diff --git a/docs/mld2p4-2.1-guide.pdf b/docs/mld2p4-2.1-guide.pdf index 2b747c38..eb31b76b 100644 --- a/docs/mld2p4-2.1-guide.pdf +++ b/docs/mld2p4-2.1-guide.pdf @@ -18,7 +18,7 @@ q 0 0 412.451 4.981 re f Q BT -/F19 14.3462 Tf 192.132 548.586 Td [(A)-350(guide)-350(for)-350(the)-350(Multi-L)50(evel)-350(Domain)-350(De)50(c)50(omp)50(osition)]TJ -5.512 -17.256 Td [(Par)50(al)-50(lel)-350(Pr)50(e)50(c)50(onditioners)-350(Package)-350(b)50(ase)50(d)-350(on)-350(PSBLAS)]TJ +/F19 14.3462 Tf 197.154 548.586 Td [(A)-350(guide)-350(for)-350(the)-350(MultiL)50(evel)-350(Domain)-350(De)50(c)50(omp)50(osition)]TJ -10.534 -17.256 Td [(Par)50(al)-50(lel)-350(Pr)50(e)50(c)50(onditioners)-350(Package)-350(b)50(ase)50(d)-350(on)-350(PSBLAS)]TJ 0 g 0 G 0 g 0 G /F17 11.9552 Tf 218.644 -79.389 Td [(P)31(asqua)-375(D'Am)31(bra)]TJ/F37 11.9552 Tf -22.655 -13.947 Td [(IA)27(C-CNR,)-326(Naples,)-326(Italy)]TJ/F17 11.9552 Tf 11.494 -29.39 Td [(Daniela)-375(di)-375(Sera\014no)]TJ/F37 11.9552 Tf -181.63 -13.948 Td [(Univ)27(ersit)27(y)-326(of)-326(Campania)-326(\134Luigi)-327(V)82(an)27(vitelli",)-326(Caserta,)-326(Italy)]TJ/F17 11.9552 Tf 179.561 -29.39 Td [(Salv)62(atore)-375(Filipp)-31(one)]TJ/F37 11.9552 Tf -134.787 -13.947 Td [(Cran\014eld)-326(Univ)27(ersit)27(y)82(,)-326(Cran\014eld,)-327(United)-326(Kingdom)]TJ @@ -48,21 +48,21 @@ endstream endobj 134 0 obj << -/Length 3902 +/Length 3888 >> stream 0 g 0 G BT /F15 10.9091 Tf 503.021 740.002 Td [(i)]TJ 0 g 0 G -/F17 14.3462 Tf -409.421 -35.866 Td [(Abstract)]TJ/F42 10.9091 Tf 0 -24.352 Td [(MLD2P4)-514(\050Mul)66(ti-Level)-514(Domain)-515(Decomposition)-514(P)87(arallel)-514(Preconditioners)]TJ 0 -13.549 Td [(P)88(a)22(cka)22(ge)-449(based)-448(on)-449(PSBLAS)]TJ/F15 10.9091 Tf 151.873 0 Td [(\051)-401(is)-400(a)-401(pac)28(k)55(age)-401(of)-400(parallel)-401(algebraic)-401(m)28(ulti-lev)28(el)-401(precon-)]TJ -151.873 -13.549 Td [(ditioners.)-487(The)-347(\014rst)-347(release)-348(of)-347(MLD2P4)-348(made)-347(a)28(v)55(ailable)-347(m)28(ulti-lev)28(e)-1(l)-347(additiv)28(e)-347(and)-348(h)28(ybrid)]TJ 0 -13.549 Td [(Sc)28(h)28(w)27(arz)-443(preconditioners,)-471(as)-444(w)28(ell)-444(as)-444(one-lev)28(el)-444(additiv)28(e)-444(Sc)28(h)28(w)28(arz)-444(preconditioners.)-775(The)]TJ 0 -13.55 Td [(pac)28(k)55(age)-366(has)-366(b)-28(een)-366(extended)-366(to)-366(include)-366(further)-366(m)28(ulti-lev)27(el)-366(cycles)-366(and)-366(smo)-28(others)-366(widely)]TJ 0 -13.549 Td [(used)-362(in)-362(m)27(ultigrid)-362(metho)-28(ds.)-531(In)-362(the)-362(m)27(ulti-lev)28(el)-362(case,)-370(a)-362(purely)-362(algebraic)-362(approac)27(h)-362(is)-362(ap-)]TJ 0 -13.549 Td [(plied)-402(to)-401(generate)-402(coarse-lev)28(el)-402(corrections,)-419(so)-402(that)-401(no)-402(geometric)-402(bac)28(kground)-402(is)-401(needed)]TJ 0 -13.549 Td 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[(\051)-431(is)-430(a)-431(pac)28(k)56(age)-431(of)-431(parallel)-430(algebraic)-431(m)28(ultilev)28(el)-431(precon-)]TJ -152.9 -13.549 Td [(ditioners.)-564(Th)1(e)-374(\014rst)-373(release)-373(of)-373(MLD2P4)-373(made)-373(a)28(v)56(ailable)-373(m)27(ultilev)28(el)-373(additiv)28(e)-373(and)-373(h)28(ybrid)]TJ 0 -13.549 Td [(Sc)28(h)28(w)27(arz)-443(preconditioners,)-471(as)-444(w)28(ell)-444(as)-444(one-lev)28(el)-444(additiv)28(e)-444(Sc)28(h)28(w)28(arz)-444(preconditioners.)-775(The)]TJ 0 -13.55 Td [(pac)28(k)55(age)-396(has)-397(b)-27(een)-397(extended)-396(to)-397(includ)1(e)-397(further)-396(m)28(ultilev)27(el)-396(cycles)-397(and)-396(smo)-28(others)-396(widely)]TJ 0 -13.549 Td [(used)-384(in)-384(m)28(ultigrid)-384(metho)-28(ds.)