs0rlGp)F\v| J/奟3п^OQl \dE:Q 1b 4U3׷K]^%QMz 3)jk%+4`4婥[&T[.f4E'wmUc6~꣩M1v̗鋿4,QncJu 9JԕmNgGmoys -8(DX?/1)3}nڄ).y# vluXo x.~~JA%TmsBkN4_Q.ӳ3-mV?rh W(',n7ݬ!/ՔؒߕzM 2P fдZ]fKlZpߟAUYf<} y[ 56JQ@c :C2A?8+!҅-aw[dD12~(:HKU8p bU!oB'6Kқٲ8L_麮TO"JuD`_KVSyxgg-O6 Nܶ Q!\RyW #& 3\r_,HeR@ jMgNːp{b4~cmz 5z달XPqߢ&n* J#Z `A~i=jPZ0S7QD-ٱ x^䐜Wd% H1A$we]6grh&7KZcM_zr IMi_4iK4knkrQ7ф%^%LjiHnNcemؔ<.%KPdgCo :dz_* Љ%O6pO|PjFFq:*ս0'8I7; 4[W]Y|/]S ܁#ZYHIt2n+!V> i\ DzKis[5VN̈́)Y"ŠjfoCw{)l "QzϜM -8}poŝZm cվ &}_x-19ks,ft(m];1 y~U@.4wOoVpi@nhƀMhXq"VW@9 zٻxB F8:\  9~p-2NfQ䗀qh0#M} zZջiebpc!gtfJ3^ G~{߄ z?ƺnwh DgAv)n@D ƃV'h鈖o#tB,Ҭ]VFǪ֡ҸˬA|YQ)Gv_ T:,rYG'S{gֆq3İDt* JmWbC -4\h^y_^P7kICnK"?/NOn4 YHG`TŘ&"t1J .aK.Tq'W .>cOq'(z t %DlDuSEװ {1ԛ;o#aJ hI+;H;Eѝ=nG[;0rd*NzGye7s8# -q?9; D'ؽle,P!ôJ%s(~VkhY3T.~>c:MF=%?:$ؤN*l %p8D$>)HމYuc얗{w -endstream -endobj -532 0 obj -<< -/Length1 2760 -/Length2 23453 -/Length3 0 -/Length 26213 ->> -stream -%!PS-AdobeFont-1.0: CMR10 003.002 -%%Title: CMR10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup -/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /KZBLKD+CMR10 def -/FontBBox {-40 -250 1009 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR10.) readonly def -/FullName (CMR10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end 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 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 98 /b put -dup 91 /bracketleft put -dup 93 /bracketright 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 -readonly def -currentdict end -currentfile eexec -oc;jAw-=%W)-{ru)rAE(@{빴Q|_R -ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ -}3{Z2zݬT2s$Z&{BJ{x< ,-.2iRnñvپ1䠕 '䓱_r"O_t3kefBݼVfj9ҳ Yh뀸{q-ɷ}W??gw1*Eh[:tWeI,v8a<{B100Z85|}Nlw]6Nbh3E`(Eޏ'Q;eԃ/.DyL5$4IG׮Ɋ\yj9.VU5Q!-赁B9dB^oVwBɎT7RsOGA b#TBv!mWT=w,ID%'MK<|]D@2O( ݎ%#_ɷVBST#z!${l\4ĸ ;5l&!〚=(fUwAeB#30>H 'L+֓jz@=s\<=\Y$D?U 6xGQnǫi%֔! -L2[)!fXc<'ȲRP3E!-:'AJ.IJCJJt&{76 -#VH/Fgw"F5wS$|oQ<Η `~<10|;,zɴ% -oߠx0sW1Fx gmxVyѝ"]#z~pv Ũ.rB9$nYCC1td@#8kNԋK;ԓlF( ،N;d*<Ʀs9ZQ@It%[)7&hn Y'a¶T'Xrߙ/n_nJL (@ -К -N{KF^kbn~`L]aU{vLܺ41$rmAsnZ*=sob@{y !CC{c.WZ0n bpgsPd$-\ԛ&L27JBs/g(xQ,t>[8͓GsŸ:R$9]6&my)ivjWLRB^RBalx_Y:5M/j١!}`D&WȪQX$HߧtI .Y@nr_n܁ OtAN-L n?_^_g~Ə;`KB6eĶ ->lQp)/;S' ^:tJj@xE(0G;κQqǔkT'; ÃDHjsrxܖ -.>֯kl;&#<ښe)fFz`Ƿ?Ic@SH&<evn8F\V3aA!yy:+c!xbM։/f}3ߖ˦"G'fMsXWU}Yĵ^ %j!HOH͎_;臲Jv]# -$'Ch?5u-G:zHZ\%Uv z^By%NT⸶3=X?mJ-3iH@ܐfσkR.v'm.'SDly7 YCm^Gu5_G1t/ -41n_D>}p+fg9h$]@M`^ҹGK;5wIrqA3fAYiuYrD:dR At -,)aɺh9[ԧuS9KTKaX$wgɓO[xqǃyI(j5LIc}|h$zDUwY+Z:ϤŜ1le`u@|܈贚^6/y`a [Ί`ҾEwa ziLa}jʰ@}xWns0n*{l?Zz>8p-L&ȣK`> `%`ݿs?v˻^\*QNbf+ۼބo" ٧U zgga䎐uFљ<Xyݸ*g4?X2]4H͢^qLeoU~ 7>)ƤHnA7"{DRj)ע~eVDJ|X}ѧCrTA fP};"ӼK#ΑTF\^ԓ ; |R D\Ă Hu6QИ'Q3b;x#3S:jb%tJ/>ʡOrVށx]>)]l5o[F;,N&'i\NQIH?T:@FN SX0<)hW4fFDh.سT)^S-nw}, ZNEC Y Rez3\ -tY5`F~_xU|'XLJG@U6I \>:V_>զ9*I0}ӵ\"{3UzuFf٤Pߨ)E8Uw)gq:dj#hq so -@ -KG7"|QЇ Zzs|}LմS:fmA3S 2=[dؓJ\ܳc|tj1ƛArѮJv,K| ϕVސ -Q[^9# Tϝ̖\ua2SU;}wѧ ]*z24cL4$2Fw<`7)_ 0IZlf5\t~V= ʼ&3VYvE9c7xX y >}ķeĭ&ne3t &$5A7d˛FѦox-([ pm 'C&No#,HB>7pt[wM~)fIoxָk۷Γ]Q `f'%tYAor?9Ab e4fnJ?R I-.@eubJ80?;ܝ3{~֤i;H_-21នW``; pŎ8<)tr*xvW#xgMY\__) أ%e6ϪZ%l]Eѷ:hL|=X-:3q<ڵ;9"X>8V~}$J_v7v#DJ߄q]2I'MOkC;fJ -fEnh-m=H6ǾT&FT Y<SjO,LςBBw*aThkBGQoseqSSh R[\vQk8~Po+v> -vڥulJ,u";l-Yq_Vo~=gQAEJQݦf i~SdVqX? 0$@䃠MEAf0P_$o!4OɨT:"j 1csϼgJNqsUYK"2݈hL^ MhP.]}qn|R/yUj3ZҊM>(d%.3u66ē99ۙ:Bۉ -֦ƣQ+*Jf}ѪM'f[kR6kkIԈ6 Nl<*IqG콭7SżJY<>XwvOq3kD*niؙ. w 8!}.D|`,;(e ms[/v4]:Xq -k,!ݣKRhZci>ku=^['!߯wSlK3d[to!<, FB<(hG3Jnd8%?;,凿ֱU;4pnoe)u}5YwsTPD -7+FMghN3*s'.o9#G9AOz TH4U4w8aի5zoWzI9=9Gb8$eSZyT nȵY!4l٤Y6=Xk<2F}y.?'V}ߡ,Wo(DYv1̢MaS-| -\02HDQ7M`^Ar9 š &/Wj#\0wM'[]~ZrˇUIcٺ(eQX%l#/s70>I &1M%ET @0Y8cEJ}ljk -ul!x6&Dl_M(_lsGPPv9s_Y 2 -aj.4i臇t!\ ʑ@W^ $'e,LhR;YMnLCC+(ػ|""BZ",1': ϘѸ/Ъ%(o$߹L/`>夐F [>YXBon_e0x "Qꗛѕj LǛ7!"0GZ7.}պZш~ocP] T*NV -C+ (rRy&OYPgh__=;:IbjIN7&u'B]wfd;Es3_KՋTN47(ђmj{@?fU$R6;# ЬK5N`Ip'FD0'!VK _d - *:T0ɾ!vSw4)R`bڵxdNRwl]U#-BTp8E׵9/lP&ryQ@O={):FgC6Ef`F}5. nhD瓃f6ʁv~<yvlk^j;h vDIb7S0mQQTTBB(0dҍ2K#\ey'ڎ2xKa7:9l_b;`>qFUYyxG~+PTC }og?1gjOYEkal(7T"~ An(1P4"fR?Za@S|yopeP'Bf[L8ƒUW1YE6TYj+eo*XnsFǞ]ٵL\LtHRYn89?>R1 -EZoʧ[25"[R`ㅤ5zsV-N7~93)i~/^=ePc N1]PyxY,5~F^>Əw02:] :aFH*YyUģB9|u8uZig#]q3$D;``jsk,"AO7GL̛I:9uY!c3uxzԶ}3Mj/4R#Ѹʐ?&ww )[^ ?IFGM ˷fz?wO4Q0ga aH3ȣ2:iü,}gKg!#+8/PiRVXr{zK74œEx91(6|\}?ȓ,rj~U:"1/3`jk5\f"S('Y?cPhlVB5Jזa r#m;w+D& q\5"X`'1c9jSq3mJi"Jt}x@2<3_jjr@ԊCD9\_zhBsk|FU|AN:/6#zŵ=-(p:n7g*v4fc -nqDVC`

}璵Zʘ,Nۺj-}i51ݷHW͹Ydv" B/<@HqnۤІ$O0MK&ﵚe籧ď_U$0%@b+b5a c<_\j9f>?OXJ`ꏸ5emH=<iP͑W5UBprXҥn SYvvv->r2U\z}_' ?^O0sa|d%V" q7<І}ޛl'iIY.7y7)/ oNw0`ގq|f"zPW<gO56A<w2%7=JޥMIک65vsE]'lp=jW54~= a(j)!yPqi@n+yA#2`65B^u[܀8ydWzU:pA2mYaxj[y7R; "uuDR03ŝ[[:uck~4ADC2epS~ٝ_$CݟEM[x{Rd&AHQTQ}vSky?t"2ė> -a|^:DsѫF400WE'LЋs\냹wruz^$(bHߵh6('œz&SrJf'TǭȈhK=#^M3p'g_`ˁ.1U!q I ^biBEmO 0 D6V-2-8RM"ϲuf#MUAe_S;Ν\Oa4dՆI `d+2{G'r x]SyXNC┝YἸʨ4,`4CJGom@Sc"k4`{`gh-ɽ 5`q&{u+Eܥ "^Y`A{ce '+샢ȵ@4-O Hn"T~HNQ)ÆзK}0]e1>y`QI^O}|x`J J™|2uiNli=pM㠥\WLpjӃMlB*_r~"\\mIeEL~L=_Zs&y"Tٚ1^=:ek*myQGhuū0KT~S= 'hN*,`ύ6ImKV?v2H͕;`eA#K=oa1*XeoS.~6HD'.0]ܪxbA8qqBԧl Gul8E^n2g3" DނSb7@o7a#o-=L,K"#fw?DŽ&$Fm8z< *Vj,Jn|"TDQdz-cOS^<JUWJ,8;CZ rf;$F^PD>H9b7,>#zwP(RBЯ,7~߾'_w|ޙGmsLDbħzRf_Y.aNy6a+a:Wt0cii+H5/` S&F J-z˽'wT 4sz 7jyŹF4m3|7K˕4E_7}gBєHs?*_cr ye={vFL't5F@)hZq1"'9$eJW4%Qf`,'f h`? 13-5S[*`\uGA9L, .㙬5\lRiMNIt + 55P v/#}_wJ3^aU| 'S -ޓV+䯁:!r %8,:wbw9F5ay$j֕~P)UHzK5S}@t$FdB4%Dso, p5u}&vX0(B@,N;~os#Pl UvkB|T޽nk]v%Z ?d:yqCllu4"4ǑlZg3h5`ΣG`}X˧}XAYGz<#=;&=݀}R~-. #.C13PDվF"UƯnm'ɞ⟲\iflM"T -(0-ʱ!1u!( 80M}zoeaKQ)?΍e[cLuY,.n(Mܝ]ͪۡ?Nj-sʸ6V*Sz wn<>iYʬ9Kݝ20幨5LE>0GMCr\z+  R[85xfvqsKl"kQ#+{RX7#K. $A?-ED};g›YHıJdM8Ѐ`81/ JvqVHcJӇgפ [AN5MPľc/%/CLVb~~^1 .0 rL_\3Cw%dy[O+* x$1Ɏ}یQNS|0w8sc#.jH5*q~Y42o> yE1Ӯm"^Rn˹-vP<Ä({rͣoi\vEOڝq -cKavj+?ju6&AFRK,X.g 3<]i "̳H^C!9 +w`OWyNت< "rG [_DÚ@xM@FEm[~yXYs5Q:(TێsgQV"VG~eY/k1Rɴ}<y4!WJq}@_p}~}a/fV]FBm#:N J.Q &*cӾ\ێJW(GqکD9/OsAD촬;MH]lՄ>*P|`c ̜ A=EvNu&|"Yddk@ڒS"|jƕzIJ`=bsD }aT29N3 q\(N&C 6/߯"e67n4.2LrKI axMiNԻD|Orac:pW[ &+w}e蒃Kwͱ{B˽Tga:deŎzA~ic\fI%F#? yFZ+[^#*zX=TYHusv+%=3>wQ&S$7! n|G+D1 ;I ?:qrŸ@2x59W[ PO̮/!z?7b#.2{C8*A2SCl#7nu{TՐOLd<NoQx?Q"=L[ )N#uzM0)Lx@MZ BwN.c4C%H&[a'lIEbQ 0)iz}ĊpLvPT#Ҫ`NA`$(j)vLV8-00 2buX(b[zw >tUB`,/lj}F65ɔr6toņuB'@"Ѭ}ЈU+U[fi Fl3z<]L?aJ}7VuL ?/>nVz!Zq2$JI^|m.nЈ7W[̚~UFߏy'Zl}&|Qu$B8~jq8. -Ymyb5Ld؛G{ -2n ؀ %+:;IM%s[hsԝk8[ f=0"!@v3LuЀi0(sWR1Ey|y=at~B9cd7y|Um j.Suhiƫ{,K*nj2D|.<(r4|mt5qcGHc8VMhFDFwϡaeғq/ -#Z,j`|d矸FϬ_=[#K c;˞?KdL1 -"[W8Q%Q"i"Y8IO:8ҷ(f^il2JMch*d!N(yJA -bkl3-M27˹7;ca?}_#HeA1÷|Fʷ!lWM3ceyI"R}g}|≒`3 -sʄ dQ sTl!{L_glJ}o/tLhQ7K@*9ڰyC0{؝}6]$4Iҹwci<0c8xXaZOܩQ#gu&eS-퐱sNG]B҃kZN;n+EjbBCis!tB'*!:c s.˨/G4% akkp`4"NZcjDyߵ\QdyXڀteA?itun)%SZ_nt.R@ʥ(Ow*LςC:ǞJHxm$!եj -eП 7Y;'o~s҇¤5]9NT@"@wE?nSb~ɄN : .Q 7X -؄>9Kq!Zp4nK!IT4,"{Xyq ݯ Bҥ*Mm- _|!3HqNoJ_=59|l`"ʫ}2sh`^"W"#o_ۿSJJ*aưھ"~;vjjVp{e86Bn$$y,K#9 H%cE)*)^ (Ib'ݵsˤ S@~h1uΨ -E -yћBG/ȢcVZOؽn1Ze6Di{.X@Wc۹ I K!X6,6kxFUs$nۚ*-pŻA|N]*Rxƭ"(B/KkI?.[Gb{$CѫQ̀=mo:ɈS^WeI{nY#J&0>d9Jŧ 15 ->ZnW^n˨m e(UŚjF^~u+x+`:z*O>h$Nvqмq%ޜ>Uy~? b^{wZk($

 =}z_I -偻!(˛SrS;hFDE}ԊDN1sg6uDh.\|HkP]4B~3!9KTZb/W #l71839E$Rm =:z&Lq;x=3@}$<0{5C>.Jz))8T5W7i˘TkaB`8nI$V\{ahP&| C ܱynGd#7\]8/}ǝIԃj $4]J~8C[|I -Lh>#Co& -oˡx&9 :X -4K|.ܜmaf䯓ln7OuoIܕԴjʈl>"i+S;u6e\ĝ};@4O^fh2 r ÁgNcl}s3YX tH#Ε=]'+E O7=929:KucѵپmhP4` -Uqw"+WiЂMkcFhvJq Rt'~КܩHLMI6K`u> -dÛF&PP~[5vJ PC 4F\Є8^^L[(Ԥ}RԚntb(7{iI4e`$诏V[pb1\h҉+sT#.9EIlX@`A+ -꩷3ҟDi8=}3LQ=eQ OAGHW \`={ݾ3(GuFO/&>x=ZM#yf ?,= 76KJGVWj!t=L(sOjЬb넜vq#`snW"QyU9GUзJ+V_umRG~] 'szbl0ܵz|5Ucͨ޺A(G 7-$ S4Q3'3XD .^2Cұ泔UT ͋H4E"Z.4N;A;(+NgL?_Ə1m53&,t=PѹY:/БQp1?u+Q>x!V?&аu5hT8 0-g>2,LƢG~ږtgw9O4U_T%@%8WUT|M --si{BzΜa6>IY_R{ ڧ/kwɭOܱ Ѐr.04BE½ TFXK*Pݚ؁Uؒ;ҷhd+K;ywx2y5ﵰD:#=d -cPcGQīBkܘJ~MЙU1fm}OM&yC/(KU@:o;tkI15n"g$f[۠'ʦU/r=btw#ɽdf'!VK _4,DtfA=gy<'cӼ2k2#U[+=Vx\v`T)*+vQ"_Ϟ}އ6ygr-GŴڕA>F ={FiTV;n wZ&r8g i!k . 7J2"x+ڧ}l!T80+ \cMgg>4x5fddVl2uŃ# FuG19$O&GsNKYջ ݕa'_f0y)ϰΥH@}OyP.V"C(W)y4*߇?]Zt5AMlTB5{F*&Jzis]ރIԿj&ޝ1]:힖]ѰCc1G 5jA V!ؤoC@`Sb_dr#u[ãp̀EFLmO^Һ%c?rvtqMٝԳnj`8|. E/;EiRl{5|;O yjy"$2wlp$|2R@'E~t,R)da +O,|ےTOB -Mh1&==CgNjU{m\]_2{FA??f]B0]#,C~puG#?59U6~pt[bu)Tn1Z,ᄄ7i3a_ݓD5DTj&_PUnr/~;+2!5?SRڶE+!5]^OZ0F : -Ei(3(8V daSl"h7/‹=]33uP, @Zן&6:to 0K@Q&o\!/Cm]7ڭARѠXhg7ʭ1 k){ܕFP.p\ -xسƙ)5A -x2q%fQ5LR~>DYp031ˢm`Dlje/ RLK1:+9'֙ug5r]xSpGVo E|E1JN?k_hVɃa2 14D (+wĮ;j7G)؟eXb-g9q~ 'd̸|t)Jf,J52Z§ؘPa?ZԳծ4R?"֜PpfM\=p:-gWJe XB7R#\*Zpiwc݅(LEao"So -xEqlaZnVv!ȧX݉ kƒ:i%)>:oH^bU{GG0Wy+ѵy$.^O!3$[9$9y"eP4 5"e yl>h8Ͼ$=IIDpj=F -6@2  F_åSW \e`e`b?# Q@LMUi(MF u.N&&=z9BnI'x}-LUj -j;БXVȈ^JCŽhډjE˶_xS]8@]$c*f_'0%P$f\׳B:USFAGv̿ٽRMk=.ySwkMOFdv2b;P5EYs,dk ]>b;i6=l8Xɾ 0y@TqgC\{uMoU>TX7zFA{%nò1N8H`,} -7(.u,K#!ɦo&+՚i0:R]e2 -[݈fZI,hrd¥g ia;[Mtţ}j~tvIUdtsܘ, 8K]>KYye}RE\x-{ C،2+&f>4 ,[!z='meǗ4&;h6С+3`]teNkf$%O7X~Q&#Kl`k7G)7LU9 RGK t,{W_?'@Yp[6E;ۑORaM'}wt$. -endstream -endobj -534 0 obj -<< -/Length1 1947 -/Length2 12428 -/Length3 0 -/Length 14375 ->> -stream -%!PS-AdobeFont-1.0: CMR12 003.002 -%%Title: CMR12 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR12. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup -/UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /ZTRAPY+CMR12 def -/FontBBox {-34 -251 988 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR12.) readonly def -/FullName (CMR12) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end 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 78 /N put -dup 79 /O 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 102 /f put -dup 53 /five 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 118 /v put -dup 119 /w put -dup 121 /y put -dup 48 /zero put -readonly def -currentdict end -currentfile eexec -oc;jAw-=%W)-{ru)rAE(@{빴Q|_R -ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ -}3{Z2zݬT2s$Z&{BJ{r̗m1l(zNRr^&%:(/IߺHm!4JxI7bs,OiOl75R 9z(X*Rhn5&g\c9`EgwT!xIJz҈v*lcoƿsdm^%=谺D +u9#3P _] )w -UA8 HuG:DJ(W;]-0<.gSB NlZOLӡ5^9:K*|F -{É ڇE,q>j0^x떲Q'X酉i ;yZPt>p1SV}:ުad0h{JA)Θ[ U=y5pRU&0'-8tIAx*̣$!gRHS;RVU?!lM٬2gO.T7wϓ)?CߠVb7^kJ;c -N* ٍG|Ucͮߢɨl6h6[ 2ߵПZvUlP|%)VǸm׫=&a -Js_̲y|{R6ĴʗB7jIȘ2a% @74 @4(.= `h'p+xvX}?G3D:^ӟ*&4prx5e^hk@S_̎Cl^^}ڶ-q9@e @|wMrc9P(TkruY@MnuW`%?Q8wG3g; dlo 2 Uu6C֋%YT'Rjo1Mn}L+:O/`@ӟӎ4J -B $YaհH Ag0IQ<;v|<6G@tqX>ɏpI%(Xv7}19lAKڮ6]+l_6'3`k*T (]65R-[(EAJ!3s:e*Aܣ ZEsNьmcЪ..> ˆ>Q&x̹znkCfqW-ٕ6qo*p+.gjlZrht?3:2ty&F!w^9vӐy*'ImtӮ:dN#LaRx!d!R *9SDdkb$Vdž^t4}h5eHNrHI,O6'l -NO#xa OTV-(!JZyX !]z@. 5-DL5_rHqg/r秂gͯP%x d꿖xAcŘʺϡYd(*:od`AMPb-nt]#lg&eb5d*OE 5 UThlv9_)$pC+(M ռPVOptcC`ՠ0IJ85YA('针1J ) =n?Epaq\')_4}KY+d>^cV60EZt,)ie Oӟ5ni8B5*Ƅxn@EDP>e$I^na Y>k#w?p͓t!_1 dr{d ,@]+ضCzn{0RUK,&Ձ\ƭТ1LB#Jp0 XJK7ZLD"afI1?jt'8:/(IGʵ6 <+r xj=9zI!ƶreGNXNpA4Us]b;g-L:/ڮpaؖ:1xǔ`V&EE?c CۗǙ77-`$Mv|&sČ 6X!g#ndχ[w䄁n(dَoo_o2<ݻ  xMI^ -[$dDTZ jķi|O.E9wbSsBz֚ȴ!2g6bcrۑW1A"nX14nKOC-NA=9g5=W^x(xڞEt8}NIDʄ!"]}FET2mRi< r3a0!fS&W{V_ ħ/Wc - 15y8/ V㯧٧򁂝*^F}#? P掸-~m~j𔜒FvV K.\'YƎZ|9&fr7ᶀQ~n- L5Q/[[ORue>G zjP˯,jW灔Rڮu7q jml -3!9ri `u8!5$cUUO;~}ۨd>̖ glUov+"Q%z=$Uu<J6RGʴ̇vm%û]=PC}_2k& ;eG7גI0Qf/ e!S|2F;֐n3:Gj)~kM'AR>CM^}]dLBu(w& GJ*ԾS0|CxoiNK@N@f2ްir7%x478˷턀Ȣ5k~:Dwp";jA `SR\Y.wNCky~uH#(8N7 v/I g;0Mf{ؒF3 SwHnp}D0yafA3?E.RB偗cU|O+U$r=هn5`̕,/^r;5?9>QNGZigp={_ș0H>(˴uWӥz|T̴VIMf*ߣ6c^֟}@_ϷW&)#׀+$ɐ2i_Bzv`]C]c+老ь*M0\omV -,T[a'rھٷ=+.t_,'P)Чr*4Wp$ U{-тB qڠ -a`O|qd3ú$/|MR-` ;6M|şg~Y u[l(oԁglEwք+pdڳXlDXuG b2Me *eiRXx8AEnS\RyEƒjT91Pr]T|u0zWMS=nkčeԍ,AFk/b\vI QDksh>`aP(~j%P> -GWlL?ݑ&hu&A$%9c\P "G(" z+"ڸVH1GڟHxYTҫs-pSCq: -99xec]R{zC?yOS.+T#``" kk2A>&^Rz=f)gjAݓ'xbBPd<^Ҏ,!ávm J!*5ҋ.5(K>++4y@B[Y -`͑!-|RVMr6 d$jwe(%.`. t -`n1h nzeR#nmOنwwOu*NkxcV9Hq82ɤ3՛.S+@&\]bWߡ!Nޥpa0fln -ED pCr:Q=̝W8{mCUط;Qtߪjƚ|YQ4C<ZeoDr%`ʶ@B>:o%1+A%1{$vK* 1u+SpĊ))2"yLo)5 ?=tpB,RbIth*NAoٟ(/'J 2nbqʻoHsTV}1a^/J!F揟b,%uΧ -(8 ɑ_/CVgUu5"J-;ćGAQ*K̻(:r>|حZV8j= VMܤI*6S3B ՚ Ԁ:(3yNӓξS/ d&@ϖ>W4hJ&x ǞtRV{wW=E.GD;юJKFD.;AdPfCOR4!]?.D HR>Tr~?ۿ+|a`d\#dkܨ<^>gvP v&$m`n٢g!;wDAगaDYVcY$c&$A4R 7aOP 2>?nvt2 x4F~þS\BC¦Ts:!GK"~Gf2O=;ǁui? C -BǜL69.*_ -#y~R=E#)Cbg}a\INgTҕ(.fYʥc~`[yJ-4q4;뭬@Dh-65Vg zԛE0_yĹn&N!fPY_&u)W&+I/ D#Km;iݶ<P3g}h,3=;̓+ 38{M7jP?Nw,ux,0^lMgŭõMr"LOg]Ő\.خYzIiE.x kyEb*űx9qMDjS@h5D!yF2b;㢶JuC,>(IFd1@h$)Z?5lPT~}]VS a'N7{tiPB޽Ap{a/U~PWt%qtR0їwZ۳+eqI<Y̭yJ|]^mtD,"Ο?k<B 9T[e؈4i6kh|BNd6dݺw/OY?%l]"/N O>#/KԅQPPEYc_ث0KR}YZrHR='?²=.Eں ͉!1C}*Rvf6Z!7 $ b3jҷW5ںE}#:ڭ+:b!zP!SbZ - fogGc#`6=Rdz9K-q` ˥V$~. T%YtFҲoWK8=dB۴=1(n$^GtF} @-|;yC%Ky_[cVվmfD:q|xXG?n;e:jRs8[wgF1Tů|9{pj.y*Jj̉5k-6,D&xm;n1=a7=:ud9fzevD~e 1CZ86ڎ nh1aN7ܬ(R<\mlTR ݊txܥjT~Xq}_~bTɊD~svS7ci G,(Ū7RどCn9`W||d!4SnXzOdMM%[$A-(*4@聧P!xG(Lze9meaey6%y ҋΜlO"FӢ*35|ONCLN)0Tu \kd(_H!V&]$zFMY+ZcL~/dg0tsW@(Ybs+qS8NQ,SqyhyZO0_eZreu_|7d#5 ox8\QD'mm5q(\5 -1m> TV67=tC u,JGtXY- Jf4Mc}aClz4İWl_=B[[ox<2Ͷ#:lA 5B{%񸉾- -n&]@ -jGf/hmi`.P49! ֈP"~h:aywԉCk;-w'_+##L_ F*xݺ$ulh\ee{s1idwG6r8^7Nd5.ʚcLs񴝃25 ˜xFeL>ܖ9٠ ob2ߴ h1ăU2?QB}6_Lo~Ƽ2 M:u͑Đvu=2GX,tA5=N>F IWw`dZ[lz!⚠w%o4|8Dş o9bZeO='-C-DPXL*a.TdCoˊ)4s`^,1p ~`qx-nAjcM(ag { -ȖI'ij@Gal^ 5D(Y`]`20;a+JwYTf/.ƒ< ifN-PTX ~ϰ{u'4K^9Oeuේ ! -VӉ;#)7!X".Zd</n5}3ݍi&JukR^BpVe&zΪW]"3'm] -5YDӣvWΖ%BfYeu"L,ėipZz -YQN\ jjkr ! cE4P H٥Sa.(}"/?"ti=y8Ƈ9!PLz}/Bt b!2!  I,Ԏ ̃՛}m茩h,eZxz  =*oi+swo?j.56TM8%2~#M^)bքY7wO+XҎpLBDSb֝Ɨ:_Tev$e`JgoRrKx4oVN'5PY'Ӑ1p90)NsЌ7BT{Ejxx?6BCȸ B(l~4rԺΨfY?.gȔ@, D/َ&NF]ŽT@"$kkim[Dؙ1zdu_3vm*H) Θvcq  bpz|DWwR n}*l6 #6#UY2z|Ӱ>\` Kh$̗@YM:;k@GDR>Ah,auKoU8>xvM*'tite'e@2H

