From 65ddac356d50024f8e304bd6146aa8fbd8491316 Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Mon, 29 Feb 2016 14:46:31 +0000 Subject: [PATCH] mld2p4-2: Docs updates for DIAG/Gauss-Seidel --- docs/html/img100.png | Bin 251 -> 250 bytes docs/html/img101.png | Bin 193 -> 600 bytes docs/html/img102.png | Bin 210 -> 251 bytes docs/html/img103.png | Bin 610 -> 193 bytes docs/html/img104.png | Bin 650 -> 210 bytes docs/html/img105.png | Bin 336 -> 610 bytes docs/html/img106.png | Bin 660 -> 650 bytes docs/html/img92.png | Bin 328 -> 201 bytes docs/html/img93.png | Bin 207 -> 243 bytes docs/html/img94.png | Bin 293 -> 328 bytes docs/html/img95.png | Bin 337 -> 207 bytes docs/html/img96.png | Bin 667 -> 293 bytes docs/html/img97.png | Bin 467 -> 337 bytes docs/html/img98.png | Bin 250 -> 667 bytes docs/html/img99.png | Bin 600 -> 467 bytes docs/html/node12.html | 2 +- docs/html/node18.html | 69 +- docs/html/node20.html | 18 +- docs/mld2p4-2.0-guide.pdf | 8944 --------------------------------- docs/mld2p4-2.1-guide.pdf | 389 +- docs/src/userinterface.tex | 29 +- mlprec/mld_base_prec_type.F90 | 4 +- tests/pdegen/Makefile | 7 +- 23 files changed, 321 insertions(+), 9141 deletions(-) delete mode 100644 docs/mld2p4-2.0-guide.pdf diff --git a/docs/html/img100.png b/docs/html/img100.png index 453c05790692e7419b175439df44d35c6a6cc231..1244b45e3fa129e88ca1ceb429f702ac2376d218 100644 GIT binary patch delta 184 zcmey(_={1oGr-TCmrII^fq{Y7)59eQNGkxbJPR|BEUCD(f1;vKeTAosV~EDYYE(<6MKXQ_bTzF?jnR)LjQDia!+d3x9vbO}FS z$Z4>mj)6ECkO4!Bx j?prx0%U|m|j0}zil6jeqeEAJP$1r%h`njxgN@xNAE#f@7 delta 185 zcmeyx_?uC&Gr-TCmrII^fq{Y7)59eQNQ(inJPR|B6r8GXV4|W=eWj<1V~E7mptH1)`^XcHN1_*M>l#%VPnd;2u)dIX?m#``iFK(DtS2a(I-qypz=86v#&YIn zcIQ6E3AGK4t_?3G4wo(vTIS57%XNl*#w&+sCUzo833GmYV(d7}q7pev?7-T~o(;w~ lQ{)tGyqCLpqJ9d{ExA(D+xRC&L;zjG;OXk;vd$@?2>_+0Mf?B& diff --git a/docs/html/img101.png b/docs/html/img101.png index 06cc29ded3b2065ecb7879d40427a96fc66ea77f..f8eef1828f38f5a8ca528fef4c93f5503a395ed3 100644 GIT binary patch delta 582 zcmV-M0=fOc0oVj3iBL{Q4GJ0x0000DNk~Le0001W0000d1Oos70K;q=a{vGUFp(u6 ze?UM$nwpvo4GjPQ0B2`sjg5^oG&C1e${_#%00DGTPE!Ct=GbNc00GuXL_t(YiS3b3 zC~ zZ5>F`BIF`}E^fRxE8gzTVOlrsw_fvpfA9DE{Jy{U2KeuiibvHe@3p)62bDmX=?PW( zftxM5kzS1-R_yo0Rxpdr7|>$>`Xb_qy{Aj-%m8yysD8h{#$jboLl4vCYf6BO7@V(= z;7TS^*vVnWE+Ex4Ut*6{>IRyFA&w>N!n^5+)57S(2mL%VJk#-b@%;w&>DA?!nl@+_e(J5-A}Y}wgR&P;PR zRS?#mGT4Ap--~rpKgIX=)5DPPqoLTgV2}tQqRF$utHER|xFE5an zo}S*@+iPNC;=&fF%=lwiWZn=JZ9eqQ8! 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-
+
- + + (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

-
+
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-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 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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 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[(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 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[(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 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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 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[(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 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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 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-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 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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}#? 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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 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(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