-597(In)-384(the)-384(m)28(ultilev)27(el)-384(case,)-397(a)-384(purely)-384(algebraic)-384(approac)28(h)-384(is)-384(ap-)]TJ 0 -13.549 Td 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[(allel)-382(implemen)27(tation)-382(is)-382(based)-382(on)-383(a)-382(Single)-382(Program)-382(Multiple)-383(D)1(ata)-383(\050SPMD\051)-382(paradigm;)]TJ 0 -13.55 Td [(the)-331(in)28(ter-pro)-27(ce)-1(ss)-330(comm)28(unication)-331(is)-330(based)-331(on)-330(MPI)-331(and)-330(is)-331(managed)-330(mainly)-331(through)-330(PS-)]TJ 0 -13.549 Td [(BLAS.)]TJ 16.937 -13.549 Td [(This)-353(guide)-354(pro)28(vides)-353(a)-354(brief)-353(description)-354(of)-353(the)-354(fu)1(nctionalities)-354(and)-353(the)-354(user)-353(in)28(terface)]TJ -16.937 -13.549 Td [(of)-333(MLD2P4.)]TJ 0 g 0 G 0 g 0 G ET @@ -722,7 +722,7 @@ endstream endobj 193 0 obj << -/Length 7739 +/Length 7908 >> stream 0 g 0 G @@ -732,23 +732,23 @@ BT 0 g 0 G [-378(General)-378(O)30(ver)88(view)]TJ/F15 10.9091 Tf 406.997 0 Td [(1)]TJ 0 g 0 G -/F17 14.3462 Tf -406.997 -35.866 Td [(1)-1125(General)-375(Ov)31(erview)]TJ/F15 10.9091 Tf 0 -25.759 Td [(The)]TJ/F42 10.9091 Tf 23.408 0 Td 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[(Domain)-268(Decomp)-28(osition)-268(preconditioners)-269(\050see,)-281(e.g.,)-281([)]TJ 1 0 0 rg 1 0 0 RG [(3)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-421(23)]TJ + [-269(23)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-420(21)]TJ + [-268(21)]TJ 0 g 0 G - [(]\051,)-442(to)-421(b)-27(e)-421(used)-420(in)-420(the)]TJ 0 -13.549 Td [(iterativ)28(e)-334(soluti)1(on)-334(of)-333(linear)-333(systems)-1(,)]TJ/F22 10.9091 Tf 186.98 -26.681 Td [(Ax)]TJ/F15 10.9091 Tf 17.447 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(b;)]TJ + [(]\051,)-281(to)-269(b)-27(e)-269(used)-268(in)-268(the)-269(iterativ)28(e)]TJ 0 -13.549 Td [(solution)-333(of)-334(lin)1(e)-1(ar)-333(systems,)]TJ/F22 10.9091 Tf 186.98 -16.123 Td [(Ax)]TJ/F15 10.9091 Tf 17.447 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(b;)]TJ 0 g 0 G /F15 10.9091 Tf 182.57 0 Td [(\0501\051)]TJ 0 g 0 G - -398.512 -26.681 Td [(where)]TJ/F22 10.9091 Tf 31.935 0 Td [(A)]TJ/F15 10.9091 Tf 12.208 0 Td 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[(used)-333(in)-334(m)28(ultigrid)-333(metho)-28(ds.)]TJ 16.937 -14.407 Td [(The)-285(m)28(ultilev)28(el)-285(p)1(rec)-1(on)1(ditioners)-285(implemen)28(ted)-285(in)-284(MLD2P4)-285(are)-284(obtained)-285(b)28(y)-284(c)-1(om)28(bining)]TJ -16.937 -13.549 Td [(AMG)-263(cycles)-264(with)-263(smo)-28(others)-263(and)-264(coarsest-lev)28(el)-263(solv)27(ers.)-421(The)-263(V-,)-278(W)1(-)-1(,)-277(and)-263(K-cycles)-264([)]TJ 1 0 0 rg 1 0 0 RG [(3)]TJ 0 g 0 G @@ -756,7 +756,7 @@ BT 1 0 0 rg 1 0 0 RG [-263(19)]TJ 0 g 0 G - [(])]TJ 0 -13.549 Td [(are)-392(a)28(v)56(ailable,)-407(whic)28(h)-392(allo)28(w)-392(to)-391(de\014ne)-392(almost)-392(all)-391(the)-392(preconditioners)-392(in)-392(th)1(e)-392(pac)28(k)55(age,)-406(in-)]TJ 0 -13.549 Td [(cluding)-367(the)-367(m)27(ulti-lev)28(el)-367(h)28(ybrid)-368(Sc)28(h)28(w)28(arz)-368(on)1(e)-1(s;)-384(a)-367(sp)-28(eci\014c)-367(cycle)-368(is)-367(implemen)28(ted)-368(to)-367(obtain)]TJ 0 -13.549 Td [(m)28(ulti-lev)28(el)-462(additiv)28(e)-462(Sc)28(h)28(w)28(arz)-462(preconditioners.)-829(The)-461(Jacobi,)-494(h)28(ybrid)-461(forw)28(ard/bac)27(kw)28(ard)]TJ 0 -13.55 Td [(Gauss-Seidel,)-366(blo)-27(c)27(k-Jacobi,)-365(and)-359(additiv)28(e)-360(Sc)28(h)28(w)28(arz)-359(m)-1(eth)1(o)-28(ds)-359(are)-360(a)28(v)56(ailable)-359(as)-360(smo)-27(others.)]TJ 0 -13.549 Td [(An)-279(algebraic)-279(appr)1(oac)27(h)-279(i)1(s)-279(used)-279(to)-279(generate)-279(a)-279(hierarc)28(h)28(y)-279(of)-279(coarse-lev)28(el)-279(matrices)-279(and)-278(op)-28(er-)]TJ 0 -13.549 Td [(ators,)-283(without)-270(explicitly)-270(using)-270(an)28(y)-271(inf)1(ormation)-271(on)-270(the)-270(geometry)-270(of)-270(the)-271(original)-270(problem,)]TJ 0 -13.549 Td [(e.g.,)-256(the)-237(discretization)-237(of)-237(a)-237(PDE.)-237(T)84(o)-237(this)-237(end,)-256(the)-237(smo)-28(othed)-237(aggregation)-237(tec)28(hnique)-237([)]TJ + [(])]TJ 0 -13.549 Td [(are)-392(a)28(v)56(ailable,)-407(whic)28(h)-392(allo)28(w)-392(to)-391(de\014ne)-392(almost)-392(all)-391(the)-392(preconditioners)-392(in)-392(th)1(e)-392(pac)28(k)55(age,)-406(in-)]TJ 0 -13.549 Td [(cluding)-394(the)-394(m)28(ultilev)28(el)-394(h)28(ybrid)-394(Sc)28(h)27(w)28(arz)-394(ones;)-424(a)-394(sp)-28(eci\014c)-394(cycle)-394(is)-394(implemen)28(ted)-394(to)-394(obtain)]TJ 0 -13.55 Td [(m)28(ultilev)28(el)-498(additiv)28(e)-498(Sc)28(h)28(w)28(arz)-498(preconditioners.)