 W>K^f̥gn=ܢх¨@It2Țl|Os IN*w.-v??bG%t2Pw\ `T]˼@)Dy^_EO0vxgE u*B1 FQh>3 -`qMz`jac.a$uϺ趍dʳ:~ڜNM,5)'K3)]O?s@D8zD]NF=l!T -~]ᙌ T$:A bx6Ӂ:SUscItA)#r[޼-Rʝ65\YފYSu2tQASŒe4GS -f-ZAМ/]g@( -endstream -endobj -536 0 obj -<< -/Length1 1374 -/Length2 6054 -/Length3 0 -/Length 7428 ->> -stream -%!PS-AdobeFont-1.0: CMR7 003.002 -%%Title: CMR7 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR7. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMR7 known{/CMR7 findfont dup/UniqueID known{dup -/UniqueID get 5000790 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /TQVOAL+CMR7 def -/FontBBox {-27 -250 1122 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR7.) readonly def -/FullName (CMR7) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 49 /one put -dup 43 /plus put -readonly def -currentdict end -currentfile eexec -oc;jAw-=%W)-{ru)rAE(@{빴Q|_R -ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ -}3{Z2zݬT2s$Z&{BJ{ޣ\u3]G~ 7G!/ Q FM~f/m*i("!i -K5> ţ d,J^,]^ -z* +khjOwq k&,_?Ɉc"n?W)Ջ kÖ投`Z/S *?c|Wgoʮbi8hesQiɺ4)FvP Vؐpik`j`EU)oW jBNfPTa_$ uDd3QBZSfyu4 螨x঺N<1Xk7I>%} -'T)~$I%qPI#-MVxkx@޼ۜZJ6h=hAڰ:#obv0e\¡0cPBz{f=d1G'{1@dD~yXrDOZE.ϐ=(%^/2V)(mfR20`މTLm/QL zKMmͥ +^vA -oEGxvXIxAW>xCª5!w^ ĥv(4,-eӻ?/R?Dqeq-xE $ܘ*3oᮘY+0{+N.>ψ'=IJ -f]̇C"spn21 {3=Ej4ZN2 -K~*w?#9; -A)Py 7}^muF2x~m64&G?r\|6L)ew¦ØB+rBc۞3v -!:0{uL -âAj}{q3W^B'(Yhn0WRS?u Zin=ٽڠǘ){s=m\ul^GhN@(s x6bM'*'6?nA{,1{E.RxmN4k(wl30M\Er -pty o> -{a_S -[D.tIEӽ ]fVՓj7Va_a"-{#- -:bO[)HAXE뻔Ug2zOqq" rI~$>s0Y@Ȩ5{I>y炲oCA2=B?"R -g_,~q.E| noϗT6;i?Xb4}teL1~&LdZ}2W.4.^%*D|Z?7W1 * DD?P_toKL'c ߇mS>-#| ;[R1ڢ` -@@onh.VF+w3ݟ)RX#9sz4X"#bwL{cFNj'ƌQԑt2Tn~. |_ߐk(Fm -n8*Y3".g~3SBج!͗s8 +݆ iD7D#oEMP00pn̋E\ٮ+7_ QzRĉ iDoB=|n$2bVÛWRu^]72# -x7SE5OU:?oq W\qPt<hR,v7EbZ5=>Û֜#hSRA>2O?l"q(DOuk4_}Ǟ# `N0N_CB<=gKO1/a!!ԓ(`J˭9.R˨y1jlnL`f~ͪuJjwD19K^W7L(ҿkH8rC/_! 1gg` bu VdoT_E$ LZCbΏ)#ue*<m}}<Z1]7n=6c~#`oM`IGCcIR(f 1?>+YKCZ%s)pxHODRhL⩩? -F,@۷l-%xWuLT7a5 -b=oюca -rPYqf3UeQ6ju! tYL,#Ev8?@<m?ĸӿY7^U0M`X,oz N]CSpbӿ\{2,1ߣT&JRCu& /D#eΓ|}J-ozOYTC]i/ K^QaCi{;ᤩ`; -@WCk2YHG$JԓO>K+ +F. %KWWZ ucQRT1 >r튌;FG֧':ũdXn|I]ͨxq/1siN$bppa5DC$6lg*4/*$Mmd$$0el7aa (w3\\XAȿ4`]|v21) d6.7FkC/1J5deGñqvTߞN|@\%eC_>$X8cB'f{ nQZNr Rn}R1Bz _Мך-Ekjmnk"5j/2~bE9#FmY۩~|NDpTT6Z%H ctjz3\ */09R[Ƣ3/c4֪K^ 3b%B@$Md$8(sPWcY:2N&q4$ -VYvHS Gr +?6>s{&@ Xz #xHH+D%vZ~WO?V33N FӁ9 -[" "rme{3L7gdzR`QK8\ڕf0h <8 y -9\PD^1L1̄\$CFblMQz.Iۯ8fv -%ڞOBTVHY+pJ}S -ɲmpJ3Yas ݟ*SQYLBP_[HWBQgf `~[x/yp -vi >zxup^ľ@#uw<4b,m*}p…N{fE@fNg.`d"ŵr sr45S-U_x`F#忐{[R7{km7oK A 'иo7ՐޛH a7 7> -stream -%!PS-AdobeFont-1.0: CMR8 003.002 -%%Title: CMR8 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR8. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMR8 known{/CMR8 findfont dup/UniqueID known{dup -/UniqueID get 5000791 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /CGCFOU+CMR8 def -/FontBBox {-36 -250 1070 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR8.) readonly def -/FullName (CMR8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end 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 -currentdict end -currentfile eexec -oc;jAw-=%W)-{ru)rAE(@{빴Q|_R -ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ -}3{Z2zݬT2s$Z&{BJ{r̗m1l(zNRr^&%:(/IߺHm!4JxI7bs,OiOl7_gѳs6;P}tx,IvJ3Yʫ] -=~Hrl;H :(xP/PL͍SI'sb~|PpNcOAͧBV")Th^Cx(Ry,s)+Hߋ;m*?>H"%N;8'bGZÕbd ^i$iaesF)l:}3X - Mv%GN,Ҧ/~`Љ"JO238ڐi -]IGcf7Ԁ2ڣ}T  @ &x߳8h -{ga5Lw'~=OLcgPv9F˛z%e|O/bV K ^Ć8ԇ<)M<m;疑}Od1]ZSmPf4Ժ)}MPg2вl1gFޢp V}{<[5iJOY>5XZ$157~Zڕ-UDm?3δ쩄'V+RGpyDHvx{pcL1w¾ FMNg(S ?)?;@ṂBN߬GXDio n PSSXD[kg[tU^?f27#xUým`jck$u:RمiEUա<.^Y&ۆo9s> û -8jzIC%oOn8Rg#;D2(J+|Gk9ڲփey/9+,-b3w9W7} z᣹өUyTpt_24a6s!O #i׌$޳\Apr$w5\plYn1upd[lk!lRv4_x_$V[HZKr\wu%_F ^ =ԝȆCf%-۷R>Qt@2 )~zx6mXFVCEOxJ -jFmh)XɽЇ8{u c*;e?blV|@-jAf9Vb 8Tdj4!VerZvZ,eV҆?0 -ZWGvl~و[5rL}qTvmjCbM:gÇ VOiڪ#|ym-4-, fFxWpsX!6q-M'ŏ"1,sxɵISĜV"^j73EvV(T^K-k?Ӓ.;d{)pBh+4uU *:m;<%s!- -8X+p&4jO^1TpvD^ x$+flx7=1S6>rMz 40] XC 2ƺ_s5uD^'? jeq (ӓQEuf%x(m"B (brqYqu]ΫHgp7:NQAdYQk(|_S/8aV%'ov"U2!kh5Q?)投g&J$,jS]&1Fq**X*ilSfN{qZ '@dnl{"KDŚ 4tTY9X}4heQ l_7@ZUĩ/Ac*A\4;N{45L=!V5. }rKqS*'R=:tF_}OV-F=;*ZGoe -ED,A$ CÚI9:Fω/%`,miSs1M>l搣Z՟_tJqǙJkuBy#+1HLabL 剙 Wb])Qjfnpht;\܌8:,{=JE2[WD{D7ܻ9'Jޞ#11j:n+G,,ls3݂FITHH`v=%.ayKyMBn!Sukyv"5Dz -֧'4Q| &֨ӷRc3k&ӼJ 4m [[h|]5 -9Jȍ -0g_ -wn{QAnGgIH]E oV值4:(\TYs7HAe{Ю?VN,pPTlΟ fg;I?"BDyв LM> -E,4c| -}=xbK2^^WUAV7xQ~e#EJf/5R2 jn@FԚI&d|+.;b^ɺN(S k< q/3?׏ƚ~sďS}V7+v8kܩ!ȿ}x =7Z}ǜ]c!j~?}&bXqiE3xmΏZ6զE7C+:Kꉓ~FdNg1Gκ%ׁۃ1ýwCl檬q1FQf1Ż9\@¼(ň^Eг%( fJz^ ' R 2͏aǃYֆZZgd U9/|VϽT_&$_=1zGGx /"Fo<,*#Yo:a&jCȯťuK`uŽ /uwaEt #l!} j؇'*eRh-.h;hMoجcx(iw N̸u T=6^ V$[f@[sk4kJ@/SOnYJ\"mz{1*JKْ|(nwCָ 4&j_G.Yb[J87*"&!Ν&${G?`lê);&|vMÞ\SSELok.N&@`S9eϋci n "*z(N(`(j>C1*CɚIbtrjcWqt?[Ii56߫AښIJ'{-Al$h;m#Q5dd0u3+CcZы|1B]; T}݁{*!O^5 ;6Iˑm-x@ʏs[2 NCb+i+Ɍnu}jlD=_}ٹ*13?9r5\ʥB24"F#KLE*Bmw c,ɰh,<#fx%+L54yR#Ss+j%rqJH엮`S|'a!7[Z&.BvK94{~ͯ'ElB9 6gŠnS&}FL5r1}X蝻?;HǯPO*E4%_Qy. +1}ށ;\SlKE@%ŤQ"%VD󩉬y!;0j`.(9d !0;/[ċ>#qod]O>=z-)dgWl|nLղ FEHқ\~l'҄u6UeGBnKM̉OeӁV?hoR5y?ݙvĸZ@'+my5@:pqU`y -2~&@ʹNt;=ΰ oY+KۛFtz/zRk]z,l93& ^ y&\ -v+vXuC2I~gs="(pQ"RQSq1x̦,1fɈ[G]x&͕k5E' zFm]mT{ςh1Z(vtO:kТ4oP~Ԣ 豟l;ݳ1`yI@!fLE6<+w/_+XNVLTI?Yuk6rga tq=M=?u4~h7ajGw֖ˣՙb8|7_Aǵ2s>@rk&$n·nٿ`ϼdKDNf60ƀ4#&649߮XGOUSV9'&F#U@VreN)tX{bn̷|C'Ob^Jp$:2}osre 3ꁈ&v -5ϯ8,FtwҒ W?"eoɌ,ei6 ŹpX Sx^ -•{H8guݤ؇󺂏9Wk"[NfXMY=q Z+)2B]\)|pWp=Z:6HbH$`+i4$P0 -O{O+Dak֤TE2gy0nLswmHR2U gj~}h:H`gs4<7(j>]1+ClyD'"U]=sڎ QkҠfxw - q"Ziը[/VOc#r6\Qq~n9@x0'sts?fb)Ϻ3V:3݀U0nĦ(Wi4w;;! -endstream -endobj -540 0 obj -<< -/Length1 1647 -/Length2 7851 -/Length3 0 -/Length 9498 ->> -stream -%!PS-AdobeFont-1.0: CMSY10 003.002 -%%Title: CMSY10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMSY10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup -/UniqueID get 5096651 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /WYYAGH+CMSY10 def -/FontBBox {-29 -960 1116 775 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY10.) readonly def -/FullName (CMSY10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end 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 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 91 /union put -readonly def -currentdict end -currentfile eexec -oc;jAw-ᾉYň5t&נ{hLGqB`d˗Pة|*x\ޖHtEB-gedog7Q`[['W73sZ9 m !tAY!$tY\r[uTIUiBy[Ȝŗ3Kï6zJ!˒Js&B5C"m&`7Ӣƻ3ugNC O~̶uo5=_T/ h,$B%dʘ3l MoYLڶ~3^`12]=l8B6PlpfW< %PIN!ju#,.iXnȼ‡o$ҁXꑷI5V*E6tKo_)RPG;Z@9"V3TTLN Y:Akڬ6̠==80~DQ Q^br/2^KZh`N'Jt4iBYҁ7ޟBU_~\fXAZl_ZƎý'xHbG:"l5CU[aLrf 1[;4p^NpqBD '؅93M&9{ VD 8 aе2n.hf -l?K[$Gp/JzcF8vP3/XO6yAo~]WqDMY4ߧY̢XPEL2_2 oH{ -1x'u|o WNRE홹&lF\LRh1Fb}+l C] (vfo+fM}l?c*ވ"^R]miKOҎ!I ӲR_tW;u@(#t*̧ U{|Q}a3Fl8xtHWA­;!V CVov?³;=>,㧫\"RvRCإQDh -@_,˜kbflAIP^wٚdIHzk(c3xɁSUPIf{KΩs Y/v[L%O@HdjyTõVmqgC9zTC/t~Řo*9rIojUKxj. ,+b1ֲ IlDLQZ3P-no'$F zg!Ј*oj-Nͥͭo8KwQgݍp*1^.֊ LV~m la ]%."`_QipŎs5y.Xͮ)Td1Kk̊jn0zGqaWQ%zJX3tIy0ľ.#[#D#EԂppF*ޘvrOdn7n f9*X:>Ǽ:*Lf͍9&aj;+{0 )AgðK*XKV'zZA) n TÙLJ^Di[:s<ܸ2!U|#5VfUqP}|=G5O|Ps9}* -+gpA,,=|j25Cɂ7 ./Fɹ0tRẊ."we hPempJo@▁_A3QBV~$9Ej= -]? {w_53Fgӿ4BAq41Pf ,Sş6r[v` xG$.} ̔ϾF͙c=f!*˽./wĉR8(@ًz c@N&Imݣ>X!me@lW"VCH8kՑŨj]n3X>Jz?D=Nbn {qbY(>"8*苾ky3o H Dw] d{EʥËw.$Vhtzk$kk$]4cfCW@3plQQ晉b/pTqF8_AnQmK{&z;<տm[i7뜣'*qXTnt<Ռk/?2m)fy#(`%{!Q/0&sxfB+rE[tgOKQ$$=ל?d@3c)]3%*M}H饞;Cdrp1jFcstG'C\p))_)( MM - qv&C3NLZswTPu{sϰP+-UFUP"KΆ+Ye7?0(idL;gk9(YI-l`;`AH:YHb1H{wR^Yњ, -$FԖHDV?pyїP%F=BGKPh~N[I_ꈀCTzf <Ӗ`4|mE1J'$`}R \N2kfaouJ73vKW{M3?׏M]:W;vX;B X.PI;?!T . sU]䮃=X 5rMt>y=*bC~^ tArl'Ŧ\؟L냡P&7ttuGz;Kg4э;u)";SvC~?J/F"6U.0>+KQӄ0"ӫ=sxoJ]ת!w6O.}t5V˩+7Us֩yēTC5GrgU5$&|~G8 Mv(jt Ϣn]]QWOؑm. R[ИoNng IF:?tؐSUOcj2Cm[O7>kWkX' #t'Xd9+E7Nd8{]m/ ׎dvYYwop!EP7F?ojP9"gBP;B^QO3*B 3un$I_Oe` -$`}-9Q/ĥMe?Ұh]b _2<͖+tª[ϜJO@%MI tv\/bMVF05+kI2W9>f} Ķ3tj|" -[LhY)o57k#%H\,x|ssxH͆|;` v%گT[c]e"GUj߫ytvx:udQuZy_Td"b+O]lx'6w6XCDKOf(g@w]fV[~1F^A3v Ovү2v -zT0b#[zyϒ$e1k5dRA`(Ņ@{=yW>>y@U;=H;c{30ü^ծ)ՙ-{OO2R´xQwBgБS"תlbz;Iy\EprkM @@e&3lʉtS%)/pR"2u -Ee5+ٰsZ'bQSlj zvހ~%.Kz\NE,eV2=Mo)-JcV:U2Ѹ>1ȓ"QWOё4*Oz.cjcY&=7Y,A5nIF/?̊ ]as.N/ ,McewW0#]٪3w]2f˨n'_ MuH -OMlC7h ?p|`e(ӛ|*{dgHPNDYLQsRd=҅^\#ZHd; -D+ZQb7QŅP#?8ՓF,(韓v>%U9ͫNDOQkOL?{(-aǣUsљN#^&Ԇ[MJB, VsPeQOB,s%v623}.D|`,;(`tQ)l!Tr+u=[Ҽ4`h-?2D#e+%-tU>kxߣ**؂X?`]!&d)BgzFmwGVÂM\nI{`"S$O05AGXVNIQkι,ymo-D$S8dL-OwQu7@g53vN<6ᒥ)9}'u~~Vf<*ߋ8H/2T8;w؋ZsxVev6q/4w-7kLPCCx#uZ+6# b4R?ڂ$Sm:|ϛ%Ly j#&+I*p`r"O M6ӖlGMuT껵OKlbē -_EGS/,+iơjF<0U[z)dG`NdZ=J;QUN%xg?ŗk -ZQDx/0~o4 \C~qD99pe:\ -N~E}1P߅\msy;*[@k~ #MEh!Ei*X,H%sX QkPtJYl}t@Fh0 bh' @li:WMĝ݁>$Mx)ipn[_Gz:%^ AT$,wdkoM9.} DLRgu]ag{#Zd1[ <^+hk - -~ ȈQNQHܕ4w B2_F)Y?,7OΥ7ne@SdkJFC"_l/V50DTҦW2(\&tZQ<~\8~J(Nc2/Xt0`(ۖ~4Uy1.ج u"XBʫi;kQ)Cd6آޗ| *Gs,ĜJgڤS=WXdenFBaH4+)'L9efD*ԓ!UW6]doz9[;ͯ9>* Cxe/7aA  Wc1 zsl3)n:K w9j)y.n>7V!j+(zrŁ>ܦ&bbV b6r`FR!"H-* -o319(5[ rHJ< &8xs12PIխ.2.[D&)ThGawLdYj+#&uo+?v|2s`(v;-#|LoUXN¥$*q8LozIKT'yΌ= h2*e9%y ai)Ȁ_Xe -_po{Ķ?|nM2isB{ZѽT$P>LEUzӞ.TNIA4힟8 xYsJLD}+2+C~}`⨱c77=k&Y΅IBr_Z4bc#\KAQ 7<9j(t7 -CQ4F@VfUQו ˺8ۑᗡF D]e'sdMRj?&_zsϦ�w -K87m -endstream -endobj -542 0 obj -<< -/Length1 1371 -/Length2 5904 -/Length3 0 -/Length 7275 ->> -stream -%!PS-AdobeFont-1.0: CMSY7 003.002 -%%Title: CMSY7 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMSY7. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMSY7 known{/CMSY7 findfont dup/UniqueID known{dup -/UniqueID get 5096648 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /PXBGHL+CMSY7 def -/FontBBox {-15 -951 1251 782 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY7.) readonly def -/FullName (CMSY7) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 0 /minus put -readonly def -currentdict end -currentfile eexec -oc;jAw-ᾉYň5t&נ{hLGqB`d˗Pة|*x\ޖHtEB-gedog7Q`[['W73sZ9 m !tAY!$tY\r[uTIUiBy[Ȝŗ3Kï6zJ!˒Js&B5C"m&m1$0m jAirOJϴ2&7.BbR{媀E S.9/wG<#/[ә4ػjzzq,I˂ڣzx b-NHa?C*֨i֕,'u?(y/$p셝srψSCo&ͰBZƎJV)Hɳqa?; j!8·'(zr>0t~@B7>tXv=ֻt*ch,߭y%bwbc2 -At5qm#O:JjݒcZ$4HPv-V[(a75feLԍ۱2_xgc^L|_ 7Bc콁1'mԂ W -o bKPfAOܑ`Ax2zl 6܄x}NܱǞ̖cv[^."cvc$#;a$3|4x߽ -(a@cRn6phؚZfzz?K $YJo/q.1f JBw'4?}D/& Z=Vͪ7E ɍ}ʜDtǪĿ!X96E'<m&)JSw4!3δͺϳVJq,UZÄ[JսQK *L8ⅳӣ@0g|ȰF`Tk2қ׍Ƈ#xb`Y@ ɞno{avXik$i='CPEs&>#MX6E!H5&Bc+.s1(R9 PZSIA H){y,䲚9Ө蠂ӎTs9hoqVa#ai$% -eq#*!24S"xSMGd+׼d.0rMVBhQzо;7XbGǀe4oxu$]'eU5 vi Un2\=6XF%d蛳F!@}}qEybaW!izsKB/)PȀ(eKϯXt-}V$3LygX4rG[~W 3d<Dit\_~/̦2a(V2ڼN5>DLduN7:~%Ǐ|4=R/X)$I՗- oZk~%E :A@%!&ѯ3f8ldMR-,0Fn'YGwu_*bXw=AYq>\;B *Ps: ykX`ƗX){qbudog6Ņ)Y>6!X ]|Vmby1\2=謫p@Bo=EpV5%CWTn*q 24L&}5V $10G^ZԖ,䴧yuUCFDcl|Nz Lj-w>O`"'ň"p= yz!ӡ >okkTeA\-UuC6blap !]/ikqU2ϡqGG5fW I2S56 kD6آ=rE1?t0_L4*+QAQ02|ۖ]IX۫Ջ ޜ* _R߉Y%N56_쾦fr[pSH1+ VsĤQ/yepԈ+ Zܐ50Z7sk{15ֈڒ _pƴz hN  kCJ LgNOM\2 g+<}?j|;Oz^h3ػ$68F~g?_8{uhx%4|BAij%Q8[7 gT{5p~ktGwԈ2O3 fXMEO ތPHb;'5 5AM#SShᘣ vq-DnZ;ڶϪMX_IѲOp5a B%9]Z!; vK4Pmb%ۦ{) sqH;jv{{-k+HOWͦO:G2y>q(94(kB^oR[/~C2 %k M{p5@ew?O|;䁾džyF1 N/hXjlhwTM^^meHa@lU"!ZkÄ>-=IJ-RA*P@!u)v]e$z_;Wr<E :L=uD I0CƜzǿ70vR[`)+:|ntsy1~u -|SYi`zrF{jGE^WH7(g}MV-*dqα[^ ׈/yđ 'Ti:yLieIFxpQ,iMNcgWK<UĭOr--t -c%WR?7PQ4R M6z^(?NJiw/Sf -~'|෕N5"~ 2H*/ ~/b=/j1>~Dg(ˉ^`evs $t=Eҝ;e.\-G k!*5vٿNPZKk^wc/B!co -ךkC96M­д1z.`CMkfQ9b}L&>}x^baљ0VOH:^jJ 7kwVD= I˪|΄ׄB| eJ+7lZMڳ7A4TPpMΩURf+1啿*wΫywf#Ά) }Tn$LXPY80m]-i)eS2oYlu[|0j\<<[@ w)8Áo ڿ()H)g={ѵ]?E~T(X'`Tʗ" A@a8S$S-U% -i!PVyZsuR}(t?i_a| h{ڹJ-س`xVD&`p + ıjO-N5VFG㝽*Kģ\k. lXSc|r[]͘Q&!aXt[rKR_4R {!%3.} --B+ޙi~Ճh K*,/hPj{` DCw_h/p3eH/IA)ik#U ]`&o(k3>al=K -/3@A|G+TBR׃ 3OABl{sl"17 k_e-QNFQ -*i=F8*%=Mm[͡]7H/e/cEr\4tE>I28ݳT fL C#h -wBūdr|{T5Qo2?PmeЄ.-Ϭ]lƿ84c:üSR($t}< -H yY>f.RⅬj }+PjE.Xg8KG_0!ozW*4]xĪ 3m6 rj͘uv>lLWwPNqGލu2 p;ݐz Ih=IJ  -RX+%FR1z -D:g{Y}3>6 KQhl [Ć.^^c}.s^֜G>?WJXe і{*nxzv4y۫tQ/x`k4ٞvqK_<-k{怣;-fڙ٤7TD r8׺zrA l%|wcu?g'-|G/ UF> -stream -%!PS-AdobeFont-1.0: CMSY8 003.002 -%%Title: CMSY8 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMSY8. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMSY8 known{/CMSY8 findfont dup/UniqueID known{dup -/UniqueID get 5096649 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /VOEFGO+CMSY8 def -/FontBBox {-30 -955 1185 779 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY8.) readonly def -/FullName (CMSY8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 0 /minus put -dup 2 /multiply put -readonly def -currentdict end -currentfile eexec -oc;jAw-ᾉYň5t&נ{hLGqB`d˗Pة|*x\ޖHtEB-gedog7Q`[['W73sZ9 m !tAY!$tY\r[uTIUiBy[Ȝŗ3Kï6zJ!˒Js&B5C"m&a[9taFF!@-d}bŲO k1툡cJ(@ -6|4M4fV>C ;̹xjRAgd@-#:ɭ܎zAvx?RXeT&aחٿjy;Z.NxVL<8/2ʺHC˱_.U+nӅ#tE[unnVhJ94 }p&G(m7[m!^=>c -"=" pƀH?r? ^~_[Dzv -SU]nV,'Vaɡ0h3];hwd轍m5zkP4:7φ6.B6QԈi[gU@h5e.\ -KQR6r Z܊#zT!<*y]Bءx0Xq$Zcۧv H1*rބ'^6Wο \YmYR?y!G 5d%Kb[H:G~ ]L cNӵ Zz 1[;4p^NpqBD '؉'͛Xčk|GQPE4^ј=|%Z)`>cÉ|J)_lw$[VT6f -=ܟ* ipLEr -R?qvt rST#0gM]%{gYՆa3WD,&h!كq^  -K A~7VŖBxMD26yo:!"D ;m#'WC -\ys&k}ZAGjRm&]뇦nWc5&6"בD׮0ѱY$ۮD>wRǀZa8Ps:)"E66#w¨g~$}6Is m8TK$)ƒ( Yw@þ3h[Uƹ # bc -)!.W`cɗA‚$w?A -$O@c>ҐE2I]Rǿ+ȐLf: 1s O5iW Lf1vP&2lp2IKB'wG`rI[Lj(ybePm(ﲻ;e]t8!U$aoC|r?j5hm28Ouеdmv_1ƶaEb s,c7yPaXQO(xkqdQ7cv -]{< |gKXop׊cz{W [:R!J0pc1cBVKV!TląYIly*2 ӶJed6C(ZL9_@Yq>x/袗O8">􀬪Sf-O'&MYRdW!@/!~q~#X-uGtߟi,i&oX9+a>s\1Q N4ąe0Ht싒`H -;`Ec!ߑ6PM#8~WrguuCEdϮT(>E.6h3ݬLo#['b=S>p؂E㤊4Լ_#*[;H6gT}y̒lo<⋷I=Qo·|dE'*]g`}@P0T 8g: ֲ-D7K'!`M\緣8o鄍/fGh㾈Q z>˶΄H[nWۭ~sC.ҙ@UMk+g߇jgQCpnZۇ\ߨz^oϷ5]w^"&âDzl$dc$'eaGyYA=qX7KT?)^٫|O(42nXk9pE=Oi/y5+86KW^6vAsЖ/ùȧRxɅPk@D:~K_ 6LeىԏQ Bz$Lq}GUgn -ETR<wҼ|"vRT -mF͹HDDܳ?v$[HY\zP.i(Ԑa7X33ATa^y:foyU+w; rT[4_#ivYBX;Njvk :Tˤ:Q\| U3̢Qi| JEIǵaga)%/D?}Z >Ŗu_6g, 㹹MUp-.ڧm8m29:a{ӱwYHޖ3#5LokU#Wc@O$rܱ-#p쮗J E!+4Y'-4\^?f j#lw{PWoze&@, " r -drIrK3/Α[&38.&EƖ~ZS.b칱@ -B6x8="؀|984VLqu_2R`i; 0@g(0*Ј鿢\sW4^U:-AcðA~KNSeOc[*@郬)}v^{ -¿`ax>eeY뜆 {%OVE㆐p,on6>}^qpVU - SErSo 5J)K79I-Ƶ*l$Tatk#%5mBMdٕ96c'V;-Ǖ-i<^bOHǰ[SZ@nkdF?4מ:g>=m˒-67dޱ&Ka[O%5hΆR+J:. ]*dEȴ3/Cg{?ktݒt$6ZB9Yi1 Ls&;yʌ]Y' 7-vpOQ" -\ay]B̗;FB_WՊ4^$"훭BBR!c cGqˡv]~ēH*9 -]C֢-ԩRj[kk~!/"Ԓ1p V% -׾_O30H*D.6z#sj*!(}#Hvz}ӣHVt,.!+l؜R .o/T8Qe>z[!\`8kTC^~.ļr.c$蕉I%֨jAÌU$!@,}R"{{,kƅL2JVMW2 JAf|:IB*GsD,\~.9D[c$+*& ~w*_.LuZI,D켈< -כiX懯/]|Qs)o}O+w] u/ -<@ZABFʹstA}꾔9: dު V@w2c.ҶVKSxXU -Lw}aoKh,LT 6^C(eǙb#t?'m'etlE3wſL73dLKk'uv6L]k9~?"}%7 -9Aa4؂}y=W=u#g&usYIs5r(S#/cTC۶=8O_Yxv5$ -uA/>̨Ůaria^LZNI>^Ƭ+ ,|>)bVºILuG:’y.4>+ -}zL=w PbA @X"o{3SPW9Vj[Ea8YÓ 8J<{3T"5cAfWsPybУBg)K.:I]Q;'s"#kx[PSFG[AO4x$W MFg?)wϪP*' #L^m3w:'QAƍgT߻5ЯvG+.HHIEj:cZ꣜\!ٗ+&;-ve;Q>&r<ޅIҎDz-)UCּpX/f_<-[c)+٤W" NGWKChQVAZqLY*DI3y,Gp 9LOSH|̄OKJn(Z&J_ƪf&tRTn3Umbjx4nPaW՟UFny3 *AsB[0js*$Gx9宕o*|n[h!P7'lKYO)S>HIUŻ*_'橫$6EM -endstream -endobj -546 0 obj -<< -/Length1 2351 -/Length2 20496 -/Length3 0 -/Length 22847 ->> -stream -%!PS-AdobeFont-1.0: CMTI10 003.002 -%%Title: CMTI10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMTI10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMTI10 known{/CMTI10 findfont dup/UniqueID known{dup -/UniqueID get 5000828 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /PJRLOW+CMTI10 def -/FontBBox {-35 -250 1124 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTI10.) readonly def -/FullName (CMTI10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end 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 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 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 -dup 48 /zero put -readonly def -currentdict end -currentfile eexec -oc;jAw-24 WEvQC<3A2kX0k^|:ٴfb,|=sLu2KZ`3ndgRw@),q՜G<&h'. ΍883 ABAԾI$s@F25ڪ,i pK>6K` %E((bsS?#;IHIRgHŗC" Axb'^;*DٕTz35'«G=F F섲.K|Lђ^Tsә,˛PS{1c ˋri,BRjl_݂tUH %!#V|6G9i/'//do1Wˋ_G -‰a vL"paS-g綇}t@{&Y`I -|ۢsifˇ]<zilWUf }ϡq^c,@{6~?JSijv$i"$O -VQ?236u`}u~㣖9ñ#M=f.bȫ G 䁡"K aI\N*Q*;G40Z($Xv*WsPn hXU;.a7X5{~MzH Tj?^ -LhIt}e&,APRNy< 9MCfQx"c<~Nh%0`ڇD+qn ;/XM wZdi3V"+$(5|.R`G[xM9s&7q%*=׶%zJ3FA%@kd/]gā2Ǧ<\%ߓnW(5uI&dI fWt]]32b驞VS~O &`hXsGA"%͗"h*4Λh`:gQgatN9"#D*$Ǫyy\ 9OE{y"QAw/Ѧi,֗665:?Sr#2 +]vV=] U8~ 4"5;;jJ+عo!窧)y.^<^gNlV:H (j$.C>drYz3D^"(ݪy?ssDt45KqcV}PI'REhܺn!p}ilqH'>2AOl2 # [˚so DtaK:}9/M]fXlf-F| Y A1Qƕ/28 S廩/^dVB [aJzH0uSo/Y`'g)5ʪ:\hYrG!y 9rhcagzoϘ$@]8 REPWhͽz]FIءz۳L|"CEw}BŽ03&pv4Q:uKw+nC~vto:a, y\Y8L sϯ~dp=n?D( =>mzN5  ,$2/"f6%)R%b8j6mqEQ-C sKD\=R3d>!YΎ9MQΕ/Vd+BW&IIpAh* ,W_UkW2G&tk+hV<$_TgLضucz9?^y(;2-~7]r&Q0[AM]fX?x]inU>%ʸ(T?. a1L.wiaH#C-`g=f) -TEGeIuEo?Fg 5s9!GYrÂ$֡ L8h:ji Dc8k.l|l| /ܚ;'(2P]< nӱ -l\C؀:ጜ'|-sy5eDeEͲ3ڗ05nv>*!d p+2~Ͽr);J;шJ2y].1'e'0\Mt:gF+mr3*ttXKuRL˨B4Pmhel[b9ʸNRr%0K.㼎b8TC{,Pu9 %" -ƛ1غ^KUIzfs'FiwG&2bDX4&"t]vU3qekZb2mHj1}q_P2|a8~kP4o_== vԑ8U5[_ )e=mʂ:1ԍb D9}F`ֿ0cnR܃IpyiS?z5qeSdqei QJV6ᤙ>ot5&2ZW$MQ:Pϼ\w/v@j=_L@wNҸ}FdX;ʊw%aMcà/bbK+2qޫffQ`" -nLo/'w ^*Waol2)&e+شg !g 'f?qwtלKZt&,<#)Y,zzп榯%1!ǠW"pu maRr1r@C( ^ tR^0Kt{տgB"ߧDf!=|Q -:( [~GsvjʓkP g/=_]Uz T,$V9jZߵ5߷tQq̮ٙGkc{ |RL ]vCAh$(5y9>8A88o1ȉSO Av??߻㹑Vks=lvbϣ8|\_%{Ҩ>&&zIWVSiUAV+Ӓ$D} Ge=fL| +)o^E`Iv7fK+sDz2s4+:>AnpT/ٸ&XɥݡT,@T;w zȼӧzekc=zaH``$4 -ϋHG^/'tWWu5*b9N&ԯ}ڷ#* -7=/|CX2W!wAk'TM<@SтkP8f>? T2K/K\ >$ɊLSN 5F=)!#8e|͓g_NQ:\UAd<@_ʴݮ -V;M5ztMmiJر]wimL˧cMѠk>HI s__Y/H%Hf]_ "5+9E2T̸CO[ g=<@2L4^էn^83rABzSiܗyUO ZĠG?mѬLlPm۪p@n,y4s:xNKXa2# -utw( 7̥>چ,Fny]fH_^;NyHU/#")t.ˀ!ϛiwx{ yC Cb|о ;7kKS1Ja9zWs˔dDXH\d۝j)3x%n'l KOmR\I5piO~5>g@Y5+9׷0ɴk8@ ,qA“D뉹4NBuytz]pȧ".?̒ѯ/l[l&R~WwB!n]8+I5wY]Hvܲ;U"ǘN4*={ZU6o+L%= &vɃu}qs,QF?RGmai?y ybxfULWQ@U-6eٹ+Iƕt!WfwmAN̼LZYLOyJQ)P2$b?IO4o OJrD:8k2?T,QY I鄳BEJ&rZb ʰOS;~qF9c#cc֙dLǤb0Ɩ˿hZRJ >*G F{;C'elIcXm ,؇6֙&Emn.RGAeŤ2W| -K; >x! MA;NJ}b3 /2ۏs))^iދ1R (ŖƮg4Ѳ4l/XR+|Ifb{h E]5[n,|8]C,BV"*NZԷɗg*`?ېPC C)LEDSSotOb \T=/st?CPfF .a(C!Db̛Exj%YKW1ޖ/Ykt@.95wHFcNDCisㄶϯZ8A6KZMhmEGpXԠ_;u/t_& \゗>fwb]>|`FsGDԝ{zРEbf\){`Tf(lωtB?B<k#Mb8I]1pW=ﻬozmU#{ ؆rbM;-uDy6)vAE)RD!i{ݚ@S:(QS~- tG+\{ rcJϬڔӻ%(,"Ze<T5Z=F+I|=;icJKSA'&7&۱eb&qA <sL-s2+(v -sC#"p$ԞK -`{W/՝+r3#"@1aW3!+NLUTYZCU8wpd>(?}_ -<.763ݚZ0(Y/ -  m CԈW}7׉<*/YJp - 1Lwi3tPpymXVy@@uoPPui -'U:^RɧQPXr+[jۋؽV%:cNΚ~{? -&>VPh<ثE Y {YɻѸ t>Zh -z;{ 3)j⁲D:(t2w2Y 󡰞yb -wA*֔܅iF# P|5.Mi# I8'-̮\NJGoܽ'˜W+˺0ۺH&yNY Z -uyvĕ1^U< YPIgVnJE %aLۆ4GAQtM4|rdujXUsܬKfC)nfb=igeE&.D7,0B-q519I;*8Ob1x%g:fIJk:7KgA%?<<-_V{ݗ@NLK8i{LʛxWS':ت1?[o뾼Ҥr_dz_Gbmh8/d`:C諘zڔ Vvѷ\"݉DEs4t/t_H[/ӡ(VJ=Ԡk - <ߥ9˧?AB)~BQMV_ ):΄* KP2B@R85.LwC㳾W$s!h:I/m\}g=}CZcSJM@NdW*-gӯ@mWg z9%J}SwnCQֹ.G58 gpTZ\_$5)z| |ʷNZ%o+`-\p3FzK?nY >1K!paA*W: !f<ϧӆL` JW>*nktP;'ʌl몬#- t):MWHj(zgy*%1:ȠxI9uuXt`d?"U^,Ij){e 3QϏ3fNj"q QF77P/'H<"?]K5͖WW$xД4fv˛?^AFt-vgH呣~qK﹥#45A!S5 X]ޑ8xa*[/~@,sH̛eq=TBgTq!w,2 -3E(rr+oVs/9_T0. |9\DĘCB;~U^[xR6qQ@njlr-9*P(⥰LjIx ^7dAC`a}D Į@ [6 ?qGʃ >[lx% jiZ7qԱwt3TwӑFv}j 'c'@WSQ3 -Ζ &ظjTS0=T kPK>!d'@f@[:Op[1Q%;l0zKHA+rһxa& [vfkLkՊaow1*ݣ$ -8,QG:!QYew\ĹRV`,Tb]H  -G6MV$CB{>2碪Хօlj_1iQiGLj,C=c%XiԷHSq>j=ܜa+A؉n.OKt)f讏 3qa[YBaJyЮbƢ'Ofʒ*{^k.{ra.=!\Dm"vTDjO @rͷt- ϣHGQOo$bFOLآ - ^%kz-wVUwڽԥ- zͥѣRj l6g.I73?~km2a| puF4N?yR0m+Y_s W=C1ی3^e݋e!8gԂ 9mm <Ly8u`Z؝T dU\q]^e }rGf>ΪcAvs7~gAXsiSo'ê\mcoX3{[grCZ_Z?ƟrsL^28 :O(7_@x9́++;:)m#׹Z؛ yx'`j\tWda_C5Փ&VV8sYmlDPV]OPb0ijE:-J1}@F[<֚7 iVMMIBa3Y!#`f§ -žMSLXȄ*Ṕ)V;oOh0_T4h7Wk.ZEٔTux> ]d,VʈcSuNv)6,iW< k;4/m0hILEY%Nv|+R^?A ̨ {nB` ݹ'*(?bI[Uc6/smƫ^U~MX`%::ٕ) %7x8;Cgqa˚APa$c $Nw7[v~Zpɖf ^#a9F920@Y`;{+=9M=f44V4%fkhS9H#ޑ=9l_WǑFoV1O [a6C[*4R퉤lKSxgu^itQM\wp#gz.0d 6r[3FVnS݃MV3Mnr -ap# X~`t);,pڦ +>`7s'+o0?r 6HSQpp RBcW0NL˂ ߼P:+|("GvÈmskOGر. qPX\?Q0P:!b0@ՈĈQ"z?]8!|f]8{ʩ(.2;QФ=_I?n0;@mN\啝D"ѕF~;އWIvY0s^A`qS&}[dôtfl 8gQ|ݛX{EBpTup+%Uxv}¢{Dž6n7}]l_ËP);P3θ*rc&[f联3iPiUke4K"7 r\Pm#PW4 VD)dp;8.߫Z ;kLN&;kGrI3fT Xs҈@c!53dz}7TNUW0n'uk Vkr׊nI|o;h ^pUj!Fj* :05zL`HRzE/nCI:À,K,:T -wngs$:&9'A?'*Erg ݮlaUBƾfk湌 -N4 wt31)RL@d6|Fc1iae I5t-e-hD4.Rfg\a[Rn[,&MI3Ρ LܘM[B1f q -nծ 4a7Ȯ&K#8Q5P䶍CHH4fnGZ$i4GEZYwx6)\Xxno $a -}1Ҩhr<=GK?7Hp*E[0sD( 7!⟼vc! =| t c`YB%'rTxRC:\j_ۖ6ycJr,(ִ)m2lj%[ 8Jt?abld}_(i2 ѽ2ZDgf8&o+lRdY o= -x럤jfR\*U(1 -95){+٧8NҠ3L*Ch9,O.psTysL1!g,qR裈 ėn_:yZ|IET m<1ߟw]>xߴG@U9&&ӸrpNZ^[ rpHm@D!oϖpH7(~HYJ#H`=N<˰]'Ttο;ōNy&.rnqdWEOWm`VTvmhyЬ&[kKX cjN &C尓Y^'ya=fcTͽ$X0-L=`5GeujmmUgIGIc0Dtv!< #VY6ț05ͯWDB`jJV|w7Yn_ -p%5e=SӞYZJS=Q)OUy9Qh.L4fa9'l\U:gL?l_ r(fD1? 31HܷRq$- EGpQe k@d0#}sBX7Hk~kHc : 81wtoAAA9%cR]#A_LQdJ/H/_.q@cZIq)ldT~$IJ=B!}C!qåMӗ Gwvq -e!Vo0LctWAkPdQ$z Hzē -@ޱa^56jpX#z |r+;"~$? qX0NPC@Q٘hn$nms#M Vw9[ͯ,SeGM ʼOY9˧s#=вwv;Т+:!*#&0;AOΝwy js -5c5ڧj͜ ^\叇XiTڨSKl?$Ժ<{ D]"KԻὖFmS9f2S&~-'4[(:Iny%orpiz7]hx*BCO$#0S0b32'Wp,I˰VDm:\h|K*!w]؞h[AhU9#)ԗePy|@xF@uJ#xsxn>y%Ď68+/S|1Hji>0a_yR E-/WO"c0(&J3#+"ɍ"@+sQm2z *[ A:g H2zQ;-TձAӫl.`%RjNnje#eϚM4y?/ٟFbgWP\S Zg/atzAj(W-oU6b9aIߌY^b6ު U(Uܩf,+5|F бKBJټoӺ %>|e$ -stJǩ}~`,nj{/`{&MjjtqnmȪ -*Yp7k'{<6C*p,1mxxٸch3X\Kt3]g(:CReA1h_ts9\*_.L [=}gY9m 3RM!bJSupԚ&O\+?EIwB #m;Oob%}o"% e{g-*ZB~ŒGU;d̃_j*ap8]j U= >QXC\wGœ>x+Ky*0xÌ~[@Ynʶ[U>RŅ:bMO =%Fm6o3?K/6d5qZX Af i -k-VqyNM~)A%5;RqvPAU{E ,B].RO3pA9[MWi+|cB#);OP@A@|u5ׇF"?X#j,nU*;OK+S 6 jT/=9r΅(j)Is>pDO;HK[ϚoEwy^uy?\'YQU'l*t ȊnO(to0 -@ -ifN2vN<_#$5G x^<)>QOIf_*b`%`{QAH&C&8gt5+!%-OC8ݿXbXBV#K5Vz-ZtIN3FD~{RȲ} *6 syP i~TB2'l@xuj~F4|9΍7)vkȅ=aq{ulNGO@LY3?A[bNu :6~P]o;Eg^")vt=ˣt>dZ~Qr߮p,+R1_Mi-"O%q~u5nD2@aRC38z`e֞aлX[fR%|1E76ws+iau3{4,et"wo){Yݺ¡Kc\)aVh:2vsN16Y/wq8(M}ip2"N}⩄fX~1PX`l zQCm^3Y){A& :UܭLJ)JjWHj].fGN1椫҃plMNJfУ4E"mVq)F+Sߊ7fmyQ|A-8IqgDE47Įo%K(db #EMƀaJ&Gi/Ֆ}+6n- -{'߭\$r㹌oJ`ƿހJ`Pup3nDXu7[3y{XǐB&wÂʓZ~Jzms(u8HH'G40(yie fQxHtjNZU8E 7AU"T~V$=+(SLf }ۮv5> (5i͋.X#X/5Yn9bʞ8# %l_)0@?eN<_1~[i8zY1WFj931 v&az-e)H9Z;aj٠ˮD)F1H*Åu;h-;Z 'yրYR$[L z/B `IA~/"c)o`;癗_MW- -Evś73R^rMlR[Rm<ie ｄڐ?_GH`iit# s"cvwB! }mxnf6+ŒhFjnVSwi5-~mbEFl[ B[e6d"F ʑf5/ox[ LT*%H 3E'Gb5$T쿼f%~٥ihW5۞Db*hҕjԯpmE񱑮C1ƪEH=Qf;Z{㳟eSXdr6@~ʽ1eIQuFm4C& [mؼ_zdfvF1gF7>(`e~S##l+O {_RP)eDF4^blĨ)Cؒ2C9ҡi).v )}(@ROh"$k^o"P3c}T|>j"0eD4+mF}Eafx02fYXFI0*$wNuCH i&"18SJ -v`a^f%5{1twxrŜ7u190wU0]*DKl޴n=9Sc `|IW*vLc,cFQXʕ1{vj eGLK9ˢ׷g!ԡ/pv?N?7x0nJ.r|'!T[#L!{ԼT#nU aFX3R+Q6c1YFX.FMX^o*GpoP+ku% -A Z\o%Ecd]$)0>xAZvyd.+ s2ԄѦ} oç_U?^$uQw"Kr*٣9E ^j ߅΁0X\q2ȀV .sT-wC*Hrw3&^ľR1dPέN 4Rxz!*7$uoӓk+>1wBٟ`z]dȵ4_=, PSH}gaU=cXk,p? pzڮJ? 'M]BܚЉ[Lv5t -ecIm%@O8O|FJْLݏ6nQUx~FHW4O Kʄ0Ď;w4ܻ򉏌[èw$nɠ"Swߙ>BEteҮtS_ ܍,C2@Z6əj#& ZMX{okB0w/kV)d -cPj.`ZG/v^/g]QG+_IL5?B|/Ymtb[U,`t0Վ@ ->.%S -܌ja7 ȯ}cJ=?C|-!S(uЍN!aU`J_ ('yFwa˫Ϧ]͇ki -NTW-h4ظrY%-{˂R߬E;"id'"z|?&$T]Ɯ6O PvǽʏWbM=Vx -B۷GLfߟӰ۵YC)zTfTd/\8&tgL\4 .84Ƈ?=A4funOo 5 7AA΅lf@^&jؽc`^/ I}&ƢW>lڗq !3!׺S!ih9E2ICJʓ"̟qYq3&3㏕s Y +XZb"MKz6K6Hš8wh Nis!#Ђo^<8k3׌6p_IuWM~`b;Ν8.ʘd.5ǫb31e٣A8PM+Il AN#!P\L[Y ^!ІlS<]OjsזV+i>|d_@ooW޶zA*z$ѠsK%4VKzq(`: l i/5Jv2wF u2-( -:0 繕Cs*{+FDDC0b7%s)bWZug6ݧ#L@-=(WHQ=dUU6i0 }"!p*1ĸi1ӷi,5% i pMۉ2 Ӂ}73ek\ Q!1xHJlN? N0Va?{Md\&c3&/oX02:m[ohBiS$B\e4{u_ 2y߳>#`ھ5Jx; wǤ#3H,ޗUfdzTZ5%yvp;?r鼁A|_`󘢮an-nw4M=grK$ݸs9I}Fy¾x[KAԟ!67> -stream -%!PS-AdobeFont-1.0: CMTI12 003.002 -%%Title: CMTI12 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMTI12. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMTI12 known{/CMTI12 findfont dup/UniqueID known{dup -/UniqueID get 5000829 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /BABWJL+CMTI12 def -/FontBBox {-36 -251 1103 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTI12.) readonly def -/FullName (CMTI12) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 68 /D put -dup 76 /L put -dup 77 /M put -dup 80 /P put -dup 83 /S put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put -dup 101 /e put -dup 102 /f put -dup 103 /g put -dup 104 /h put -dup 45 /hyphen put -dup 105 /i put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 112 /p put -dup 114 /r put -dup 115 /s put -dup 116 /t put -dup 117 /u put -dup 118 /v put -readonly def -currentdict end -currentfile eexec -oc;jAw-24 WEvQC<3A2kX0k^|:ٴfb,|=sLu2KZ`3ndgRw@),q՜G<&h'. ΍883 ABAԾI$s@F25ڪ,i pK>6K` %E((bsSD;Uѓ"":!cQMq:(MO)|$~x!A7ux(ǻISG|IQԏY=9"i1B/?xI84HrxF-}S?geXhb'N'68^o ߑT݄j"_ u3S[3^G{Wsh"NWk#IQ9dxpY JJO(UMaKDpP=|#fLV<J#o)Z.$U(X=G-Jk%_HGM %4ߴ -DQjY1=KʧHZ̛wOȃDل6C!8]g,cAo?Ҟj?;IAGYPKKɧBs_W9AD2IEWKN*3iA%t  .ox #&ShD"5{nƋ%;{.=:ٯ}]AUi =.:wv6 <n~?V+Ɉ8R rmsri40XgJ~9H)G3TA3c<;k \" -"9WB7{YZu>]=h۶#׵N=8gkS^Z΂dxZ >B/ngH$1'F%!q\sg ,YKX]goRw~IipX4_ -A6)Ā_B&mVU=J9zkt 7n/N+u'br$T47.\I0Jh>)Q԰[]" ؐ MCŕ͆Upu k{nN'ghhs }Ng*t\/j4p'2/Z{{5kݟpݞP% ?C 9AVpzGI%ZXcJ -rxgYNrfcw~B?B&&tѥn^pDF&Ixe%ci -Ⅻ5<C0C'\F֡z[R 4]=)E`͞獨YI!Jfn:W]ŗknI#‹j"BBvvмuFGN;-lK΀i(sl}HGo1Lzǝ|S+xbs*e3>:FNƉUm -C']&`W V km&怷B@ϛ&Wϑ/4 Y^O `n>nRE_l6FYnnr%p7}%|UDrZ/,#N1Hۏ.CMn)7Q7!frɘkdfN\o-6Iʨ#Rw\CǛqd*~)]Z9TŪ;De=#RƬ4WĤ>L] -\g$2$m -q﮸ݣAqdu5B爜ǫJa)ҿ =['f R}]<N⽠zЁ)#0qG32'j g&geAna>I\Rʣ8߭u4't $qi"gE;I̶(ƭ8p} ó)^"rtS_V3Kh9"$a'm.}Ʌ9Yۖ~-iB*+dခXRI Z򂌧3FFNpC)1*RV -jm#XIz93&;vNTip qs+;2"cY>'N9sgէѤVK j_Eڍؘt$/Lڒb1pUG&%Yw毞|3 L[NFL]eE|eAzMնTZ<:,.$St=SjF_pEzr}BoN, y^`*3MeixgBpC @m ۂ;;u0-Qq3C?"˯sPBveb^~֫)Ze,˒[ -y*?