-937(The)-497(Jacobi,)-539(h)28(ybrid)-498(forw)28(ard/bac)28(kw)28(ard)]TJ 0 -13.549 Td [(Gauss-Seidel,)-366(blo)-27(c)27(k-Jacobi,)-365(and)-359(additiv)28(e)-360(Sc)28(h)28(w)28(arz)-359(m)-1(eth)1(o)-28(ds)-359(are)-360(a)28(v)56(ailable)-359(as)-360(smo)-27(others.)]TJ 0 -13.549 Td [(An)-279(algebraic)-279(appr)1(oac)27(h)-279(i)1(s)-279(used)-279(to)-279(generate)-279(a)-279(hierarc)28(h)28(y)-279(of)-279(coarse-lev)28(el)-279(matrices)-279(and)-278(op)-28(er-)]TJ 0 -13.549 Td [(ators,)-283(without)-270(explicitly)-270(using)-270(an)28(y)-271(inf)1(ormation)-271(on)-270(the)-270(geometry)-270(of)-270(the)-271(original)-270(problem,)]TJ 0 -13.549 Td [(e.g.,)-256(the)-237(discretization)-237(of)-237(a)-237(PDE.)-237(T)84(o)-237(this)-237(end,)-256(the)-237(smo)-28(othed)-237(aggregation)-237(tec)28(hnique)-237([)]TJ 1 0 0 rg 1 0 0 RG [(2)]TJ 0 g 0 G @@ -764,7 +764,7 @@ BT 1 0 0 rg 1 0 0 RG [-236(25)]TJ 0 g 0 G - [(])]TJ 0 -13.549 Td [(is)-377(applied.)-575(Either)-376(exact)-377(or)-377(appro)28(ximate)-377(solv)28(ers)-377(can)-377(b)-28(e)-377(used)-376(on)-377(the)-377(coarsest-lev)28(el)-377(sys-)]TJ 0 -13.55 Td [(tem.)-441(Sp)-27(eci\014cally)83(,)-324(di\013eren)28(t)-322(sparse)-322(LU)-322(factorizations)-321(from)-322(external)-322(pac)28(k)55(ages,)-324(and)-321(nativ)27(e)]TJ 0 -13.549 Td [(incomplete)-285(LU)-285(factorizations)-285(and)-285(Jacobi,)-295(h)28(ybrid)-285(Gauss-Seidel,)-294(and)-285(blo)-28(c)28(k-Jacobi)-285(solv)28(ers)]TJ 0 -13.549 Td [(are)-333(a)27(v)56(ailable.)-444(All)-334(smo)-28(oth)1(e)-1(r)1(s)-334(can)-333(b)-28(e)-333(also)-334(exploited)-333(as)-333(one-lev)27(el)-333(preconditioners.)]TJ 16.937 -14.274 Td [(MLD2P4)-267(is)-267(written)-268(in)-267(F)84(ortran)-267(2003,)-281(follo)28(wing)-267(an)-267(ob)-56(ject-orien)28(ted)-267(design)-268(th)1(rough)-268(the)]TJ -16.937 -13.549 Td [(exploitation)-338(of)-337(features)-338(suc)28(h)-338(as)-337(abstract)-338(data)-338(t)28(yp)-28(e)-337(creation,)-339(t)28(yp)-28(e)-338(extension,)-338(functional)]TJ 0 -13.549 Td [(o)28(v)28(erloading,)-326(and)-325(dynamic)-324(memory)-325(managemen)28(t.)-441(The)-325(parallel)-324(implemen)28(tation)-325(is)-324(based)]TJ 0 -13.549 Td [(on)-424(a)-424(Single)-424(Program)-424(Multiple)-424(Data)-424(\050SPMD\051)-424(paradigm.)-717(Single)-424(and)-424(double)-424(precision)]TJ 0 -13.549 Td [(implemen)28(tations)-486(of)-486(MLD2P4)-486(are)-486(a)28(v)56(ailable)-486(for)-486(b)-27(oth)-486(the)-486(real)-486(and)-486(the)-486(complex)-485(cas)-1(e,)]TJ 0 -13.549 Td [(whic)28(h)-334(can)-333(b)-28(e)-333(used)-333(through)-333(a)-334(single)-333(in)28(terface.)]TJ 16.937 -14.274 Td [(MLD2P4)-229(has)-230(b)-28(een)-229(designed)-229(to)-230(implemen)28(t)-230(scalable)-229(and)-229(easy-to-use)-230(m)28(ultilev)28(el)-230(precon-)]TJ -16.937 -13.549 Td [(ditioners)-349(in)-349(the)-350(con)28(text)-349(of)-349(the)-349(PSBLAS)-349(\050P)27(arallel)-349(Sparse)-349(BLAS\051)-349(computational)-349(frame-)]TJ 0 -13.549 Td [(w)28(ork)-360([)]TJ + [(])]TJ 0 -13.55 Td [(is)-377(applied.)-575(Either)-376(exact)-377(or)-377(appro)28(ximate)-377(solv)28(ers)-377(can)-377(b)-28(e)-377(used)-376(on)-377(the)-377(coarsest-lev)28(el)-377(sys-)]TJ 0 -13.549 Td [(tem.)-441(Sp)-27(eci\014cally)83(,)-324(di\013eren)28(t)-322(sparse)-322(LU)-322(factorizations)-321(from)-322(external)-322(pac)28(k)55(ages,)-324(and)-321(nativ)27(e)]TJ 0 -13.549 Td [(incomplete)-285(LU)-285(factorizations)-285(and)-285(Jacobi,)-295(h)28(ybrid)-285(Gauss-Seidel,)-294(and)-285(blo)-28(c)28(k-Jacobi)-285(solv)28(ers)]TJ 0 -13.549 Td [(are)-333(a)27(v)56(ailable.)-444(All)-334(smo)-28(oth)1(e)-1(r)1(s)-334(can)-333(b)-28(e)-333(also)-334(exploited)-333(as)-333(one-lev)27(el)-333(preconditioners.)]TJ 16.937 -14.408 Td [(MLD2P4)-267(is)-267(written)-268(in)-267(F)84(ortran)-267(2003,)-281(follo)28(wing)-267(an)-267(ob)-56(ject-orien)28(ted)-267(design)-268(th)1(rough)-268(the)]TJ -16.937 -13.549 Td [(exploitation)-338(of)-337(features)-338(suc)28(h)-338(as)-337(abstract)-338(data)-338(t)28(yp)-28(e)-337(creation,)-339(t)28(yp)-28(e)-338(extension,)-338(functional)]TJ 0 -13.549 Td [(o)28(v)28(erloading,)-326(and)-325(dynamic)-324(memory)-325(managemen)28(t.)-441(The)-325(parallel)-324(implemen)28(tation)-325(is)-324(based)]TJ 0 -13.549 Td [(on)-424(a)-424(Single)-424(Program)-424(Multiple)-424(Data)-424(\050SPMD\051)-424(paradigm.)-717(Single)-424(and)-424(double)-424(precision)]TJ 0 -13.549 Td [(implemen)28(tations)-486(of)-486(MLD2P4)-486(are)-486(a)28(v)56(ailable)-486(for)-486(b)-27(oth)-486(the)-486(real)-486(and)-486(the)-486(complex)-485(cas)-1(e,)]TJ 0 -13.55 Td [(whic)28(h)-334(can)-333(b)-28(e)-333(used)-333(through)-333(a)-334(single)-333(in)28(terface.)]TJ 16.937 -14.407 Td [(MLD2P4)-229(has)-230(b)-27(e)-1(en)-229(designed)-229(to)-230(implemen)28(t)-230(scalable)-229(and)-229(easy-to-use)-230(m)28(ultilev)28(el)-230(precon-)]TJ -16.937 -13.549 Td [(ditioners)-349(in)-349(the)-350(con)28(text)-349(of)-349(the)-349(PSBLAS)-349(\050P)27(arallel)-349(Sparse)-349(BLAS\051)-349(computational)-349(frame-)]TJ 0 -13.549 Td [(w)28(ork)-360([)]TJ 1 0 0 rg 1 0 0 RG [(15)]TJ 0 g 0 G @@ -772,7 +772,7 @@ BT 1 0 0 rg 1 0 0 RG [-360(14)]TJ 0 g 0 G - [(].)-524(PSBLAS)-359(pro)28(vides)-360(basic)-360(linear)-360(algebra)-360(op)-27(erators)-360(and)-360(data)-360(managemen)28(t)]TJ 0 -13.55 Td [(facilities)-414(for)-414(distributed)-414(sparse)-414(matrices,)-434(as)-414(w)27(ell)-414(as)-414(parallel)-414(Krylo)28(v)-414(solv)28(ers)-414(whic)28(h)-414(can)]TJ 0 -13.549 Td [(b)-28(e)-401(used)-402(with)-401(the)-401(MLD2P4)-402(p)1(rec)-1(on)1(ditioners.)-649(The)-401(c)27(hoice)-401(of)-401(PSBLAS)-402(h)1(as)-402(b)-28(een)-401(mainly)]TJ 0 -13.549 Td [(motiv)56(ated)-431(b)27(y)-431(the)-431(need)-431(of)-430(ha)27(ving)-431(a)-431(p)-27(ortable)-431(and)-431(e\016cien)28(t)-431(soft)27(w)28(are)-431(infrastructure)-431(im-)]TJ 0 -13.549 Td [(plemen)28(ting)-386(\134de)-385(facto")-386(standard)-386(parallel)-385(sparse)-386(linear)-385(algebra)-386(k)28(ernels,)-399(to)-386(pursue)-385(goals)]TJ 0 -13.549 Td [(suc)28(h)-315(as)-316(p)-27(e)-1(r)1(formance,)-319(p)-28(ortabilit)28(y)83(,)-319(mo)-27(dularit)28(y)-316(ed)-315(extensibilit)28(y)-315(in)-315(the)-316(dev)28(elopmen)28(t)-315(of)-315(the)]TJ 0 -13.55 Td [(preconditioner)-403(pac)28(k)56(age.)-653(On)-402(the)-403(other)-403(hand,)-420(the)-402(implemen)27(tation)-402(of)-403(MLD2P4)-402(has)-403(led)]TJ 0 -13.549 Td [(to)-431(some)-431(revisions)-431(and)-431(exten)28(tions)-431(of)-431(the)-431(original)-431(PSBLAS)-431(k)28(ernels.)-737(The)-431(in)28(ter-pro)-28(cess)]TJ 0 -13.549 Td [(com)28(unication)-458(required)-458(b)28(y)-458(MLD2P4)-458(is)-458(encapsulated)-458(in)-457(the)-458(PSBLAS)-458(routines;)-520(there-)]TJ + [(].)-524(PSBLAS)-359(pro)28(vides)-360(basic)-360(linear)-360(algebra)-360(op)-27(erators)-360(and)-360(data)-360(managemen)28(t)]TJ 0 -13.549 Td [(facilities)-414(for)-414(distributed)-414(sparse)-414(matrices,)-434(as)-414(w)27(ell)-414(as)-414(parallel)-414(Krylo)28(v)-414(solv)28(ers)-414(whic)28(h)-414(can)]TJ 0 -13.55 Td [(b)-28(e)-401(used)-402(with)-401(the)-401(MLD2P4)-401(prec)-1(on)1(ditioners.)-649(The)-401(c)27(hoice)-401(of)-401(PSBLAS)-401(has)-402(b)-28(een)-401(mainly)]TJ 0 -13.549 Td [(motiv)56(ated)-431(b)27(y)-431(the)-431(need)-431(of)-430(ha)27(ving)-431(a)-431(p)-27(ortable)-431(and)-431(e\016cien)28(t)-431(soft)27(w)28(are)-431(infrastructure)-431(im-)]TJ 0 -13.549 Td [(plemen)28(ting)-386(\134de)-385(facto")-386(standard)-386(parallel)-385(sparse)-386(linear)-385(algebra)-386(k)28(ernels,)-399(to)-386(pursue)-385(goals)]TJ 0 -13.549 Td [(suc)28(h)-315(as)-316(p)-27(e)-1(r)1(formance,)-319(p)-28(ortabilit)28(y)83(,)-319(mo)-27(dularit)28(y)-316(ed)-315(extensibilit)28(y)-315(in)-315(the)-316(dev)28(elopmen)28(t)-315(of)-315(the)]TJ 0 -13.549 Td [(preconditioner)-403(pac)28(k)56(age.)