ݳEҞ/_ZNdEc"{u3Jn5kuL;[~d("pMKKjuAbJ6vt-*fu&%XR5Kԩ~qB׭(E:& -O.VX@Oc`&_BtOgRn-bs),+{Umځ'nC)l,į&L UHuLU'Jl6t:h]A>aR[т8˿N{f? e=Y/wث#Ƿw;o6QlEs52p[ c$bPͳŋ3s91}$q"P҉bo+ՐFsv-@\4NmP)Xݢ}_4hohF 9C]X'p4|:aB7#K7˲n"81-{N;td *a"zj2aMO)BL# {jBT39Uth3~GRb8`7.A olT"D+,K8NJS덠M`'MXN4Уvj"'LO)CD)9{;IJ=i}ԱRoF81~Sٔ&E;9+ݓ,6JSó{2HWzIpW.u7p92QݪP2^AwrͣNEޏy|gqmWU˥s* f6.LK] 3>MoUs J77b,$y~ + ,hϖqztDFktQ!QBl(4>:hvqID*7W5zGsq\X7vmm)NkH7:T\Fn8!J ->ONZ - -a8"5n ZJd!b6`=Ԏ -m:3ڑYK)yhfghۥPAc'SU-|G8ȓ|/"MKkI ri^{jD<;pzjA#x;|#`'u䝈AEGn 4yhߠ}4ji׈)BAl@7BhyoBbf\8GS3ˏN޵dX,{4@&U.1l&PK ֬Q{m'c%usr6Ϻ#!Uv -.-@WͲEdq]VhR.fdݱogr3xlیqsŶ#ayi4mwLD&Y4@1w*Oҿ,=+ܾuʁU]2hv~L1- -Q}f`gEk`Tk%猲3*૏J]I\ӷ70aFj&lyzb&wG]ps4nv_$2^ 屽jQ)&#q)b~9춚氮Mh`8JV߅EBb|̩Ua_| 8 L~ҷVExwwżkif8gxm(Ÿ -> -=MlT?y=F .?$W!Ѡ3ZEIW~QijIo=uB\a|> 2 H9<ۚuRw9liYTV'g9j3e"ob -3yg7{6PZ9mT$/ /_`ɗ}p6V [3'VFm(uCseF:oC,$TJa -B(#hmM2CCгnzqYHMߢ% ]02u\kA̖`K!;ǔ*&K)f*M9CV#jfis3];J2{c|5B4@ -5k9M}96cmlAmkў%soC=H .2a\ 4 Ho Ca!3{jv\0S%-hd|akQ@5qI;i&l9$]:]{R}YwRup^kؖ>>yg62swMf>#FyC'S5쀾[Z&xħ~"bAX!&.B׭ (4V}iM?\0$[L~]8T2\V%#hiW(㾛9(O5)Io`>!bIA^SgYEO/*>zVn":k -56_*4|s -0dž*A͆2hAg0/.W^fr>tEN*`p<7 w*!q_'׊ѹpn,P\Vn-53c@gş7Ra;2L1K\#FYIV9*:PmvMF7 Zh=Y ~'NQESVe?1mZ;# xO3]$,(lK"jlx)̂17d\L-!ӒV8 DAT]ѭ.OE/MUx`y5=7K$"Up+,6_ݭLs_X[(*)"}RF $:)CBGo-–Qбd51p9нr2fQ)S0b8TÄ\V}6:K\Dz:xp_]@xCtdgnlINFo3 -+5U^Pl'B -gK "<(|fu!/-q=qo}G*';~kn|eO9D^X,R:@A/W ,!e5]5H!P{SGt֯}=K_y2R|kFh8v$}93'$3i2rIٍ>MPv*ս?챡0> ?lC_ :'!m\Pڪ[x[P[ĊQ)|}2y^E$9QeC$~)WKm:4!ˋOU%5F.a6_^ЦgJD Ёp%>kD (PmFfXߘOzrW] Ɠ12OĐ'`'b d/>/#Rksa1Q*fs(^^bTuU:@u奼I%}gV]b1X(^R)Tx~Yڼ\1a9%h*".OƱlc#liL9cХP S9u!bPq|gf! hj=܌^{kc͗|v-!x3l@ _QԄmFpO~L9iǢ*`Tx Kʙ̈.Ǫ4c(?˳v -M'Zo᫔.3ƊQX`܌"5P T&Xv1s&8.Y[ޥ=P,<!HE*"hoDM9>u8 -؏ , BZ(I h̖JD+beT]-Ej#,6=jYs[rzC]/GN1bɍq#X]է4ewpT -D[BJGJiݎʱeHU3)R'I=rul `L7ʤ`Gil[<crsEl|ͫvf `͎t?Ng3O4 !{| د%O-MM?.xC.4)C#e;C幅k`Q)&k|U@ 憿}K lzQj-@k*-O5ØQܵ?N]rScTaU>i}5,qdkpˍ#ǝ-QU,@ ͐Mwxk)d(\p4}_M IK31g<&(&=^ÅSC~x\%*G8\5A{U9[a>(r- DYtBȠXT:CJ\VйTF}5wײUg~̤QV)2`8D]}v,ʽfcSlae;.Sq& ` {JtЂ92QRf3>8HWb:TۦV6a\pz0x/Q;\v=Z; Iꏡ:䃐R¢GD' z*:'4kZ;t{c{Ң v-{5rHw:ܘ*a`a5k^}p- ?h3OJ*QvH&@N{Ӊ> |`cmιfS4)+O*V+ la>t#]lֶ'q:R`N^˄qԴ_2,)f(ڸ>D: >W:;ܿBͺi>2V` Waw ) -v8qQT^gCתOj\/v&Br8bNED/ V_raD&MmKn>z.e_Sbin =oA;]ݔ?ye|z4}/!%ut`Z]mMe,{:ݔ~̈́6̋\mسydan>Q1"&6`lɢ"%II$Bis's1*? ,T9K9ZrπP  btK= "oLNـ\:o쮧p"YfvDqP30`xnR8VrCyț+䓙)EGDοܾa6 ->Jf!Z]&S1 *uT͌)9X$)IS=rnնUyxK3Q$I$N"]oh~W=0L%$&2ESHlI$с r:ԞIPW&&Or jO@a$eLo"v<ۥIT@c~n/*%u},G- -; -lYPtb!*)b.h 7pWc -b\QɩϑC|ܺv `ć~8U+X/@C./@û(WJM x4ݶW\/-C*"y))Py0M(ִ;eBUsc -` t8Vٴڙn϶,E䕏 q2!p9$mNFh -endstream -endobj -550 0 obj -<< -/Length1 2768 -/Length2 19783 -/Length3 0 -/Length 22551 ->> -stream -%!PS-AdobeFont-1.0: CMTT10 003.002 -%%Title: CMTT10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMTT10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMTT10 known{/CMTT10 findfont dup/UniqueID known{dup -/UniqueID get 5000832 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /EXISZL+CMTT10 def -/FontBBox {-4 -233 537 696 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTT10.) readonly def -/FullName (CMTT10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch true def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end 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 90 /Z 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 37 /percent 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 55 /seven 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 -currentdict end -currentfile eexec -oc;jAw-=%W)-{ru)rAE(@{빴Q|_R -ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ -}3{Z2zݬT2s$Z&{BJ{=מ0).|˿!:[LI0lr9G$}/X S`p*p+fwwFGO^ȇ r+dMvNy{YK[z[f -ܷBDq}M8|j${jpxxSƫEu -7%ɑ4\ 9b \)[FU.q4Z8KzwwylϦI5bjcZ,7ɪK:#@Jd@ѻFM_d#g+=>ZaWNH5Y/ .rpf{0D|6@;]/h|.RAɰKml^&W܀{mFՙ3FK~I7@T7AMOP.;ݐH+iX;}jYXEu5ǻpېBIᡊS 7pQ40cH4u[ wYÖ2[tʖڣ?hb*$ -dƥ`$ P :")|UƩfDtd§=5+j7%i@)шT/qUF1tEςҷݢ@ Ѣ1ãF^R?-¦q^!*1gw24/3@\7zaz1).ExY'Ȫ5Fc=nj2cw1 3bI]y: f֡ꋓfg%p^`('m K'K '>EPN,:M{S3G2R@6\?-^X'F.qhYlawNUpͧ`M9_Jgbw! ̼sāTҔDb:Wq!]iơw`褩'`h^ TTInHel䶢͒à`じ 'p(=Y1UѬ/OT -%`&{(K:.CiK9xH-vE4x_5叠ٺ,dl5'bbq,H. O8 NNnZGquDZMgd/.o~*ĽẾʿep˵ -1}oK({AsM`?  }|^ڧ(1vMXAj!Vk5=&Yiw|vCPezFލ`FJO!zơãE.)8At`+o z`!|a*dU ).tIhq*0q>NU 3ȏ7Ā9Ot[3|5r0p8ߕWqDLŽ{`dw|ׄ GJz/H'Z$MΤ8Z̈<7{LpV)%k3ToCn}4>ZrȰ{rUZ9EGu49>`oq/~x▏S|f9׬?X.uBxfGbE.wW;o, BLkkK{9fgg,l|&Ma*$v#ܶ>7Ucö'nNЙ1WƫV Nu+947yG( "zoO_|cZzB@ZAݾ@aexb?>"YTgBlٍ9UFJ?"[p] phU8Փz޾L?:K;W%X$؇:b9pF^dBJR(6[-T*4!yY`'M( MPA#fT"f"?eX&RE ]2L6 ?h)8&/Baf!0tM<ŋX0z1$6$}W<1ji76$4e L,vΡTuQo:=}E˨(S0.1) d#I;P]ɵR蕺I,"?bB8|GϞ\;H -nc2߯xX1!?:t#?%gSe[ze} h)D j-O6vzu@b ixc`r&r Iڹ_> 1SSdY$`)­:] R]FITkxjgbHd.(: -﫜.%pq>>^zx,{^c]r6oެtHTC O;q]8$yBoLr {=f$' F}*%*tdsCNzc5G~¸e 2d]bsz':aWA>4+ -5u=JTH8Yn{-t}PtJx8R.\{`u[%37\rnNJFk Oj+WesMV)JYV˛81d#JL1?M?"śbQﾹfcӟr ar4ד@dv5꺜5eDfR+c=PisX8mm;EL]H|S° #ȿl S6e!3BYTg}TTaΈfgX_+t12)A{ߨcװzP*Q˩SRd*lN؏bjɇwu_ŧ03_m=/Quf -'I N?qj) -ʎӲ+Ar⻩6&HДC9mr|7rG%:Jr<(gG^Ĵ~xP^KYYD˓"$?f7ښ}Xo3'+Te|7~x9Fʓ u -ih -9Nt9uicsJw -cZ|$C[ie ";3|AzFY4WSHʘJ᧞)~%b[O?;Rw߹E5?"W|;ծI6X'\dKs}2{QA)wJtXi3uR3Tq5b|~<27bA}LXO6/'`:8gI$G,M`y}Gꦜ?)c7K !8Bʽl. ouv -KS?0Z<M^oE "1\eάI SsBITve赡 Rkvl$|i0qp -QxroHQvzŃe4`eb?V'ax * ǡ~MCC0"rsSC=y [^ՔI1d#J9&I# g߶c*B+FWndM}RYubPvc?_gMk5Zoof~G>ص͈,gk]E8?`aN/`p22it (/[@|;C]ar6X W,COQY``J_Bhq8 !;.*ĿLMbMKa{boKInUowg3Ս|Rq?'SoIV\]iTgȋ[_Z_j5'N8wM%+E:v -"Ӫax;Y `m e"bsiq>,Znè3Œe(go =$Rܬ'J:cj3f2 -N:3CC;Ov"<ȳA?9=ԇa{M˻&}Lnu4۟V[+._b$t1.}c{<0PBW*ZCƛOS 0aS5Ε-}7-*IC{1ȹAZųrO(G n69i5bDN'wL ,j"WvyMbfv&,ՆHѶG[f&Px&I뤏i=(˗z:[} $>]IlvyPd[tzw;hc9X S8{՝YJ4ks'$r+t7))m&LWQ L7)g͑".f E* -M:7jm !'3x<[r n^s:^M{9Eŷ8Bt2W<<#,CM|պOݭXG.|3q]U*viEk ՞z݇Tߔ5#V:e6- 0jmϕ-1S:XޅUk)b)`.OϚs 2/ؒCT?fc{$&3mR^خPV)R*dD"\ۦWR^ʧ!h:{Ѫ«i8)vv0>H<)T<{sU@ 9Q(Q& HzD -tՑEac=){ "v>+w[t}5+0?%ଠrYKra;\HieG?p0cv;zi4 ,ަ{Digt!H%T DrlZ-{lY|mFuPFLz˜ )B䫷.1Gfoz-@5OQiIgwb]AR|΢GY , -0ZMBWq"F(AB <53E l.pH \KCyo/Q*^E ٯֹa"gE4{bT\hS걹 ]uNEu1nJTf`n=ӝ@u5=z -Hv+\Q}1:8 S4cJH'.]JL -,Uaq,AF$;tf`F«+.Ї*d{ jo'rOdŏ/'P3CÙtl"oM-V b[RirU2q-m-cA*=G%uWAj-بĤK YFs<7*ȗ_({u\yM~]|nX '-HjVYwch:\߈ۧ<^R+~v*&s߽_Z^rWcLi((U5wx yH}<MG`Pza4"SmRc.D/&7i9̅ĸa3QU&J-^:WjЀyVYJIʿ9 ZL!ii 6'1Ns6#YEI:9Nq)h=R\U!bꆳD󄅱}( 6֘s\f#Xd {T.[St++ƒψ~@)^a&Ǎ:m<6wCy,ʣz Cѽ&^d^w!o'1zHaxsc -63|`kssyguf$#Z4uH`4PtQKLx&|n&76C,T]IJ#a~ףUƙhcNf¹V){kU/b) ڈ_Sʢ@9;%i -ֽ1_o{Bc:cM_7p6bLWE,}9VeOg'hdZ}/%f9P=B}%I=4N_ [*ZJyy!&D.g?efN),eoClF=?fs`Hg<| vAYՓvW;LdIAAkx;pl<+Fi:a,?߯*~>жL3sT)?jTRM$"h !V"񛍞I>׺Co_py\N)BӃ:-p*4vMŜ%~82*UOMGoA#ꁂ ρ!ƹ,#'`FAA:L #]L8`ʨ -b>O -xr"RQ''Q>5cY,YbӪCmzEoϯ$u6Hx 6wL220>FagZEfnǓ5tU3HoyxX*sl~6:n7Z>}/Yx NJ"'_. Nx-,1@?vX*:6Jpa+#{f;L3\#2;$GY6Cf-҄^ a`S?'՝XT! ^|Ih[JHg`-1˭޷Aj{F0db[etcyy63&1Rj\T1f:ܫ`(i u- -իbl-Sc6FߖjZv-2QH t ѣ!YlT+|zQ;4ee<0x'(pj;-6Џ. 6U|ѨopѨf%T>d[A@fN7v))rN>[ؕ u kHYL}]L'|G~ -a;G#S.`JTF?Kv0dN"C+WW~2WJa -0Ĵ9-Io9mTd{5L3ZjݮR.g1@*1VfU~i*#"6,Ab7K =W!4ܯ -cyt@pyӻocH^XT2xo  }盏\^2Sӡbf!I: 79MM -!^j  ϨG.j{zQׁ4B|1W#U׾ӫxIԎ^/W} Tux\ c۲a]Ca#V>cSQm)7`+^E)Of{F" -HaS|JQ(QSulB- wQM +(i,Xʃ/_&q[?bG(f 1#fRr'U HRdߖyQ e55U3${UO$auBE -6fKƸԥYnfoJw9c F3nɃ2, o7Q#@4hG]+ESj^u qAԯJ9pvqM1JjPnMh@a1M6Ӥx;CHKemd~m?Ǭzig͏˰{Kmob -3_O~sTEyٮ%Ľ1$ -;xAv7 -D)iN .Eupb*:gl|SHQkԓ9"|z{f;S;7|2`%`bRӵ789F찄jR1zB(fFxstY*9G|&4;tV񧦏?G%k-}V,𬴁 n2Ya-^Rtuw2uܶ'ljj -% - s Ggd ->>bjYq?e]rA[~Y&M^C;;5lP`Yo۝QZ$!"˳\h:g[if(zc9:'_q7P&ljaz #?Q&gMpitSV$S=4:a<1E/-N=* bh説' R(\R=?@}{@A*_υf6j~Cj\mG -~%#W퉨í_n~/|P#i48Ѓ-YWQ>ܡv%w&*8+LUۉ^ӯ/H>RvXtfgd[g|ƏH;}BcFd&yAH ^kH)5/'fb)h Lb̤L$xXmΙVM9-Yh śU6,j/Lጲ ,]* [T̜w֤Gw.Mi+1b%x}G/X֒6[VavW -bzQ?Ddt^h'$.Ӝ):KLuGׇ/̠~8CsWRBȬDR^Ѱ_8L'Ծs2 -YijO+v~~v*W>ήojw֮ ֡WZ xFV7v"o*ۿ`~Q'pX<ܰ.-la=S3<;an93X w1rYdxtsu)}y -0T8d;Iqk "BD6=yEOdwMd18AVzzqm#8xIqy-W  rzR'٨kI>%rtfD)8#nAC 6}IA,? ؁|[#{72.ױ 3X [ "U75^Yd mOB%!)O~JҩD3T[R3Ss6GNo:yhԇ&UOԐX<kaCMIϸ_-RX2PuZ<}tgA@1,(PpAF F*  T")sUs2'"=\ Х✢ -U$#RZCơ֣dZ'`x8-`G~>3\0j6}Lt`JJAODmw!<T7BQ2 B5[\!d+DѐPC[ޤeRLp[nd#ѣo9v7Wq7SL ,T JQoSc#߯pA( 1w|.MCh5 ʬ<@ g53<)<|H˧\"Ǝ5D I6a -2uEFV9&"]$Znp3I>r —,8^T}WhS܊ttt4'RC kơrޅ o5r PHRDzϸXayۺ*u94ޭp5}I[3QZ3 -0rF&m@I%\5wcZ3&%~/! >Xьeypk#ޘUx+?hxTe6eS-DBNJZXl[xWg@oLi}4\jׂ}qدo3Vh"⡠b/6g8m|Fیx<*|ĘFMymN' nt]/' -=j:Q)"$z}Y+ {]J\mew&[\~Q 4{]y5U]O8F JCw/op6Vw+ۧmPieJF5"Sk*A:^=D"{YMq6'SZo*qRnQIqZT8.+T6a1n4k954~ˇ&8,Cp'lrWlcNgw4U?84c_ 뎕ƔܓgoLJV1 ]f~j @Ln"0tP^$ݴ_g# ]L2QY]$ztYeg?Zܹ נּ-wf,8&&~2BErytɁϵ&KgmDžVxx}F~q!$gκP=fכʵ,͡CQn.pG!.(%*/Ca 0@ F.dgg&ErcrER|҆i?dU'4s!\iS?>Vl_D=gġ( rN>y]nJ;'Md&~$ $ ЄL.-":W폇Dͻ2Foki3r*Thx=bi4΂jM';4* $!w1jϨ9c秶cF%4n(bC[Ax?y գV8m-7YZUG2zCCb:2(H2Xvos<}N;4BubzF,h需'e-fzSD_S𰈻؊fw4}w]3*@wX\%Zm=?K2Wʭl ru}rkkeVUN $@ H@͚KnZšUuĮr72QqOv"%qrWBR?Iy_ +Wc#MUFiܪZ5%ڴJ:My(2>/ ON `3|tKdrplG#f <"qB$ڤt' Ss*"4dxժApwVr$Y8.NX*yr<@ QWBaR<0-[D?'avPY*m(Y+QmC:i5N)tM1}#jl;SIk897}cY"d5&@ L86)\5p6~C8h~-BPABWPw}`nD;`§_Ž&DI^weONoEKhLnlЇ3(:*K)nVH- m7wB[[Y[VdJMhtQ1V2y7MГ*2O bXȪY5T %="ɐ\~@`1UiFġvf] ]/}d''9%֙J?&GG̩DA7hC,T@Yt޺gmF( 6?{]βCTh#|(9@:IuEww9FP aGMr"P5WnRn)`PJ?ba$/;mxkSsDR1[> VKOΎ4\jPfe6yvu$B,CIL@"}'\ 0]_M&\ISBM ʇh Ns:-괒،\2YS9QvN4dݤ> Hsk YT_f0:΋ݨJz -³ډ[Aَ+Msʎ"}hE3 .SrT9s%SK{&붙rwiI .~aq:k2 ]8HE+TseBys!(a>\OvlTh8:_O>GTw$ƯM22H_(MT4@Kg; XINz3@)sD߆UedgLϻL}:a. .ƈ v8)mI9Q"Z&uoL̉Q@ce* Hotw4DxKp"8Tf@~/ERj.a;vpAO=AZD'`^gbܣ7ڼņP*{ʹ%XÅk죵K pwica: k| -4T+jy]Rߓ|N`[-+ͱ݇Q^koqSk?wMY`.|d GX:4?V5փs.j|钤$1w ߽5Ďb l~\OS i~;kI})#hKgyrMDpN-.A.^^ -\sچZ\i l~ʔz7gyx3>mGaX#5[cO?r9W8S1CiJb{< ]<^{1!]8Q?uJJh)w~[)ɚ 3). Q:'=uĎ^xTF#h 3:f*L:Ƃ>2ι2tVT@KJC1CcNInJ *\oxc" 8wck^VM+;h͞X >r x:{쨿a |s66,S`+oڧ0R%؀dA^)' c39R, Q]WEˍ26˧j\5ϾH)2@ᨩl@-^Y /4Z閄 )Ξ=Zg\,990 d;ROm[7KZ+ܦ`{z q__s KDr!:I]hhjcs~Z_7c(Bh+N#%E~[ ~!Z;f›?ey,|`VNurSOFm,+nq#\pf1 -yc_I_B ,B[YM#V&ZvJz᭲p%6ݽc;ٱ,%;y!4UUЙ$R ?pb>\ϯDa"j g>Ί?2 7 D>PhjZ6AoJn`獒 ľrNLܳ_5^.p$Iڅn%:s~%T+dR<π;h;p$A Y}@ڞU8r,X1 39KAq#)ڝ'Ը>8M@&V3RG cY,D^J%؉aoa ҕJ|hm"~7ٕP@VX֚PB)+-}]HIńL0ϡRֺ9ԹōEg ɗ/cQ"V4nC`)<:Xt)Ap]!bQ8!/xVb&J%0r`;Qb37WJ/5jBZ&`0Y 2*A?m^-yLjUU{~֬.w2 cMQND%s|he O.ibmpV.\'Ÿ;c" -l[-ϣlo\L6uXmg>׵0),<iʦ61p5|ݒ^_y,?]1N(PyPs碍__ڳBM%lzWXV~`ȁѶ:zȟi`C ɐe΍v/EަIz0?X߆<+.Xpi -æde< 7hOy!yGM= ?h  c? T~^vn& h ^U8UB}="rb-#!̼7eLM6b2vOʕZ 2Sp+'"E -{aL?uX:yCJ9%%?ǞrTR*xk.ms;!䮓M_j>Z*[˳p2gnq0TŻz0o NJɡ+) FkHDvs7CQ}0.M#s7ChScN7W\GH=9ָgYurRd̖x9l sU L* 8:7CB Æ籵 JY,~f"MJVGF"|m/r![$c[udٺHt&Jd%QG۟Kիt5 ^ø7J -endstream -endobj -498 0 obj -<< -/Type /ObjStm -/N 100 -/First 940 -/Length 22123 ->> -stream -497 0 499 20 500 246 501 300 502 991 503 1550 504 1648 505 1680 506 2304 507 2694 -508 3325 509 3941 510 4605 511 5215 512 5722 513 6361 514 6840 515 7192 517 7828 519 8180 -521 8538 523 8882 525 9203 527 9527 529 9750 531 9973 533 10227 535 10791 537 11129 539 11349 -541 11579 543 11920 545 12140 547 12369 549 12782 551 13058 155 13627 108 13766 121 13905 279 14045 -173 14183 278 14322 321 14460 275 14598 120 14736 110 14874 320 15012 277 15148 174 15284 322 15422 -276 15557 171 15692 109 15831 200 15970 111 16109 175 16221 236 16333 308 16445 393 16557 437 16669 -472 16781 552 16893 553 17006 554 17078 555 17143 100 17211 96 17281 92 17363 88 17444 84 17513 -80 17595 76 17677 72 17759 68 17841 64 17910 60 18028 56 18084 52 18202 48 18271 44 18340 -40 18458 36 18527 32 18609 28 18691 24 18773 20 18842 16 18960 12 19041 8 19121 4 19186 -556 19278 557 19446 558 19607 559 19771 560 19999 561 20207 562 20444 563 20642 564 20849 565 21018 -% 497 0 obj -[892.9] -% 499 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] -% 500 0 obj -[877 323.4 384.9 323.4 569.5 569.5 569.5] -% 501 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] -% 502 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] -% 503 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] -% 504 0 obj -[826.4 295.1 826.4] -% 505 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] -% 506 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] -% 507 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] -% 508 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] -% 509 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] -% 510 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] -% 511 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] -% 512 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] -% 513 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] -% 514 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] -% 515 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] -% 517 0 obj -<< -/Type /FontDescriptor -/FontName /JVXWMJ+CMBX10 -/Flags 4 -/FontBBox [-56 -250 1164 750] -/Ascent 694 -/CapHeight 686 -/Descent -194 -/ItalicAngle 0 -/StemV 114 -/XHeight 444 -/CharSet (/A/B/C/D/E/F/G/H/I/K/L/M/N/O/P/R/S/U/a/b/c/colon/d/e/f/fi/five/four/g/hyphen/i/k/l/m/n/o/one/p/period/r/s/seven/six/t/three/two/u/v/w/zero) -/FontFile 516 0 R ->> -% 519 0 obj -<< -/Type /FontDescriptor -/FontName /VZSPNB+CMBX12 -/Flags 4 -/FontBBox [-53 -251 1139 750] -/Ascent 694 -/CapHeight 686 -/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 518 0 R ->> -% 521 0 obj -<< -/Type /FontDescriptor -/FontName /WARYBH+CMCSC10 -/Flags 4 -/FontBBox [14 -250 1077 750] -/Ascent 514 -/CapHeight 683 -/Descent 0 -/ItalicAngle 0 -/StemV 72 -/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 520 0 R ->> -% 523 0 obj -<< -/Type /FontDescriptor -/FontName /QZSJAN+CMEX10 -/Flags 4 -/FontBBox [-24 -2960 1454 772] -/Ascent 40 -/CapHeight 0 -/Descent -600 -/ItalicAngle 0 -/StemV 47 -/XHeight 431 -/CharSet (/braceleftBig/braceleftbigg/bracerightBig/parenleftbig/parenrightbig/radicalbig/summationdisplay/summationtext) -/FontFile 522 0 R ->> -% 525 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 524 0 R ->> -% 527 0 obj -<< -/Type /FontDescriptor -/FontName /OFGSEC+CMMI6 -/Flags 4 -/FontBBox [11 -250 1241 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 85 -/XHeight 431 -/CharSet (/C/delta/i) -/FontFile 526 0 R ->> -% 529 0 obj -<< -/Type /FontDescriptor -/FontName /CFAIUE+CMMI7 -/Flags 4 -/FontBBox [-1 -250 1171 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 81 -/XHeight 431 -/CharSet (/T/e/l/n/v) -/FontFile 528 0 R ->> -% 531 0 obj -<< -/Type /FontDescriptor -/FontName /VCFHMD+CMMI8 -/Flags 4 -/FontBBox [-24 -250 1110 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 78 -/XHeight 431 -/CharSet (/A/C/E/H/L/O/P/R/S/T/delta/i/j/l/m/n/r/s) -/FontFile 530 0 R ->> -% 533 0 obj -<< -/Type /FontDescriptor -/FontName /KZBLKD+CMR10 -/Flags 4 -/FontBBox [-40 -250 1009 750] -/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 532 0 R ->> -% 535 0 obj -<< -/Type /FontDescriptor -/FontName /ZTRAPY+CMR12 -/Flags 4 -/FontBBox [-34 -251 988 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle 0 -/StemV 65 -/XHeight 431 -/CharSet (/A/C/I/N/O/R/S/T/U/V/a/c/colon/comma/d/e/f/five/g/hyphen/i/l/m/n/o/one/p/period/quotedblleft/quotedblright/r/s/t/two/v/w/y/zero) -/FontFile 534 0 R ->> -% 537 0 obj -<< -/Type /FontDescriptor -/FontName /TQVOAL+CMR7 -/Flags 4 -/FontBBox [-27 -250 1122 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle 0 -/StemV 79 -/XHeight 431 -/CharSet (/one/plus) -/FontFile 536 0 R ->> -% 539 0 obj -<< -/Type /FontDescriptor -/FontName /CGCFOU+CMR8 -/Flags 4 -/FontBBox [-36 -250 1070 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle 0 -/StemV 76 -/XHeight 431 -/CharSet (/equal/one/two/zero) -/FontFile 538 0 R ->> -% 541 0 obj -<< -/Type /FontDescriptor -/FontName /WYYAGH+CMSY10 -/Flags 4 -/FontBBox [-29 -960 1116 775] -/Ascent 750 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 40 -/XHeight 431 -/CharSet (/Rfractur/backslash/bar/braceleft/braceright/bullet/element/greaterequal/minus/negationslash/propersubset/propersuperset/union) -/FontFile 540 0 R ->> -% 543 0 obj -<< -/Type /FontDescriptor -/FontName /PXBGHL+CMSY7 -/Flags 4 -/FontBBox [-15 -951 1251 782] -/Ascent 750 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 49 -/XHeight 431 -/CharSet (/minus) -/FontFile 542 0 R ->> -% 545 0 obj -<< -/Type /FontDescriptor -/FontName /VOEFGO+CMSY8 -/Flags 4 -/FontBBox [-30 -955 1185 779] -/Ascent 750 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 46 -/XHeight 431 -/CharSet (/minus/multiply) -/FontFile 544 0 R ->> -% 547 0 obj -<< -/Type /FontDescriptor -/FontName /PJRLOW+CMTI10 -/Flags 4 -/FontBBox [-35 -250 1124 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 68 -/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/zero) -/FontFile 546 0 R ->> -% 549 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 548 0 R ->> -% 551 0 obj -<< -/Type /FontDescriptor -/FontName /EXISZL+CMTT10 -/Flags 4 -/FontBBox [-4 -233 537 696] -/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/Z/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/percent/period/plus/q/quotedbl/quoteleft/quoteright/r/s/semicolon/seven/slash/t/three/two/u/underscore/v/w/x/y/z/zero) -/FontFile 550 0 R ->> -% 155 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /JVXWMJ+CMBX10 -/FontDescriptor 517 0 R -/FirstChar 12 -/LastChar 119 -/Widths 510 0 R ->> -% 108 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /VZSPNB+CMBX12 -/FontDescriptor 519 0 R -/FirstChar 12 -/LastChar 122 -/Widths 515 0 R ->> -% 121 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /WARYBH+CMCSC10 -/FontDescriptor 521 0 R -/FirstChar 39 -/LastChar 121 -/Widths 511 0 R ->> -% 279 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /QZSJAN+CMEX10 -/FontDescriptor 523 0 R -/FirstChar 0 -/LastChar 112 -/Widths 501 0 R ->> -% 173 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /SQUASS+CMMI10 -/FontDescriptor 525 0 R -/FirstChar 14 -/LastChar 122 -/Widths 508 0 R ->> -% 278 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /OFGSEC+CMMI6 -/FontDescriptor 527 0 R -/FirstChar 14 -/LastChar 105 -/Widths 502 0 R ->> -% 321 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /CFAIUE+CMMI7 -/FontDescriptor 529 0 R -/FirstChar 84 -/LastChar 118 -/Widths 499 0 R ->> -% 275 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /VCFHMD+CMMI8 -/FontDescriptor 531 0 R -/FirstChar 14 -/LastChar 115 -/Widths 505 0 R ->> -% 120 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /KZBLKD+CMR10 -/FontDescriptor 533 0 R -/FirstChar 11 -/LastChar 127 -/Widths 512 0 R ->> -% 110 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /ZTRAPY+CMR12 -/FontDescriptor 535 0 R -/FirstChar 34 -/LastChar 121 -/Widths 513 0 R ->> -% 320 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /TQVOAL+CMR7 -/FontDescriptor 537 0 R -/FirstChar 43 -/LastChar 49 -/Widths 500 0 R ->> -% 277 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /CGCFOU+CMR8 -/FontDescriptor 539 0 R -/FirstChar 48 -/LastChar 61 -/Widths 503 0 R ->> -% 174 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /WYYAGH+CMSY10 -/FontDescriptor 541 0 R -/FirstChar 0 -/LastChar 110 -/Widths 507 0 R ->> -% 322 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /PXBGHL+CMSY7 -/FontDescriptor 543 0 R -/FirstChar 0 -/LastChar 0 -/Widths 497 0 R ->> -% 276 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /VOEFGO+CMSY8 -/FontDescriptor 545 0 R -/FirstChar 0 -/LastChar 2 -/Widths 504 0 R ->> -% 171 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /PJRLOW+CMTI10 -/FontDescriptor 547 0 R -/FirstChar 11 -/LastChar 122 -/Widths 509 0 R ->> -% 109 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /BABWJL+CMTI12 -/FontDescriptor 549 0 R -/FirstChar 45 -/LastChar 118 -/Widths 514 0 R ->> -% 200 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /EXISZL+CMTT10 -/FontDescriptor 551 0 R -/FirstChar 33 -/LastChar 126 -/Widths 506 0 R ->> -% 111 0 obj -<< -/Type /Pages -/Count 6 -/Parent 552 0 R -/Kids [103 0 R 113 0 R 117 0 R 123 0 R 151 0 R 157 0 R] ->> -% 175 0 obj -<< -/Type /Pages -/Count 6 -/Parent 552 0 R -/Kids [169 0 R 192 0 R 197 0 R 210 0 R 222 0 R 228 0 R] ->> -% 236 0 obj -<< -/Type /Pages -/Count 6 -/Parent 552 0 R -/Kids [233 0 R 238 0 R 243 0 R 253 0 R 272 0 R 293 0 R] ->> -% 308 0 obj -<< -/Type /Pages -/Count 6 -/Parent 552 0 R -/Kids [305 0 R 317 0 R 331 0 R 350 0 R 368 0 R 382 0 R] ->> -% 393 0 obj -<< -/Type /Pages -/Count 6 -/Parent 552 0 R -/Kids [390 0 R 395 0 R 401 0 R 407 0 R 417 0 R 425 0 R] ->> -% 437 0 obj -<< -/Type /Pages -/Count 6 -/Parent 552 0 R -/Kids [434 0 R 439 0 R 445 0 R 450 0 R 458 0 R 463 0 R] ->> -% 472 0 obj -<< -/Type /Pages -/Count 6 -/Parent 553 0 R -/Kids [469 0 R 475 0 R 481 0 R 485 0 R 489 0 R 493 0 R] ->> -% 552 0 obj -<< -/Type /Pages -/Count 36 -/Parent 554 0 R -/Kids [111 0 R 175 0 R 236 0 R 308 0 R 393 0 R 437 0 R] ->> -% 553 0 obj -<< -/Type /Pages -/Count 6 -/Parent 554 0 R -/Kids [472 0 R] ->> -% 554 0 obj -<< -/Type /Pages -/Count 42 -/Kids [552 0 R 553 0 R] ->> -% 555 0 obj -<< -/Type /Outlines -/First 4 0 R -/Last 4 0 R -/Count 1 ->> -% 100 0 obj -<< -/Title 101 0 R -/A 98 0 R -/Parent 4 0 R -/Prev 96 0 R ->> -% 96 0 obj -<< -/Title 97 0 R -/A 94 0 R -/Parent 4 0 R -/Prev 92 0 R -/Next 100 0 R ->> -% 92 0 obj -<< -/Title 93 0 R -/A 90 0 R -/Parent 4 0 R -/Prev 64 0 R -/Next 96 0 R ->> -% 88 0 obj -<< -/Title 89 0 R -/A 86 0 R -/Parent 64 0 R -/Prev 84 0 R ->> -% 84 0 obj -<< -/Title 85 0 R -/A 82 0 R -/Parent 64 0 R -/Prev 80 0 R -/Next 88 0 R ->> -% 80 0 obj -<< -/Title 81 0 R -/A 78 0 R -/Parent 64 0 R -/Prev 76 0 R -/Next 84 0 R ->> -% 76 0 obj -<< -/Title 77 0 R -/A 74 0 R -/Parent 64 0 R -/Prev 72 0 R -/Next 80 0 R ->> -% 72 0 obj -<< -/Title 73 0 R -/A 70 0 R -/Parent 64 0 R -/Prev 68 0 R -/Next 76 0 R ->> -% 68 0 obj -<< -/Title 69 0 R -/A 66 0 R -/Parent 64 0 R -/Next 72 0 R ->> -% 64 0 obj -<< -/Title 65 0 R -/A 62 0 R -/Parent 4 0 R -/Prev 56 0 R -/Next 92 0 R -/First 68 0 R -/Last 88 0 R -/Count -6 ->> -% 60 0 obj -<< -/Title 61 0 R -/A 58 0 R -/Parent 56 0 R ->> -% 56 0 obj -<< -/Title 57 0 R -/A 54 0 R -/Parent 4 0 R -/Prev 44 0 R -/Next 64 0 R -/First 60 0 R -/Last 60 0 R -/Count -1 ->> -% 52 0 obj -<< -/Title 53 0 R -/A 50 0 R -/Parent 44 0 R -/Prev 48 0 R ->> -% 48 0 obj -<< -/Title 49 0 R -/A 46 0 R -/Parent 44 0 R -/Next 52 0 R ->> -% 44 0 obj -<< -/Title 45 0 R -/A 42 0 R -/Parent 4 0 R -/Prev 20 0 R -/Next 56 0 R -/First 48 0 R -/Last 52 0 R -/Count -2 ->> -% 40 0 obj -<< -/Title 41 0 R -/A 38 0 R -/Parent 20 0 R -/Prev 36 0 R ->> -% 36 0 obj -<< -/Title 37 0 R -/A 34 0 R -/Parent 20 0 R -/Prev 32 0 R -/Next 40 0 R ->> -% 32 0 obj -<< -/Title 33 0 R -/A 30 0 R -/Parent 20 0 R -/Prev 28 0 R -/Next 36 0 R ->> -% 28 0 obj -<< -/Title 29 0 R -/A 26 0 R -/Parent 20 0 R -/Prev 24 0 R -/Next 32 0 R ->> -% 24 0 obj -<< -/Title 25 0 R -/A 22 0 R -/Parent 20 0 R -/Next 28 0 R ->> -% 20 0 obj -<< -/Title 21 0 R -/A 18 0 R -/Parent 4 0 R -/Prev 16 0 R -/Next 44 0 R -/First 24 0 R -/Last 40 0 R -/Count -5 ->> -% 16 0 obj -<< -/Title 17 0 R -/A 14 0 R -/Parent 4 0 R -/Prev 12 0 R -/Next 20 0 R ->> -% 12 0 obj -<< -/Title 13 0 R -/A 10 0 R -/Parent 4 0 R -/Prev 8 0 R -/Next 16 0 R ->> -% 8 0 obj -<< -/Title 9 0 R -/A 6 0 R -/Parent 4 0 R -/Next 12 0 R ->> -% 4 0 obj -<< -/Title 5 0 R -/A 1 0 R -/Parent 555 0 R -/First 8 0 R -/Last 100 0 R -/Count -10 ->> -% 556 0 obj -<< -/Names [(Doc-Start) 107 0 R (Item.1) 280 0 R (Item.10) 356 0 R (Item.11) 357 0 R (Item.12) 358 0 R (Item.13) 428 0 R] -/Limits [(Doc-Start) (Item.13)] ->> -% 557 0 obj -<< -/Names [(Item.14) 429 0 R (Item.15) 430 0 R (Item.16) 431 0 R (Item.2) 281 0 R (Item.3) 282 0 R (Item.4) 323 0 R] -/Limits [(Item.14) (Item.4)] ->> -% 558 0 obj -<< -/Names [(Item.5) 324 0 R (Item.6) 325 0 R (Item.7) 353 0 R (Item.8) 354 0 R (Item.9) 355 0 R (appendix.A) 95 0 R] -/Limits [(Item.5) (appendix.A)] ->> -% 559 0 obj -<< -/Names [(cite.BLACS) 496 0 R (cite.BREZINA_VANEK) 178 0 R (cite.CAI_SARKIS) 296 0 R (cite.Cai_Widlund_92) 256 0 R (cite.EFSTATHIOU) 297 0 R (cite.MLD2P4_TOMS) 288 0 R] -/Limits [(cite.BLACS) (cite.MLD2P4_TOMS)] ->> -% 560 0 obj -<< -/Names [(cite.MPI1) 183 0 R (cite.MPI2) 216 0 R (cite.PSBLAS3) 181 0 R (cite.PSBLASGUIDE) 182 0 R (cite.SUPERLU) 225 0 R (cite.SUPERLUDIST) 226 0 R] -/Limits [(cite.MPI1) (cite.SUPERLUDIST)] ->> -% 561 0 obj -<< -/Names [(cite.Saad_book) 289 0 R (cite.StubenGMD69_99) 283 0 R (cite.TUMINARO_TONG) 284 0 R (cite.UMFPACK) 217 0 R (cite.VANEK_MANDEL_BREZINA) 179 0 R (cite.aaecc_07) 286 0 R] -/Limits [(cite.Saad_book) (cite.aaecc_07)] ->> -% 562 0 obj -<< -/Names [(cite.apnum_07) 287 0 R (cite.blas1) 215 0 R (cite.blas2) 214 0 R (cite.blas3) 213 0 R (cite.dd1_94) 257 0 R (cite.dd2_96) 176 0 R] -/Limits [(cite.apnum_07) (cite.dd2_96)] ->> -% 563 0 obj -<< -/Names [(cite.para_04) 285 0 R (cite.psblas_00) 180 0 R (equation.1.1) 172 0 R (equation.4.2) 334 0 R (equation.4.3) 335 0 R (equation.4.4) 336 0 R] -/Limits [(cite.para_04) (equation.4.4)] ->> -% 564 0 obj -<< -/Names [(figure.1) 310 0 R (figure.2) 371 0 R (figure.3) 385 0 R (figure.4) 386 0 R (figure.5) 387 0 R (page.1) 106 0 R] -/Limits [(figure.1) (page.1)] ->> -% 565 0 obj -<< -/Names [(page.10) 255 0 R (page.11) 274 0 R (page.12) 295 0 R (page.13) 307 0 R (page.14) 319 0 R (page.15) 333 0 R] -/Limits [(page.10) (page.15)] ->> - -endstream -endobj -585 0 obj -<< - /Title (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS, V. 2.0) /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-1.40.15)/Keywords() -/CreationDate (D:20160229132757Z) -/ModDate (D:20160229132757Z) -/Trapped /False -/PTEX.Fullbanner (This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014) kpathsea version 6.2.0) ->> -endobj -567 0 obj -<< -/Type /ObjStm -/N 18 -/First 153 -/Length 2751 ->> -stream -566 0 568 164 569 329 570 493 571 656 572 813 573 988 574 1163 575 1368 576 1583 -577 1773 578 1882 579 1994 580 2104 581 2215 582 2302 583 2392 584 2425 -% 566 0 obj -<< -/Names [(page.16) 352 0 R (page.17) 370 0 R (page.18) 384 0 R (page.19) 392 0 R (page.2) 115 0 R (page.20) 397 0 R] -/Limits [(page.16) (page.20)] ->> -% 568 0 obj -<< -/Names [(page.21) 403 0 R (page.22) 409 0 R (page.23) 419 0 R (page.24) 427 0 R (page.25) 436 0 R (page.26) 441 0 R] -/Limits [(page.21) (page.26)] ->> -% 569 0 obj -<< -/Names [(page.27) 447 0 R (page.28) 452 0 R (page.29) 460 0 R (page.3) 199 0 R (page.30) 465 0 R (page.31) 471 0 R] -/Limits [(page.27) (page.31)] ->> -% 570 0 obj -<< -/Names [(page.32) 477 0 R (page.33) 483 0 R (page.34) 487 0 R (page.35) 491 0 R (page.36) 495 0 R (page.4) 212 0 R] -/Limits [(page.32) (page.4)] ->> -% 571 0 obj -<< -/Names [(page.5) 224 0 R (page.6) 230 0 R (page.7) 235 0 R (page.8) 240 0 R (page.9) 245 0 R (page.i) 119 0 R] -/Limits [(page.5) (page.i)] ->> -% 572 0 obj -<< -/Names [(page.ii) 125 0 R (page.iii) 153 0 R (page.iv) 159 0 R (section*.1) 7 0 R (section*.2) 154 0 R (section*.3) 99 0 R] -/Limits [(page.ii) (section*.3)] ->> -% 573 0 obj -<< -/Names [(section.1) 11 0 R (section.2) 15 0 R (section.3) 19 0 R (section.4) 43 0 R (section.5) 55 0 R (section.6) 63 0 R] -/Limits [(section.1) (section.6)] ->> -% 574 0 obj -<< -/Names [(section.7) 91 0 R (subsection.3.1) 23 0 R (subsection.3.2) 27 0 R (subsection.3.3) 31 0 R (subsection.3.4) 35 0 R (subsection.3.5) 39 0 R] -/Limits [(section.7) (subsection.3.5)] ->> -% 575 0 obj -<< -/Names [(subsection.4.1) 47 0 R (subsection.4.2) 51 0 R (subsection.5.1) 59 0 R (subsection.6.1) 67 0 R (subsection.6.2) 71 0 R (subsection.6.3) 75 0 R] -/Limits [(subsection.4.1) (subsection.6.3)] ->> -% 576 0 obj -<< -/Names [(subsection.6.4) 79 0 R (subsection.6.5) 83 0 R (subsection.6.6) 87 0 R (table.1) 359 0 R (table.2) 360 0 R (table.3) 442 0 R] -/Limits [(subsection.6.4) (table.3)] ->> -% 577 0 obj -<< -/Names [(table.4) 448 0 R (table.5) 361 0 R (title.0) 3 0 R] -/Limits [(table.4) (title.0)] ->> -% 578 0 obj -<< -/Kids [556 0 R 557 0 R 558 0 R 559 0 R 560 0 R 561 0 R] -/Limits [(Doc-Start) (cite.aaecc_07)] ->> -% 579 0 obj -<< -/Kids [562 0 R 563 0 R 564 0 R 565 0 R 566 0 R 568 0 R] -/Limits [(cite.apnum_07) (page.26)] ->> -% 580 0 obj -<< -/Kids [569 0 R 570 0 R 571 0 R 572 0 R 573 0 R 574 0 R] -/Limits [(page.27) (subsection.3.5)] ->> -% 581 0 obj -<< -/Kids [575 0 R 576 0 R 577 0 R] -/Limits [(subsection.4.1) (title.0)] ->> -% 582 0 obj -<< -/Kids [578 0 R 579 0 R 580 0 R 581 0 R] -/Limits [(Doc-Start) (title.0)] ->> -% 583 0 obj -<< -/Dests 582 0 R ->> -% 584 0 obj -<< -/Type /Catalog -/Pages 554 0 R -/Outlines 555 0 R -/Names 583 0 R - /PageMode/UseOutlines/PageLabels<>2<>6<>]>> -/OpenAction 102 0 R ->> - -endstream -endobj -586 0 obj -<< -/Type /XRef -/Index [0 587] -/Size 587 -/W [1 3 1] -/Root 584 0 R -/Info 585 0 R -/ID [<4DF7B28C358F123EFFC239F357749D38> <4DF7B28C358F123EFFC239F357749D38>] -/Length 2935 ->> -stream -Ny6Y=XWV"U  -#T  $S +R6Q7PDOTN5M5'L58K5WJ 5]I!"H#$'G%&,F'(2E)*7D+,=C-.AB/0EA123745%4-6:89>;3<,&A?@CDEFGHIJKLMNOPQRSTUVWXYZ]B[\$`^-_cba.x3(07^FbYXW_ -    q_5 %Y!PQ[ZN()',&T*O\/-.130v28845:<9;>?@ABHE=CKLIJKLMNOPQRZ[GXFS+2/)'UVW`aGHIM]\]_YI^JVbc555a5`[595 555 5 -5 55T5 .*1555555555 *55555555 5!5"5#5$5%5152535.55&5(5)5*5+5,5-5754555;5<50595/;{565K5=5>5?5@5A5B5C5D5E5G5:_65F5O5P5Q5I5L5Hz<5J:5R5M5N5U5T5X5S5V5Z5[5^5Y5\5a5b5c5`5_9  -   =;&Mx #$%"(!&*-)+0/3.ܹ1<5846;:>9,<B?t@RCWDcSTU  -   `Zc/R gmb6(Z( 6!O""#=>?@Z[\]^_`abc7v4777777777 7 -7 7 7 7777sdN -endstream -endobj -startxref -557390 -%%EOF diff --git a/docs/mld2p4-2.1-guide.pdf b/docs/mld2p4-2.1-guide.pdf index 649c0489..7d0a656f 100644 --- a/docs/mld2p4-2.1-guide.pdf +++ b/docs/mld2p4-2.1-guide.pdf @@ -3361,7 +3361,7 @@ endstream endobj 435 0 obj << -/Length 4494 +/Length 4559 >> stream 0 g 0 G @@ -3489,7 +3489,7 @@ q []0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q BT -/F44 10.9091 Tf 563.081 143.921 Td [('DIAG')]TJ 0 -13.549 Td [('BJAC')]TJ 0 -13.549 Td [('AS')]TJ +/F44 10.9091 Tf 563.081 143.921 Td [('JACOBI')]TJ 0 -13.549 Td [('BJAC')]TJ 0 -13.549 Td [('AS')]TJ ET q 1 0 0 1 625.752 112.758 cm @@ -3503,7 +3503,7 @@ q []0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q BT -/F15 10.9091 Tf 695.229 143.921 Td [(Basic)-434(p)1(rede\014ned)-434(one-lev)28(el)-433(preconditioner)]TJ 0 -13.549 Td [(\050i.e.)-534(sm)-1(o)-27(other\051:)-847(diagonal,)-584(blo)-28(c)28(k)-535(Jacobi,)]TJ 0 -13.549 Td [(AS.)]TJ +/F15 10.9091 Tf 695.229 143.921 Td [(Basic)-434(p)1(rede\014ned)-434(one-lev)28(el)-433(preconditioner)]TJ 0 -13.549 Td [(\050i.e.)-357(smo)-27(other\051:)-491(Jacobi)-357(\050with)-356(diagonal)-356(lo-)]TJ 0 -13.549 Td [(cal)-333(solv)27(er\051,)-333(blo)-28(c)28(k)-333(Jacobi,)-334(AS)1(.)]TJ ET q 1 0 0 1 899.632 112.758 cm @@ -3572,7 +3572,7 @@ endstream endobj 440 0 obj << -/Length 10037 +/Length 12420 >> stream 0 g 0 G @@ -3588,385 +3588,471 @@ q 0 g 0 G 0 g 0 G q -1 0 0 1 14.002 196.767 cm +1 0 0 1 14.002 265.708 cm []0 d 0 J 0.398 w 0 0 m 565.57 0 l S Q q -1 0 0 1 14.002 183.018 cm +1 0 0 1 14.002 251.96 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q 1 0 0 1 -292.625 -715.095 cm BT -/F44 10.9091 Tf 312.605 902.178 Td [(what)]TJ +/F44 10.9091 Tf 312.605 971.119 Td [(what)]TJ ET q -1 0 0 1 417.795 898.113 cm +1 0 0 1 417.795 967.055 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F41 10.9091 Tf 423.773 902.178 Td [(d)22(a)67(t)67(a)-378(type)]TJ +/F41 10.9091 Tf 423.773 971.119 Td [(d)22(a)67(t)67(a)-378(type)]TJ ET q -1 0 0 1 536.768 898.113 cm +1 0 0 1 536.768 967.055 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F44 10.9091 Tf 542.746 902.178 Td [(val)]TJ +/F44 10.9091 Tf 542.746 971.119 Td [(val)]TJ ET q -1 0 0 1 639.432 898.113 cm +1 0 0 1 639.432 967.055 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F41 10.9091 Tf 645.41 902.178 Td [(def)89(a)22(ul)67(t)]TJ +/F41 10.9091 Tf 645.41 971.119 Td [(def)89(a)22(ul)67(t)]TJ ET q -1 0 0 1 718.51 898.113 cm +1 0 0 1 718.51 967.055 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F41 10.9091 Tf 724.488 902.178 Td [(comments)]TJ +/F41 10.9091 Tf 724.488 971.119 Td [(comments)]TJ ET q -1 0 0 1 872.198 898.113 cm +1 0 0 1 872.198 967.055 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q q -1 0 0 1 306.627 897.914 cm +1 0 0 1 306.627 966.855 cm []0 d 0 J 0.398 w 0 0 m 565.57 0 l S Q q -1 0 0 1 306.627 870.616 cm +1 0 0 1 306.627 939.558 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F44 10.9091 Tf 312.605 888.23 Td [(mld_sub_ovr_)]TJ 0 -13.549 Td [(SUB_OVR)]TJ +/F44 10.9091 Tf 312.605 957.172 Td [(mld_sub_ovr_)]TJ 0 -13.55 Td [(SUB_OVR)]TJ ET q -1 0 0 1 417.795 870.616 cm +1 0 0 1 417.795 939.558 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F44 10.9091 Tf 423.773 888.23 Td [(integer)]TJ +/F44 10.9091 Tf 423.773 957.172 Td [(integer)]TJ ET q -1 0 0 1 536.768 870.616 cm +1 0 0 1 536.768 939.558 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 542.746 888.23 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 542.746 957.172 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 ET q -1 0 0 1 639.432 870.616 cm +1 0 0 1 639.432 939.558 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 645.41 888.23 Td [(1)]TJ +/F15 10.9091 Tf 645.41 957.172 Td [(1)]TJ ET q -1 0 0 1 718.51 870.616 cm +1 0 0 1 718.51 939.558 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 724.488 888.23 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 724.488 957.172 Td [(Num)28(b)-28(er)-333(of)-334(o)28(v)28(erlap)-333(la)28(y)27(ers.)]TJ ET q -1 0 0 1 872.198 870.616 cm +1 0 0 1 872.198 939.558 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q q -1 0 0 1 306.627 870.417 cm +1 0 0 1 306.627 939.358 cm []0 d 0 J 0.398 w 0 0 m 565.57 0 l S Q q -1 0 0 1 306.627 816.021 cm +1 0 0 1 306.627 884.962 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F44 10.9091 Tf 312.605 860.733 Td [(mld_sub_restr_)]TJ 0 -13.549 Td [(SUB_RESTR)]TJ +/F44 10.9091 Tf 312.605 929.675 Td [(mld_sub_restr_)]TJ 0 -13.549 Td [(SUB_RESTR)]TJ ET q -1 0 0 1 417.795 816.021 cm +1 0 0 1 417.795 884.962 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F44 10.9091 Tf 423.773 860.733 Td [(character\050len=*\051)]TJ +/F44 10.9091 Tf 423.773 929.675 Td [(character\050len=*\051)]TJ ET q -1 0 0 1 536.768 816.021 cm +1 0 0 1 536.768 884.962 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F44 10.9091 Tf 542.746 860.733 Td [('HALO')]TJ 0 -13.549 Td [('NONE')]TJ +/F44 10.9091 Tf 542.746 929.675 Td [('HALO')]TJ 0 -13.549 Td [('NONE')]TJ ET q -1 0 0 1 639.432 816.021 cm +1 0 0 1 639.432 884.962 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F44 10.9091 Tf 645.41 860.733 Td [('HALO')]TJ +/F44 10.9091 Tf 645.41 929.675 Td [('HALO')]TJ ET q -1 0 0 1 718.51 816.021 cm +1 0 0 1 718.51 884.962 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F15 10.9091 Tf 724.488 860.733 Td [(T)28(yp)-28(e)-501(of)-501(restriction)-501(op)-28(erator:)]TJ/F44 10.9091 Tf 0 -13.549 Td [('HALO')]TJ/F15 10.9091 Tf 42.331 0 Td [(for)-731(taking)-730(in)27(to)-730(ac-)]TJ -42.331 -13.549 Td [(coun)28(t)-354(the)-354(o)28(v)28(erlap,)]TJ/F44 10.9091 Tf 90.45 0 Td [('NONE')]TJ/F15 10.9091 Tf 38.222 0 Td [(for)]TJ -128.672 -13.549 Td [(neglecting)-333(it.)]TJ +/F15 10.9091 Tf 724.488 929.675 Td [(T)28(yp)-28(e)-501(of)-501(restriction)-501(op)-28(erator:)]TJ/F44 10.9091 Tf 0 -13.549 Td [('HALO')]TJ/F15 10.9091 Tf 42.331 0 Td [(for)-731(taking)-730(in)27(to)-730(ac-)]TJ -42.331 -13.55 Td [(coun)28(t)-354(the)-354(o)28(v)28(erlap,)]TJ/F44 10.9091 Tf 90.45 0 Td [('NONE')]TJ/F15 10.9091 Tf 38.222 0 Td [(for)]TJ -128.672 -13.549 Td [(neglecting)-333(it.)]TJ ET q -1 0 0 1 872.198 816.021 cm +1 0 0 1 872.198 884.962 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q q -1 0 0 1 306.627 815.822 cm +1 0 0 1 306.627 884.763 cm []0 d 0 J 0.398 w 0 0 m 565.57 0 l S Q q -1 0 0 1 306.627 761.426 cm +1 0 0 1 306.627 830.367 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F44 10.9091 Tf 312.605 806.138 Td [(mld_sub_prol_)]TJ 0 -13.549 Td [(SUB_PROL)]TJ +/F44 10.9091 Tf 312.605 875.08 Td [(mld_sub_prol_)]TJ 0 -13.55 Td [(SUB_PROL)]TJ ET q -1 0 0 1 417.795 761.426 cm +1 0 0 1 417.795 830.367 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F44 10.9091 Tf 423.773 806.138 Td [(character\050len=*\051)]TJ +/F44 10.9091 Tf 423.773 875.08 Td [(character\050len=*\051)]TJ ET q -1 0 0 1 536.768 761.426 cm +1 0 0 1 536.768 830.367 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F44 10.9091 Tf 542.746 806.138 Td [('SUM')]TJ 0 -13.549 Td [('NONE')]TJ +/F44 10.9091 Tf 542.746 875.08 Td [('SUM')]TJ 0 -13.55 Td [('NONE')]TJ ET q -1 0 0 1 639.432 761.426 cm +1 0 0 1 639.432 830.367 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F44 10.9091 Tf 645.41 806.138 Td [('NONE')]TJ +/F44 10.9091 Tf 645.41 875.08 Td [('NONE')]TJ ET q -1 0 0 1 718.51 761.426 cm +1 0 0 1 718.51 830.367 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q BT -/F15 10.9091 Tf 724.488 806.138 Td [(T)28(yp)-28(e)-560(of)-561(prolon)1(gation)-561(op)-27(e)-1(r)1(a-)]TJ 0 -13.549 Td [(tor:)]TJ/F44 10.9091 Tf 21.445 0 Td [('SUM')]TJ/F15 10.9091 Tf 31.465 0 Td [(for)-259(adding)-260(th)1(e)-260(con-)]TJ -52.91 -13.549 Td [(tributions)-622(from)-623(t)1(he)-623(o)28(v)28(erlap,)]TJ/F44 10.9091 Tf 0 -13.55 Td [('NONE')]TJ/F15 10.9091 Tf 37.999 0 Td [(for)-333(neglecting)-334(them.)]TJ +/F15 10.9091 Tf 724.488 875.08 Td [(T)28(yp)-28(e)-560(of)-561(prolon)1(gation)-561(op)-27(e)-1(r)1(a-)]TJ 0 -13.55 Td [(tor:)]TJ/F44 10.9091 Tf 21.445 0 Td [('SUM')]TJ/F15 10.9091 Tf 31.465 0 Td [(for)-259(adding)-260(th)1(e)-260(con-)]TJ -52.91 -13.549 Td [(tributions)-622(from)-623(t)1(he)-623(o)28(v)28(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 ET q -1 0 0 1 872.198 761.426 cm +1 0 0 1 872.198 830.367 cm []0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q