-653(On)-402(the)-403(other)-403(hand,)-420(the)-402(implemen)27(tation)-402(of)-403(MLD2P4)-402(has)-403(led)]TJ 0 -13.55 Td [(to)-431(some)-431(revisions)-431(and)-431(exten)28(tions)-431(of)-431(the)-431(original)-431(PSBLAS)-431(k)28(ernels.)-737(The)-431(in)28(ter-pro)-28(cess)]TJ 0 -13.549 Td [(com)28(unication)-458(required)-458(b)28(y)-458(MLD2P4)-458(is)-458(encapsulated)-458(in)-457(the)-458(PSBLAS)-458(routines;)-520(there-)]TJ 0 -13.549 Td [(fore,)-298(MLD2P4)-290(can)-289(b)-28(e)-290(r)1(un)-290(on)-289(an)27(y)-289(parallel)-290(mac)28(hine)-289(where)-290(PSBLAS)-289(implemen)28(tations)-290(are)]TJ 0 g 0 G 0 g 0 G ET @@ -781,22 +781,22 @@ endstream endobj 217 0 obj << -/Length 5503 +/Length 5319 >> stream 0 g 0 G BT /F15 10.9091 Tf 86.4 740.002 Td [(2)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ 0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(fore,)-298(MLD2P4)-290(can)-289(b)-28(e)-289(run)-290(on)-289(an)27(y)-289(parallel)-289(mac)27(hine)-289(where)-290(PSBLAS)-289(implemen)28(tations)-290(are)]TJ 0 -13.549 Td [(a)28(v)55(ailable.)]TJ 16.936 -13.549 Td [(MLD2P4)-342(has)-341(a)-342(la)28(y)28(ered)-342(and)-342(mo)-27(dular)-342(soft)28(w)28(are)-342(arc)28(hitecture)-342(where)-342(three)-341(main)-342(la)28(y)28(ers)]TJ -16.936 -13.549 Td [(can)-458(b)-28(e)-458(iden)28(ti\014ed.)-819(The)-458(lo)28(w)28(er)-458(la)27(y)28(er)-458(consists)-458(of)-458(the)-458(PSBLAS)-458(k)28(ernels,)-490(the)-458(middle)-458(one)]TJ 0 -13.549 Td [(implemen)28(ts)-458(the)-457(construction)-457(and)-458(application)-457(phases)-457(of)-458(the)-457(preconditioners,)-489(and)-457(the)]TJ 0 -13.55 Td [(upp)-28(er)-433(one)-433(pro)28(vides)-433(a)-433(uniform)-433(in)28(terface)-433(to)-433(all)-434(th)1(e)-434(preconditi)1(oners)-1(.)-743(This)-433(arc)27(h)1(ite)-1(ctu)1(re)]TJ 0 -13.549 Td [(allo)28(ws)-413(for)-413(di\013eren)28(t)-413(lev)28(els)-413(of)-412(use)-413(of)-413(the)-413(pac)28(k)56(age:)-604(few)-412(blac)27(k-b)-27(o)27(x)-412(routines)-413(at)-413(the)-412(upp)-28(er)]TJ 0 -13.549 Td [(la)28(y)28(er)-305(allo)28(w)-305(all)-305(users)-304(to)-305(easily)-305(build)-304(and)-305(apply)-304(an)28(y)-305(preconditioner)-305(a)28(v)56(ailable)-305(in)-305(M)1(LD2P4;)]TJ 0 -13.549 Td [(facilities)-432(are)-432(also)-433(a)28(v)56(ailable)-433(allo)28(wing)-432(exp)-28(ert)-432(users)-432(to)-432(exte)-1(n)1(d)-433(the)-432(set)-432(of)-432(smo)-28(others)-432(and)]TJ 0 -13.549 Td [(solv)28(ers)-334(for)-333(building)-333(new)-333(v)27(ersion)1(s)-334(of)-333(the)-333(prec)-1(on)1(ditioners)-334(\050see)-333(Section)]TJ +/F15 10.9091 Tf -203.265 -35.866 Td [(a)28(v)55(ailable.)]TJ 16.936 -13.549 Td [(MLD2P4)-342(has)-341(a)-342(la)28(y)28(ered)-342(and)-342(mo)-27(dular)-342(soft)28(w)28(are)-342(arc)28(hitecture)-342(where)-342(three)-341(main)-342(la)28(y)28(ers)]TJ -16.936 -13.549 Td [(can)-458(b)-28(e)-458(iden)28(ti\014ed.)-819(The)-458(lo)28(w)28(er)-458(la)27(y)28(er)-458(consists)-458(of)-458(the)-458(PSBLAS)-458(k)28(ernels,)-490(the)-458(middle)-458(one)]TJ 0 -13.549 Td [(implemen)28(ts)-458(the)-457(construction)-457(and)-458(application)-457(phases)-457(of)-458(the)-457(preconditioners,)-489(and)-457(the)]TJ 0 -13.549 Td [(upp)-28(er)-433(one)-433(pro)28(vides)-433(a)-433(uniform)-433(in)28(terface)-433(to)-433(all)-434(th)1(e)-434(preconditi)1(oners)-1(.)-743(This)-433(arc)27(h)1(ite)-1(ctu)1(re)]TJ 0 -13.55 Td [(allo)28(ws)-413(for)-413(di\013eren)28(t)-413(lev)28(els)-413(of)-412(use)-413(of)-413(the)-413(pac)28(k)56(age:)-604(few)-412(blac)27(k-b)-27(o)27(x)-412(routines)-413(at)-413(the)-412(upp)-28(er)]TJ 0 -13.549 Td [(la)28(y)28(er)-305(allo)28(w)-305(all)-305(users)-304(to)-305(easily)-305(build)-304(and)-305(apply)-304(an)28(y)-305(preconditioner)-305(a)28(v)56(ailable)-305(in)-305(M)1(LD2P4;)]TJ 0 -13.549 Td [(facilities)-432(are)-432(also)-433(a)28(v)56(ailable)-433(allo)28(wing)-432(exp)-28(ert)-432(users)-432(to)-432(exte)-1(n)1(d)-433(the)-432(set)-432(of)-432(smo)-28(others)-432(and)]TJ 0 -13.549 Td [(solv)28(ers)-334(for)-333(building)-333(new)-333(v)27(ersion)1(s)-334(of)-333(the)-333(prec)-1(on)1(ditioners)-334(\050see)-333(Section)]TJ 0 0 1 rg 0 0 1 RG [-333(7)]TJ 0 g 0 G - [(\051.)]TJ 16.936 -13.55 Td [(W)83(e)-347(n)1(ote)-347(that)-347(the)-347(user)-347(in)28(terface)-347(of)-347(MLD2P)1(4)-347(2.1)-347(has)-347(b)-28(een)-347(extend)1(e)-1(d)-346(with)-347(resp)-28(ect)-347(to)]TJ -16.936 -13.549 Td [(the)-341(previous)-341(v)28(ersions)-341(in)-341(order)-341(to)-341(separate)-341(the)-341(construction)-340(of)-341(the)-341(m)27(ul)1(ti-le)-1(v)28(el)-341(hierarc)28(h)28(y)]TJ 0 -13.549 Td [(from)-320(the)-320(construction)-321(of)-320(the)-320(smo)-28(others)-320(and)-320(solv)28(ers,)-323(and)-320(to)-321(allo)28(w)-320(for)-320(more)-320(\015exibilit)27(y)-320(at)]TJ 0 -13.549 Td [(eac)28(h)-378(lev)28(el.)-579(The)-378(soft)28(w)28(are)-378(arc)28(hitecture)-378(describ)-28(ed)-378(in)-378([)]TJ + [(\051.)]TJ 16.936 -13.549 Td [(W)83(e)-347(n)1(ote)-347(that)-347(the)-347(user)-347(in)28(terface)-347(of)-347(MLD2P)1(4)-347(2.1)-347(has)-347(b)-28(een)-347(extend)1(e)-1(d)-346(with)-347(resp)-28(ect)-347(to)]TJ -16.936 -13.55 Td [(the)-369(previous)-368(v)27(ersions)-368(in)-369(order)-369(to)-368(separate)-369(the)-369(construction)-368(of)-369(the)-369(m)28(ultilev)28(el)-369(hierarc)28(h)28(y)]TJ 0 -13.549 Td [(from)-320(the)-320(construction)-321(of)-320(the)-320(smo)-28(others)-320(and)-320(solv)28(ers,)-323(and)-320(to)-321(allo)28(w)-320(for)-320(more)-320(\015exibilit)27(y)-320(at)]TJ 0 -13.549 Td 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[(linear)-230(system)-230(comes)-230(from)-230(a)-231(standar)1(d)-231(d)1(isc)-1(retization)-230(of)-230(basic)-230(scalar)-230(elliptic)-230(PDE)-230(problems.)]TJ 0 -13.549 Td [(Ho)28(w)28(e)-1(v)28(er,)-284(this)-273(do)-28(es)-272(not)-273(necessarily)-273(corresp)-27(ond)-273(to)-272(the)-273(smallest)-273(execution)-272(time)-273(on)-272(parallel)]TJ 0 -13.549 Td [(computers.)]TJ/F17 11.9552 Tf 0 -29.074 Td [(5.1)-1125(Examples)]TJ/F15 10.9091 Tf 0 -20.595 Td [(The)-262(co)-28(de)-262(rep)-28(orted)-262(in)-262(Figure)]TJ 0 0 1 rg 0 0 1 RG - [-488(2)]TJ + [-262(2)]TJ 0 g 0 G - [-487(sho)27(ws)-487(ho)28(w)-488(to)-487(set)-488(and)-487(apply)-487(the)-488(default)-487(m)27(ul)1(ti-le)-1(v)28(el)]TJ 0 -13.55 Td [(preconditioner)-339(a)28(v)55(ailabl)1(e)-340(in)-339(the)-339(real)-339(double)-339(precision)-339(v)28(ersion)-339(of)-339(MLD2P4)-339(\050see)-339(T)83(able)]TJ + [-263(sho)28(ws)-262(ho)28(w)-263(t)1(o)-263(set)-262(and)-262(apply)-262(the)-262(default)-262(m)27(ultilev)28(el)-262(precon-)]TJ 0 -13.549 Td [(ditioner)-371(a)28(v)55(ailable)-371(in)-371(the)-371(real)-371(double)-371(precision)-371(v)28(ersion)-371(of)-371(MLD2P4)-371(\050see)-371(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-339(1)]TJ + [-371(1)]TJ 0 g 0 G - [(\051.)]TJ 0 -13.549 Td [(This)-465(preconditioner)-464(is)-465(c)27(hosen)-464(b)27(y)-464(simply)-465(sp)-28(ecifying)]TJ/F45 10.9091 Tf 253.737 0 Td [('ML')]TJ/F15 10.9091 Tf 27.978 0 Td [(as)-465(the)-465(second)-464(argumen)27(t)-464(of)]TJ/F45 10.9091 Tf -281.715 -13.549 Td [(P%init)]TJ/F15 10.9091 Tf 38.192 0 Td [(\050a)-351(call)-351(to)]TJ/F45 10.9091 Tf 47.243 0 Td [(P%set)]TJ/F15 10.9091 Tf 32.464 0 Td [(is)-351(not)-351(needed\051)-351(and)-351(is)-351(appli)1(e)-1(d)-350(with)-351(the)-351(CG)-351(solv)28(er)-351(pro)27(vi)1(ded)-351(b)27(y)]TJ -117.899 -13.549 Td [(PSBLAS)-312(\050the)-311(m)-1(atr)1(ix)-312(of)-312(the)-312(system)-312(to)-311(b)-28(e)-312(solv)28(ed)-312(is)-312(assumed)-312(to)-312(b)-27(e)-312(p)-28(ositiv)28(e)-312(de\014nite\051.)-437(As)]TJ + [(\051.)-558(This)]TJ 0 -13.549 Td [(preconditioner)-365(is)-364(c)27(hosen)-365(b)28(y)-364(s)-1(impl)1(y)-365(sp)-28(ecifying)]TJ/F45 10.9091 Tf 220.848 0 Td [('ML')]TJ/F15 10.9091 Tf 26.888 0 Td [(as)-365(the)-365(second)-364(argumen)27(t)-364(of)]TJ/F45 10.9091 Tf 130.352 0 Td [(P%init)]TJ/F15 10.9091 Tf -378.088 -13.55 Td [(\050a)-306(call)-305(to)]TJ/F45 10.9091 Tf 45.76 0 Td [(P%set)]TJ/F15 10.9091 Tf 31.97 0 Td [(is)-306(not)-305(needed\051)-306(and)-305(is)-306(applied)-306(with)-305(the)-306(CG)-305(solv)27(er)-305(pro)28(vided)-306(b)28(y)-306(PSBLAS)]TJ -77.73 -13.549 Td [(\050the)-394(matrix)-394(of)-395(the)-394(system)-394(to)-395(b)-27(e)-395(solv)28(ed)-394(is)-394(assume)-1(d)-394(to)-394(b)-28(e)-394(p)-28(ositiv)28(e)-394(de\014nite\051.)