q -1 0 0 1 306.627 761.226 cm +1 0 0 1 306.627 830.168 cm []0 d 0 J 0.398 w 0 0 m 565.57 0 l S Q q -1 0 0 1 306.627 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +1 0 0 1 306.627 735.124 cm +[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q BT -/F44 10.9091 Tf 312.605 751.543 Td [(mld_sub_solve_)]TJ 0 -13.549 Td [(SUB_SOLVE)]TJ +/F44 10.9091 Tf 312.605 820.484 Td [(mld_sub_solve_)]TJ 0 -13.549 Td [(SUB_SOLVE)]TJ ET q -1 0 0 1 417.795 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +1 0 0 1 417.795 735.124 cm +[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q BT -/F44 10.9091 Tf 423.773 751.543 Td [(character\050len=*\051)]TJ +/F44 10.9091 Tf 423.773 820.484 Td [(character\050len=*\051)]TJ ET q -1 0 0 1 536.768 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +1 0 0 1 536.768 735.124 cm +[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q BT -/F44 10.9091 Tf 542.746 751.543 Td [('ILU')]TJ 0 -13.549 Td [('MILU')]TJ 0 -13.55 Td [('ILUT')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ +/F44 10.9091 Tf 542.746 820.484 Td [('DIAG')]TJ 0 -13.549 Td [('GS')]TJ 0 -13.549 Td [('ILU')]TJ 0 -13.549 Td [('MILU')]TJ 0 -13.55 Td [('ILUT')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ ET q -1 0 0 1 639.432 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +1 0 0 1 639.432 735.124 cm +[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q BT -/F44 10.9091 Tf 645.41 751.543 Td [('ILU')]TJ +/F44 10.9091 Tf 645.41 820.484 Td [('ILU')]TJ ET q -1 0 0 1 718.51 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +1 0 0 1 718.51 735.124 cm +[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q BT -/F15 10.9091 Tf 724.488 751.543 Td [(Prede\014ned)-1775(lo)-28(cal)-1775(solv)28(er:)]TJ 0 -13.549 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-693(MILU\050)]TJ/F22 10.9091 Tf 48.012 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-693(ILU\050)]TJ/F22 10.9091 Tf 38.012 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051,)]TJ -134.459 -13.55 Td [(LU)-931(from)-932(UMFP)83(A)28(CK,)-932(LU)]TJ 0 -13.549 Td [(from)-460(Sup)-28(erLU)-460(\050plus)-461(tr)1(iangu-)]TJ 0 -13.549 Td [(lar)-333(solv)28(e)-1(\051.)]TJ +/F15 10.9091 Tf 724.488 820.484 Td [(Prede\014ned)-651(lo)-28(cal)-652(solv)28(er:)-1081(di-)]TJ 0 -13.549 Td [(agonal)-541(s)-1(calin)1(g,)-594(Gauss-Seidel,)]TJ 0 -13.549 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-693(MILU\050)]TJ/F22 10.9091 Tf 48.012 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-693(ILU\050)]TJ/F22 10.9091 Tf 38.012 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051,)]TJ -134.459 -13.549 Td [(LU)-931(from)-932(UMFP)83(A)28(CK,)-932(LU)]TJ 0 -13.55 Td [(from)-460(Sup)-28(erLU)-460(\050plus)-461(tr)1(iangu-)]TJ 0 -13.549 Td [(lar)-333(solv)28(e)-1(\051.)]TJ ET q -1 0 0 1 872.198 693.281 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +1 0 0 1 872.198 735.124 cm +[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q q -1 0 0 1 306.627 693.082 cm +1 0 0 1 306.627 734.925 cm []0 d 0 J 0.398 w 0 0 m 565.57 0 l S Q q -1 0 0 1 306.627 665.784 cm +1 0 0 1 306.627 707.627 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F44 10.9091 Tf 312.605 683.398 Td [(mld_sub_fillin_)]TJ 0 -13.549 Td [(SUB_FILLIN)]TJ +/F44 10.9091 Tf 312.605 725.241 Td [(mld_sub_fillin_)]TJ 0 -13.549 Td [(SUB_FILLIN)]TJ ET q -1 0 0 1 417.795 665.784 cm +1 0 0 1 417.795 707.627 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F44 10.9091 Tf 423.773 683.398 Td [(integer)]TJ +/F44 10.9091 Tf 423.773 725.241 Td [(integer)]TJ ET q -1 0 0 1 536.768 665.784 cm +1 0 0 1 536.768 707.627 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 542.746 683.398 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 542.746 725.241 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 ET q -1 0 0 1 639.432 665.784 cm +1 0 0 1 639.432 707.627 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 645.41 683.398 Td [(0)]TJ +/F15 10.9091 Tf 645.41 725.241 Td [(0)]TJ ET q -1 0 0 1 718.51 665.784 cm +1 0 0 1 718.51 707.627 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 724.488 683.398 Td [(Fill-in)-550(lev)27(el)]TJ/F22 10.9091 Tf 62.164 0 Td [(p)]TJ/F15 10.9091 Tf 11.495 0 Td [(of)-551(th)1(e)-551(incom-)]TJ -73.659 -13.549 Td [(plete)-333(LU)-334(factorizations.)]TJ +/F15 10.9091 Tf 724.488 725.241 Td [(Fill-in)-550(lev)27(el)]TJ/F22 10.9091 Tf 62.164 0 Td [(p)]TJ/F15 10.9091 Tf 11.495 0 Td [(of)-551(th)1(e)-551(incom-)]TJ -73.659 -13.549 Td [(plete)-333(LU)-334(factorizations.)]TJ ET q -1 0 0 1 872.198 665.784 cm +1 0 0 1 872.198 707.627 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q q -1 0 0 1 306.627 665.585 cm +1 0 0 1 306.627 707.428 cm []0 d 0 J 0.398 w 0 0 m 565.57 0 l S Q q -1 0 0 1 306.627 638.287 cm +1 0 0 1 306.627 680.131 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F44 10.9091 Tf 312.605 655.901 Td [(mld_sub_iluthrs_)]TJ 0 -13.549 Td [(SUB_ILUTHRS)]TJ +/F44 10.9091 Tf 312.605 697.745 Td [(mld_sub_iluthrs_)]TJ 0 -13.55 Td [(SUB_ILUTHRS)]TJ ET q -1 0 0 1 417.795 638.287 cm +1 0 0 1 417.795 680.131 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F44 10.9091 Tf 423.773 655.901 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ +/F44 10.9091 Tf 423.773 697.745 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ ET q -1 0 0 1 473.15 656.101 cm +1 0 0 1 473.15 697.944 cm []0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q BT -/F18 10.9091 Tf 476.496 655.901 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ +/F18 10.9091 Tf 476.496 697.745 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ ET q -1 0 0 1 536.768 638.287 cm +1 0 0 1 536.768 680.131 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 542.746 655.901 Td [(An)28(y)-333(re)-1(al)-333(n)28(um.)]TJ/F25 10.9091 Tf 72.152 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ +/F15 10.9091 Tf 542.746 697.745 Td [(An)28(y)-333(re)-1(al)-333(n)28(um.)]TJ/F25 10.9091 Tf 72.152 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ ET q -1 0 0 1 639.432 638.287 cm +1 0 0 1 639.432 680.131 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 645.41 655.901 Td [(0)]TJ +/F15 10.9091 Tf 645.41 697.745 Td [(0)]TJ ET q -1 0 0 1 718.51 638.287 cm +1 0 0 1 718.51 680.131 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 724.488 655.901 Td [(Drop)-1063(tol)1(e)-1(r)1(ance)]TJ/F22 10.9091 Tf 90.366 0 Td [(t)]TJ/F15 10.9091 Tf 15.532 0 Td [(in)-1063(t)1(he)]TJ -105.898 -13.549 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-333(factorization.)]TJ +/F15 10.9091 Tf 724.488 697.745 Td [(Drop)-1063(tol)1(e)-1(r)1(ance)]TJ/F22 10.9091 Tf 90.366 0 Td [(t)]TJ/F15 10.9091 Tf 15.532 0 Td [(in)-1063(t)1(he)]TJ -105.898 -13.55 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-333(factorization.)]TJ ET q -1 0 0 1 872.198 638.287 cm +1 0 0 1 872.198 680.131 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q q -1 0 0 1 306.627 638.088 cm +1 0 0 1 306.627 679.931 cm []0 d 0 J 0.398 w 0 0 m 565.57 0 l S Q q -1 0 0 1 306.627 556.594 cm +1 0 0 1 306.627 598.437 cm []0 d 0 J 0.398 w 0 0 m 0 81.295 l S Q BT -/F44 10.9091 Tf 312.605 628.405 Td [(mld_sub_ren_)]TJ 0 -13.55 Td [(SUB_REN)]TJ +/F44 10.9091 Tf 312.605 670.248 Td [(mld_sub_ren_)]TJ 0 -13.55 Td [(SUB_REN)]TJ ET q -1 0 0 1 417.795 556.594 cm +1 0 0 1 417.795 598.437 cm []0 d 0 J 0.398 w 0 0 m 0 81.295 l S Q BT -/F44 10.9091 Tf 423.773 628.405 Td [(character\050len=*\051)]TJ +/F44 10.9091 Tf 423.773 670.248 Td [(character\050len=*\051)]TJ ET q -1 0 0 1 536.768 556.594 cm +1 0 0 1 536.768 598.437 cm []0 d 0 J 0.398 w 0 0 m 0 81.295 l S Q BT -/F44 10.9091 Tf 542.746 628.405 Td [('RENUM)]TJ +/F44 10.9091 Tf 542.746 670.248 Td [('RENUM)]TJ ET q -1 0 0 1 577.796 628.604 cm +1 0 0 1 577.796 670.447 cm []0 d 0 J 0.398 w 0 0 m 3.436 0 l S Q BT -/F44 10.9091 Tf 581.233 628.405 Td [(NONE')]TJ -38.487 -13.55 Td [('RENUM)]TJ +/F44 10.9091 Tf 581.233 670.248 Td [(NONE')]TJ -38.487 -13.55 Td [('RENUM)]TJ ET q -1 0 0 1 577.796 615.055 cm +1 0 0 1 577.796 656.898 cm []0 d 0 J 0.398 w 0 0 m 3.436 0 l S Q BT -/F44 10.9091 Tf 581.233 614.855 Td [(GLOBAL')]TJ +/F44 10.9091 Tf 581.233 656.698 Td [(GLOBAL')]TJ ET q -1 0 0 1 639.432 556.594 cm +1 0 0 1 639.432 598.437 cm []0 d 0 J 0.398 w 0 0 m 0 81.295 l S Q BT -/F44 10.9091 Tf 645.41 628.405 Td [('RENUM)]TJ +/F44 10.9091 Tf 645.41 670.248 Td [('RENUM)]TJ ET q -1 0 0 1 680.46 628.604 cm +1 0 0 1 680.46 670.447 cm []0 d 0 J 0.398 w 0 0 m 3.436 0 l S Q BT -/F44 10.9091 Tf 683.897 628.405 Td [(NONE')]TJ +/F44 10.9091 Tf 683.897 670.248 Td [(NONE')]TJ ET q -1 0 0 1 718.51 556.594 cm +1 0 0 1 718.51 598.437 cm []0 d 0 J 0.398 w 0 0 m 0 81.295 l S Q BT -/F15 10.9091 Tf 724.488 628.405 Td [(Ro)28(w)-257(and)-256(column)-256(reordering)-256(of)]TJ 0 -13.55 Td [(the)-423(lo)-28(cal)-422(s)-1(u)1(bmatrice)-1(s:)-623(no)-423(re-)]TJ 0 -13.549 Td [(ordering,)-248(reordering)-227(according)]TJ 0 -13.549 Td [(to)-253(the)-254(global)-253(n)28(um)27(b)-27(ering)-254(of)-253(the)]TJ 0 -13.549 Td [(ro)28(ws)-229(and)-229(columns)-229(of)-229(the)-229(whole)]TJ 0 -13.549 Td [(matrix.)]TJ +/F15 10.9091 Tf 724.488 670.248 Td [(Ro)28(w)-257(and)-256(column)-256(reordering)-256(of)]TJ 0 -13.55 Td [(the)-423(lo)-28(cal)-422(s)-1(u)1(bmatrice)-1(s:)-623(no)-423(re-)]TJ 0 -13.549 Td [(ordering,)-248(reordering)-227(according)]TJ 0 -13.549 Td [(to)-253(the)-254(global)-253(n)28(um)27(b)-27(ering)-254(of)-253(the)]TJ 0 -13.549 Td [(ro)28(ws)-229(and)-229(columns)-229(of)-229(the)-229(whole)]TJ 0 -13.549 Td [(matrix.)]TJ ET q -1 0 0 1 872.198 556.594 cm +1 0 0 1 872.198 598.437 cm []0 d 0 J 0.398 w 0 0 m 0 81.295 l S Q q -1 0 0 1 306.627 556.395 cm +1 0 0 1 306.627 557.789 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +BT +/F44 10.9091 Tf 312.605 588.952 Td [(mld_solver_sweeps_)]TJ 0 -27.098 Td [(SOLVER_SWEEPS)]TJ +ET +q +1 0 0 1 417.795 557.789 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +BT +/F44 10.9091 Tf 423.773 588.952 Td [(integer)]TJ +ET +q +1 0 0 1 536.768 557.789 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +BT +/F15 10.9091 Tf 542.746 588.952 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 [(1)]TJ +ET +q +1 0 0 1 639.432 557.789 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +BT +/F15 10.9091 Tf 645.41 588.952 Td [(1)]TJ +ET +q +1 0 0 1 718.51 557.789 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +BT +/F15 10.9091 Tf 724.488 588.952 Td [(Num)28(b)-28(er)-674(of)-673(sw)27(eeps)-673(for)-674(iter-)]TJ 0 -13.549 Td [(ativ)28(e)-669(lo)-28(cal)-668(solv)27(er)-668(\050curren)28(tly)]TJ 0 -13.549 Td [(only)-333(Gauss-Seidel\051.)]TJ +ET +q +1 0 0 1 872.198 557.789 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +q +1 0 0 1 306.627 557.59 cm +[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S +Q +q +1 0 0 1 306.627 489.645 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +Q +BT +/F44 10.9091 Tf 312.605 547.906 Td [(mld_solver_eps_)]TJ 0 -13.549 Td [(SOLVER_EPS)]TJ +ET +q +1 0 0 1 417.795 489.645 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +Q +BT +/F44 10.9091 Tf 423.773 547.906 Td [(real)]TJ +ET +q +1 0 0 1 536.768 489.645 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +Q +BT +/F15 10.9091 Tf 542.746 547.906 Td [(An)28(y)-333(re)-1(al)-333(n)28(um.)]TJ +ET +q +1 0 0 1 639.432 489.645 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +Q +BT +/F15 10.9091 Tf 645.41 547.906 Td [(0)]TJ +ET +q +1 0 0 1 718.51 489.645 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +Q +BT +/F15 10.9091 Tf 724.488 547.906 Td [(Stopping)-707(tolerance)-708(for)-707(iter-)]TJ 0 -13.549 Td [(ativ)28(e)-669(lo)-28(cal)-668(solv)27(er)-668(\050curren)28(tly)]TJ 0 -13.549 Td [(only)-629(Gauss-Seidel\051;)-778(if)]TJ/F25 10.9091 Tf 116.349 0 Td [(\024)]TJ/F15 10.9091 Tf 16.898 0 Td [(0,)]TJ -133.247 -13.549 Td [(then)-1253(p)-28(erform)-1253(presp)-27(eci\014ed)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)-333(of)-334(iterations.)]TJ +ET +q +1 0 0 1 872.198 489.645 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S +Q +q +1 0 0 1 306.627 489.446 cm +[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S +Q +q +1 0 0 1 306.627 487.453 cm []0 d 0 J 0.398 w 0 0 m 565.57 0 l S Q 0 g 0 G BT -/F15 10.9091 Tf 405.352 525.705 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 405.352 456.764 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 0 g 0 G 0 g 0 G ET @@ -5357,7 +5443,7 @@ stream >> % 360 0 obj << -/D [434 0 R /XYZ 366.766 4378.384 null] +/D [434 0 R /XYZ 366.767 4378.384 null] >> % 433 0 obj << @@ -5378,7 +5464,7 @@ stream >> % 442 0 obj << -/D [439 0 R /XYZ -3963.913 559.035 null] +/D [439 0 R /XYZ -4032.854 559.035 null] >> % 438 0 obj << @@ -5408,7 +5494,7 @@ stream >> % 448 0 obj << -/D [445 0 R /XYZ 530.237 4405.505 null] +/D [445 0 R /XYZ 530.198 4405.505 null] >> % 444 0 obj << @@ -7234,10 +7320,10 @@ endstream endobj 540 0 obj << -/Length1 1647 -/Length2 7851 +/Length1 1669 +/Length2 7977 /Length3 0 -/Length 9498 +/Length 9646 >> stream %!PS-AdobeFont-1.0: CMSY10 003.002 @@ -7257,7 +7343,7 @@ FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /WYYAGH+CMSY10 def +/FontName /PLWDAY+CMSY10 def /FontBBox {-29 -960 1116 775 }readonly def /PaintType 0 def /FontInfo 9 dict dup begin @@ -7281,6 +7367,7 @@ dup 103 /braceright put dup 15 /bullet put dup 50 /element put dup 21 /greaterequal put +dup 20 /lessequal put dup 0 /minus put dup 54 /negationslash put dup 26 /propersubset put @@ -7304,17 +7391,13 @@ A5 zT0b#[zyϒ$e1k5dRA`(Ņ@{=yW>>y@U;=H;c{30ü^ծ)ՙ-{OO2R´xQwBgБS"תlbz;Iy\EprkM @@e&3lʉtS%)/pR"2u Ee5+ٰsZ'bQSlj zvހ~%.Kz\NE,eV2=Mo)-JcV:U2Ѹ>1ȓ"QWOё4*Oz.cjcY&=7Y,A5nIF/?̊ ]as.N/ ,McewW0#]٪3w]2f˨n'_ MuH OMlC7h ?p|`e(ӛ|*{dgHPNDYLQsRd=҅^\#ZHd; -D+ZQb7QŅP#?8ՓF,(韓v>%U9ͫNDOQkOL?{(-aǣUsљN#^&Ԇ[MJB, VsPeQOB,s%v623}.D|`,;(`tQ)l!Tr+u=[Ҽ4`h-?2D#e+%-tU>kxߣ**؂X?`]!&d)BgzFmwGVÂM\nI{`"S$O05AGXVNIQkι,ymo-D$S8dL-OwQu7@g53vN<6ᒥ)9}'u~~Vf<*ߋ8H/2T8;w؋ZsxVev6q/4w-7kLPCCx#uZ+6# b4R?ڂ$Sm:|ϛ%Ly j#&+I*p`r"O M6ӖlGMuT껵OKlbē -_EGS/,+iơjF<0U[z)dG`NdZ=J;QUN%xg?ŗk -ZQDx/0~o4 \C~qD99pe:\ -N~E}1P߅\msy;*[@k~ #MEh!Ei*X,H%sX QkPtJYl}t@Fh0 bh' @li:WMĝ݁>$Mx)ipn[_Gz:%^ AT$,wdkoM9.} DLRgu]ag{#Zd1[ <^+hk - -~ ȈQNQHܕ4w B2_F)Y?,7OΥ7ne@SdkJFC"_l/V50DTҦW2(\&tZQ<~\8~J(Nc2/Xt0`(ۖ~4Uy1.ج u"XBʫi;kQ)Cd6آޗ| *Gs,ĜJgڤS=WXdenFBaH4+)'L9efD*ԓ!UW6]doz9[;ͯ9>* Cxe/7aA  Wc1 zsl3)n:K w9j)y.n>7V!j+(zrŁ>ܦ&bbV b6r`FR!"H-* -o319(5[ rHJ< &8xs12PIխ.2.[D&)ThGawLdYj+#&uo+?v|2s`(v;-#|LoUXN¥$*q8LozIKT'yΌ= h2*e9%y ai)Ȁ_Xe -_po{Ķ?|nM2isB{ZѽT$P>LEUzӞ.TNIA4힟8 xYsJLD}+2+C~}`⨱c77=k&Y΅IBr_Z4bc#\KAQ 7<9j(t7 -CQ4F@VfUQו ˺8ۑᗡF D]e'sdMRj?&_zsϦ�w -K87m +D+ZQb7QŅP#?8ՓF,(韓v>%U9ͫNDOQkOL?{(-aǣUsљN#^&Ԇ[MJB, VsPeQOB,s%v623}.D|`,;(`tQ)l!Tr+u=[Ҽ4`h-?2D#e+%-tU>kxߣ**؂X?`]!&d)BgzFmwGVÂM\nI{`"S$O05AGXVNIPtjɂj(k_ߘ7|gf?:5~fDo-:n|肣:%xcV-8:QoΔaaBǾn:RYsO5"wܧK%}+ogpzQDzlk$4Ǔ?<= ý*g8횫VGB +B"VC#t^?EZkE u5L!!e^lU>Λj!Zdd!UJ% H汋Şt;MZH&Y[r{pJYɃe$@S, X4yZ Wau;x߾eZ"hL%!O.\acD$)xURڞ8c, +vI4c vbaːЮҘP:]"*RX¾Kr`(XlV'v#P͡= jty9sTUGq{Ǯǚ- "X +6Twx~~.|kL%c 0(ק_r[K:Fg.+H RF[92q}YZ?/jL +m2,3S+E(C<6oBBO'z`2wL9agV%2UfluA%{dlC\9́fɭw <dөus~aT^SAs<+[\A?b}zAfrn)/qq1zN0L\T;, +A bbPr HcMX HYK~X;;O +8"25H^\5Z]+?诺 4>g2N'DIcMԙ_ vs|ؿY6@Fm6&Rl7\ِc:D%q_MIK=l|3^KN0!@j1T%nb$˙`) cܭpkm2t&!q7m&[u7`& K %{Sz#Vc7VkWKH5el?U}}#HD^b>p,Ya0I>w-@J4zq~)\En[{IR,A)Գ/nn}ΎRϣ"DH2$'9OC5ҥXxCޓ(Ӵ/K8.Fݕ+C7k=HaK< &`Qo/y:f}S 3n$Z8Ĭ2,piWZt%'CgQۢLx- 0YirG U+f^QկBke! Yű HS^YXsHxf?j%i6gac dapE[n&>$_'#m>K~@LL}y=:0٬{t7)Z{]ڽKQN|컒n0g0lvTL3 ] endstream endobj 542 0 obj @@ -7972,19 +8055,19 @@ endobj /Type /ObjStm /N 100 /First 940 -/Length 22123 +/Length 22133 >> stream 497 0 499 20 500 246 501 300 502 991 503 1550 504 1648 505 1680 506 2304 507 2694 508 3325 509 3941 510 4605 511 5215 512 5722 513 6361 514 6840 515 7192 517 7828 519 8180 521 8538 523 8882 525 9203 527 9527 529 9750 531 9973 533 10227 535 10791 537 11129 539 11349 -541 11579 543 11920 545 12140 547 12369 549 12782 551 13058 155 13627 108 13766 121 13905 279 14045 -173 14183 278 14322 321 14460 275 14598 120 14736 110 14874 320 15012 277 15148 174 15284 322 15422 -276 15557 171 15692 109 15831 200 15970 111 16109 175 16221 236 16333 308 16445 393 16557 437 16669 -472 16781 552 16893 553 17006 554 17078 555 17143 100 17211 96 17281 92 17363 88 17444 84 17513 -80 17595 76 17677 72 17759 68 17841 64 17910 60 18028 56 18084 52 18202 48 18271 44 18340 -40 18458 36 18527 32 18609 28 18691 24 18773 20 18842 16 18960 12 19041 8 19121 4 19186 -556 19278 557 19446 558 19607 559 19771 560 19999 561 20207 562 20444 563 20642 564 20849 565 21018 +541 11579 543 11930 545 12150 547 12379 549 12792 551 13068 155 13637 108 13776 121 13915 279 14055 +173 14193 278 14332 321 14470 275 14608 120 14746 110 14884 320 15022 277 15158 174 15294 322 15432 +276 15567 171 15702 109 15841 200 15980 111 16119 175 16231 236 16343 308 16455 393 16567 437 16679 +472 16791 552 16903 553 17016 554 17088 555 17153 100 17221 96 17291 92 17373 88 17454 84 17523 +80 17605 76 17687 72 17769 68 17851 64 17920 60 18038 56 18094 52 18212 48 18281 44 18350 +40 18468 36 18537 32 18619 28 18701 24 18783 20 18852 16 18970 12 19051 8 19131 4 19196 +556 19288 557 19456 558 19617 559 19781 560 20009 561 20217 562 20454 563 20652 564 20859 565 21028 % 497 0 obj [892.9] % 499 0 obj @@ -8204,7 +8287,7 @@ stream % 541 0 obj << /Type /FontDescriptor -/FontName /WYYAGH+CMSY10 +/FontName /PLWDAY+CMSY10 /Flags 4 /FontBBox [-29 -960 1116 775] /Ascent 750 @@ -8213,7 +8296,7 @@ stream /ItalicAngle -14 /StemV 40 /XHeight 431 -/CharSet (/Rfractur/backslash/bar/braceleft/braceright/bullet/element/greaterequal/minus/negationslash/propersubset/propersuperset/union) +/CharSet (/Rfractur/backslash/bar/braceleft/braceright/bullet/element/greaterequal/lessequal/minus/negationslash/propersubset/propersuperset/union) /FontFile 540 0 R >> % 543 0 obj @@ -8415,7 +8498,7 @@ stream << /Type /Font /Subtype /Type1 -/BaseFont /WYYAGH+CMSY10 +/BaseFont /PLWDAY+CMSY10 /FontDescriptor 541 0 R /FirstChar 0 /LastChar 110 @@ -8806,8 +8889,8 @@ endobj 585 0 obj << /Title (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS, V. 2.0) /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-1.40.15)/Keywords() -/CreationDate (D:20160229132824Z) -/ModDate (D:20160229132824Z) +/CreationDate (D:20160229135950Z) +/ModDate (D:20160229135950Z) /Trapped /False /PTEX.Fullbanner (This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014) kpathsea version 6.2.0) >> @@ -8926,19 +9009,19 @@ endobj /W [1 3 1] /Root 584 0 R /Info 585 0 R -/ID [<252E47806D66F0DAB10F5905A2354801> <252E47806D66F0DAB10F5905A2354801>] +/ID [<3F2A25442D85405FC76ACEFD34DF1970> <3F2A25442D85405FC76ACEFD34DF1970>] /Length 2935 >> stream Ny6Y=XWV"U  #T  $S +R6Q7PDOTN5M5'L58K5WJ 5]I!"H#$'G%&,F'(2E)*7D+,=C-.AB/0EA123745%4-6:89>;3<,&A?@CDEFGHIJKLMNOPQRSTUVWXYZ]B[\$`^-_cba.x3(07^FbYXW_     q_5 %Y!PQ[ZN()',&T*O\/-.130v28845:<9;>?@ABHE=CKLIJKLMNOPQRZ[GXFS+2/)'UVW`aGHIM]\]_YI^JVbc555a5`[595 555 5 -5 55T5 .*1555555555 *55555555 5!5"5#5$5%5152535.55&5(5)5*5+5,5-5754555;5<50595/;{565K5=5>5?5@5A5B5C5D5E5G5:_65F5O5P5Q5I5L5Hz<5J:5R5M5N5U5T5X5S5V5Z5[5^5Y5\5a5b5c5`5_9  -   =;&Mx #$%"(!&*-)+0/3.ܹ1<5846;:>9,<B?t@RCWDcSTU  -   `Zc/R gmb6(Z( 6!O""#=>?@Z[\]^_`abc7v4777777777 7 -7 7 7 7777sdN +5 55T5 .*1555555555 *55555555 5!5"5#5$5%5152535.55&5(5)5*5+5,5-5754555;5<50595/;{565K5=5>5?5@5A5B5C5D5E5G5:_65F5O5P5Q5I5L5Hz<5J:5R5M5N5U5T5X5S5V5Z5[5^5Y5\5a5b5c5`5_C$  +   =;&HW #$%"(!&*-)…+0/3.I1<5846;:>9<B?@RC DcS'@TU&  +   ih9[WkQm~#L @!s"F#=>?@Z[\]^_`abc7b777777777 7 +7 7 7 7777}| endstream endobj startxref -557390 +559996 %%EOF diff --git a/docs/src/userinterface.tex b/docs/src/userinterface.tex index 78be669b..d2822f99 100644 --- a/docs/src/userinterface.tex +++ b/docs/src/userinterface.tex @@ -192,11 +192,11 @@ according to their needs. & Basic multi-level framework: additive or multiplicative among the levels (always additive inside a level). \\ \hline \verb|mld_smoother_type_| \break \verb|SMOOTHER_TYPE| & \verb|character(len=*)| - & \texttt{'DIAG'} \ \ \ \texttt{'BJAC'} \ \ \ \texttt{'AS'} + & \texttt{'JACOBI'} \ \ \ \texttt{'BJAC'} \ \ \ \texttt{'AS'} & \texttt{'AS'} & Basic predefined one-level preconditioner - (i.e.\ smoother): diagonal, - block Jacobi, AS. \\ \hline + (i.e.\ smoother): Jacobi (with diagonal local + solver), block Jacobi, AS. \\ \hline \verb|mld_smoother_pos_| \break \verb|SMOOTHER_POS| & \verb|character(len=*)| & \texttt{'PRE'} \ \ \ \texttt{'POST'} \ \ \ \texttt{'TWOSIDE'} & \texttt{'TWOSIDE'} @@ -233,12 +233,16 @@ according to their needs. \texttt{'SUM'} for adding the contributions from the overlap, \texttt{'NONE'} for neglecting them. \\ \hline \verb|mld_sub_solve_| \break \verb|SUB_SOLVE| & \verb|character(len=*)| - & \texttt{'ILU'} \hspace{2.5cm} \texttt{'MILU'} \hspace{2.5cm} \texttt{'ILUT'} + & \texttt{'DIAG'} \hspace{2.5cm} + \texttt{'GS'} \hspace{2.5cm} + \texttt{'ILU'} \hspace{2.5cm} + \texttt{'MILU'} \hspace{2.5cm} \texttt{'ILUT'} \hspace{2.5cm} \texttt{'UMF'} \hspace{2.5cm} \texttt{'SLU'} & \texttt{'ILU'} - & Predefined local solver: ILU($p$), - MILU($p$), ILU($p,t$), LU from UMFPACK, LU from SuperLU - (plus triangular solve). \\ \hline + & Predefined local solver: diagonal scaling, + Gauss-Seidel, ILU($p$), MILU($p$), + ILU($p,t$), LU from UMFPACK, LU from + SuperLU (plus triangular solve). \\ \hline \verb|mld_sub_fillin_| \break \verb|SUB_FILLIN| & \verb|integer| & Any~int.~num.~$\ge 0$ & 0 @@ -253,6 +257,17 @@ according to their needs. & Row and column reordering of the local submatrices: no reordering, reordering according to the global numbering of the rows and columns of the whole matrix. \\ +\verb|mld_solver_sweeps_| \break \verb|SOLVER_SWEEPS| & \verb|integer| + & Any~int.~num.~$\ge 1$ + & 1 + & Number of sweeps for iterative local solver + (currently only Gauss-Seidel). \\ \hline +\verb|mld_solver_eps_| \break \verb|SOLVER_EPS| & \verb|real| + & Any~real~num. + & 0 + & Stopping tolerance for iterative local solver + (currently only Gauss-Seidel); if $\le0$, then + perform prespecified number of iterations. \\ \hline \hline \end{tabular} \end{center} diff --git a/mlprec/mld_base_prec_type.F90 b/mlprec/mld_base_prec_type.F90 index 643b00b3..54c599c1 100644 --- a/mlprec/mld_base_prec_type.F90 +++ b/mlprec/mld_base_prec_type.F90 @@ -379,7 +379,7 @@ contains val = mld_slu_ case('SLUDIST') val = mld_sludist_ - case('DSCALE') + case('DIAG') val = mld_diag_scale_ case('ADD') val = mld_add_ml_ @@ -409,8 +409,6 @@ contains val = mld_twoside_smooth_ case('NOPREC') val = mld_noprec_ -! !$ case('DIAG') -! !$ val = mld_diag_ case('BJAC') val = mld_bjac_ case('JAC','JACOBI') diff --git a/tests/pdegen/Makefile b/tests/pdegen/Makefile index 003c59ee..c6c3a2a5 100644 --- a/tests/pdegen/Makefile +++ b/tests/pdegen/Makefile @@ -11,7 +11,7 @@ FINCLUDES=$(FMFLAG). $(FMFLAG)$(MLDINCDIR) $(FMFLAG)$(PSBINCDIR) $(FIFLAG). EXEDIR=./runs -all: spde3d ppde3d spde2d ppde2d +all: spde3d ppde3d spde2d ppde2d ppde3d_gs ppde3d: ppde3d.o data_input.o $(F90LINK) ppde3d.o data_input.o -o ppde3d $(MLD_LIB) $(PSBLAS_LIB) $(LDLIBS) @@ -30,8 +30,11 @@ spde2d: spde2d.o data_input.o $(F90LINK) spde2d.o data_input.o -o spde2d $(MLD_LIB) $(PSBLAS_LIB) $(LDLIBS) /bin/mv spde2d $(EXEDIR) +ppde3d_gs: ppde3d_gs.o data_input.o + $(F90LINK) ppde3d_gs.o data_input.o -o ppde3d_gs $(MLD_LIB) $(PSBLAS_LIB) $(LDLIBS) + /bin/mv ppde3d_gs $(EXEDIR) -ppde3d.o spde3d.o ppde2d.o spde2d.o: data_input.o +ppde3d_gs.o ppde3d.o spde3d.o ppde2d.o spde2d.o: data_input.o check: all cd runs && ./ppde2d

Table 5: Parameters defining the coarse-space correction at the coarsest @@ -526,7 +551,7 @@ level.
integer Any int. num. $> 0$ 4 Number of Block-Jacobi sweeps when 'BJAC' is used as diff --git a/docs/html/node20.html b/docs/html/node20.html index 2b24d179..8aa0c889 100644 --- a/docs/html/node20.html +++ b/docs/html/node20.html @@ -69,14 +69,14 @@ This routine computes $y = op(M^{-1}) x$, where $M$ is a previously built preconditioner, stored into p, and $op$ denotes the preconditioner itself or its transpose, according to the value of trans. @@ -106,7 +106,7 @@ and hence it is completely transparent to the user.
  The local part of the vector $x$. Note that type and kind_parameter must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
  The local part of the vector $y$. Note that type and kind_parameter must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
work