-627(As)-395(previ-)]TJ 0 -13.549 Td [(ously)-315(observ)28(ed,)-319(the)-315(mo)-28(dules)]TJ/F45 10.9091 Tf 137.03 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.727 0 Td [(,)]TJ/F45 10.9091 Tf 6.507 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf 72.163 0 Td [(and)]TJ/F45 10.9091 Tf 21.013 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 83.617 0 Td [(m)28(ust)]TJ 0 g 0 G 0 g 0 G ET @@ -2464,14 +2464,14 @@ endstream endobj 415 0 obj << -/Length 7376 +/Length 7095 >> stream 0 g 0 G BT /F15 10.9091 Tf 86.4 740.002 Td [(18)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ 0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(previously)-352(observ)28(ed,)-357(the)-352(mo)-28(dules)]TJ/F45 10.9091 Tf 162.633 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)]TJ/F45 10.9091 Tf 6.924 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf 72.569 0 Td [(and)]TJ/F45 10.9091 Tf 21.418 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf -332.27 -13.549 Td [(m)28(ust)-334(b)-27(e)-334(used)-333(b)28(y)-334(t)1(he)-334(example)-333(program.)]TJ 16.936 -13.549 Td [(The)-395(part)-395(of)-395(the)-395(co)-28(de)-395(concerning)-395(the)-395(reading)-395(and)-395(assem)27(blin)1(g)-396(of)-395(the)-395(sparse)-395(matrix)]TJ -16.936 -13.549 Td [(and)-457(the)-456(righ)27(t-han)1(d)-457(side)-457(v)28(ector,)-488(p)-28(erformed)-456(through)-457(the)-457(PSBLAS)-456(routines)-457(for)-457(sparse)]TJ 0 -13.549 Td [(matrix)-385(and)-385(v)28(ector)-386(managemen)28(t,)-398(is)-385(not)-385(rep)-28(orted)-385(here)-385(for)-385(brevit)28(y;)-412(t)1(he)-386(statemen)28(ts)-385(con-)]TJ 0 -13.55 Td [(cerning)-265(the)-264(deallo)-28(cation)-265(of)-264(the)-265(PSBLAS)-264(data)-265(structure)-265(are)-264(neglec)-1(ted)-264(to)-28(o.)-422(Th)1(e)-265(complete)]TJ 0 -13.549 Td [(co)-28(de)-306(can)-307(b)-27(e)-307(found)-306(in)-307(the)-306(example)-307(program)-306(\014le)]TJ/F45 10.9091 Tf 223.484 0 Td [(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 108.817 0 Td [(,)-312(in)-306(the)-307(directory)]TJ/F45 10.9091 Tf -332.301 -13.549 Td [(examples/fileread)]TJ/F15 10.9091 Tf 101.269 0 Td [(of)-358(the)-358(MLD2P4)-358(implemen)28(tation)-358(\050see)-359(Section)]TJ +/F15 10.9091 Tf -203.265 -35.866 Td [(b)-28(e)-333(used)-333(b)27(y)-333(the)-333(example)-334(program.)]TJ 16.936 -13.549 Td [(The)-395(part)-395(of)-395(the)-395(co)-28(de)-395(concerning)-395(the)-395(reading)-395(and)-395(assem)27(blin)1(g)-396(of)-395(the)-395(sparse)-395(matrix)]TJ -16.936 -13.549 Td [(and)-457(the)-456(righ)27(t-han)1(d)-457(side)-457(v)28(ector,)-488(p)-28(erformed)-456(through)-457(the)-457(PSBLAS)-456(routines)-457(for)-457(sparse)]TJ 0 -13.549 Td [(matrix)-385(and)-385(v)28(ector)-386(managemen)28(t,)-398(is)-385(not)-385(rep)-28(orted)-385(here)-385(for)-385(brevit)28(y;)-412(t)1(he)-386(statemen)28(ts)-385(con-)]TJ 0 -13.549 Td [(cerning)-265(the)-264(deallo)-28(cation)-265(of)-264(the)-265(PSBLAS)-264(data)-265(structure)-265(are)-264(neglec)-1(ted)-264(to)-28(o.)-422(Th)1(e)-265(complete)]TJ 0 -13.55 Td [(co)-28(de)-306(can)-307(b)-27(e)-307(found)-306(in)-307(the)-306(example)-307(program)-306(\014le)]TJ/F45 10.9091 Tf 223.484 0 Td [(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 108.817 0 Td [(,)-312(in)-306(the)-307(directory)]TJ/F45 10.9091 Tf -332.301 -13.549 Td [(examples/fileread)]TJ/F15 10.9091 Tf 101.269 0 Td [(of)-358(the)-358(MLD2P4)-358(implemen)28(tation)-358(\050see)-359(S)1(e)-1(ction)]TJ 0 0 1 rg 0 0 1 RG [-358(3.5)]TJ 0 g 0 G @@ -2479,31 +2479,31 @@ BT 1 0 0 rg 1 0 0 RG [(13)]TJ 0 g 0 G - [(].)]TJ 16.936 -13.55 Td [(The)-497(setup)-496(and)-496(application)-497(of)-496(the)-496(default)-497(m)28(ulti-lev)28(el)-497(preconditioner)-496(for)-496(the)-497(real)]TJ -16.936 -13.549 Td [(single)-253(precision)-253(and)-253(the)-253(complex,)-269(single)-253(and)-253(double)-253(precision,)-269(v)27(ersions)-253(are)-253(obtained)-253(with)]TJ 0 -13.549 Td [(straigh)28(tforw)28(ard)-229(mo)-28(di\014cations)-229(of)-229(the)-228(previous)-229(example)-229(\050see)-229(Section)]TJ + [(].)]TJ 16.936 -13.549 Td [(The)-279(setup)-278(and)-279(application)-279(of)-278(the)-279(default)-279(m)28(ultilev)28(el)-279(preconditi)1(oner)-279(for)-279(the)-278(real)-279(single)]TJ -16.936 -13.55 Td [(precision)-494(and)-495(the)-494(complex,)-535(single)-494(and)-495(dou)1(ble)-495(precision,)-534(v)27(ersions)-494(are)-495(obtai)1(ned)-495(with)]TJ 0 -13.549 Td [(straigh)28(tforw)28(ard)-229(mo)-28(di\014cations)-229(of)-229(the)-228(previous)-229(example)-229(\050see)-229(Section)]TJ 0 0 1 rg 0 0 1 RG [-229(6)]TJ 0 g 0 G - [-229(for)-229(details\051.)-409(If)-229(these)]TJ 0 -13.549 Td [(v)28(ersions)-334(are)-333(installed,)-333(the)-333(c)-1(or)1(res)-1(p)-27(onding)-333(co)-28(des)-334(are)-333(a)28(v)55(ailable)-333(in)]TJ/F45 10.9091 Tf 300.455 0 Td [(examples/fileread/)]TJ/F15 10.9091 Tf 103.089 0 Td [(.)]TJ -386.608 -13.549 Td [(Di\013eren)28(t)-469(v)27(ersions)-469(of)-469(the)-469(m)28(ulti-lev)28(e)-1(l)-469(preconditioner)-469(can)-469(b)-28(e)-469(obtained)-469(b)28(y)-469(c)28(hanging)]TJ -16.936 -13.55 Td [(the)-439(default)-440(v)56(alues)-440(of)-439(the)-440(pr)1(e)-1(cond)1(itioner)-440(parameters.)-763(The)-439(co)-28(de)-439(rep)-28(orted)-440(in)-439(Figure)]TJ + [-229(for)-229(details\051.)-409(If)-229(these)]TJ 0 -13.549 Td [(v)28(ersions)-334(are)-333(installed,)-333(the)-333(c)-1(or)1(res)-1(p)-27(onding)-333(co)-28(des)-334(are)-333(a)28(v)55(ailable)-333(in)]TJ/F45 10.9091 Tf 300.455 0 Td [(examples/fileread/)]TJ/F15 10.9091 Tf 103.089 0 Td [(.)]TJ -386.608 -13.549 Td [(Di\013eren)28(t)-331(v)28(ersions)-331(of)-330(the)-331(m)28(ultilev)28(el)-331(precondi)1(tioner)-331(can)-331(b)-27(e)-331(obtained)-330(b)28(y)-331(c)28(hanging)-331(the)]TJ -16.936 -13.549 Td [(default)-357(v)55(alues)-357(of)-357(the)-358(p)1(re)-1(cond)1(itioner)-358(parameters.)-516(The)-357(co)-28(de)-358(rep)-27(orted)-358(in)-357(Figure)]TJ 0 0 1 rg 0 0 1 RG - [-439(3)]TJ + [-357(3)]TJ 0 g 0 G - 0 -13.549 Td [(sho)28(ws)-368(ho)28(w)-368(to)-368(set)-367(a)-368(V-cycle)-368(preconditioner)-367(whic)27(h)-367(applies)-368(1)-368(blo)-27(c)27(k-Jacobi)-367(sw)27(eep)-367(as)-368(pre-)]TJ 0 -13.549 Td [(and)-435(p)-27(ost-smo)-28(other,)-460(and)-435(solv)28(es)-435(the)-434(coarsest-le)-1(v)28(el)-434(system)-435(with)-435(8)-434(blo)-28(c)28(k-Jacobi)-435(sw)28(eeps.)]TJ 0 -13.549 Td [(Note)-442(that)-442(the)-442(ILU\0500\051)-442(factorization)-442(\050plus)-442(triangular)-442(solv)28(e\051)-442(is)-442(used)-443(as)-442(lo)-27(cal)-442(s)-1(olv)28(er)-442(for)]TJ 0 -13.549 Td [(the)-359(blo)-28(c)28(k-Jacobi)-360(sw)28(eeps,)-366(since)-359(this)-360(is)-359(the)-360(d)1(e)-1(f)1(ault)-360(asso)-28(ciated)-359(with)-359(blo)-28(c)28(k-Jacobi)-360(and)-359(set)]TJ 0 -13.55 Td [(b)28(y)]TJ/F45 10.9091 Tf 15.824 0 Td [(P%init)]TJ/F15 10.9091 Tf 34.364 0 Td [(.)-629(F)83(urthermore,)-411(sp)-27(ecifying)-395(blo)-28(c)28(k-Jacobi)-395(as)-395(coarsest-)-1(l)1(e)-1(v)28(el)-395(solv)28(er)-395(implies)-395(that)]TJ -50.188 -13.549 Td [(the)-300(coarsest-lev)28(el)-300(matrix)-300(is)-299(distributed)-300(among)-300(the)-299(pro)-28(cesses.)-434(Figur)1(e)]TJ + [-357(sho)27(ws)]TJ 0 -13.55 Td [(ho)28(w)-439(to)-439(set)-439(a)-440(V-cycle)-439(preconditioner)-439(whic)28(h)-439(applies)-439(1)-439(blo)-28(c)28(k-Jacobi)-439(sw)28(eep)-439(as)-440(pre-)-439(and)]TJ 0 -13.549 Td [(p)-28(ost-smo)-28(other,)-379(and)-371(solv)28(es)-371(the)-370(coarsest-lev)28(e)-1(l)-370(system)-371(with)-370(8)-371(b)1(lo)-28(c)27(k)1(-)-1(Jacobi)-370(sw)28(eeps.)-556(Note)]TJ 0 -13.549 Td [(that)-272(th)1(e)-272(ILU\0500\051)-272(factorization)-271(\050plus)-272(triangular)-271(solv)28(e\051)-272(is)-272(used)-271(as)-272(lo)-28(cal)-271(solv)28(e)-1(r)-271(for)-272(the)-271(blo)-28(c)28(k-)]TJ 0 -13.549 Td [(Jacobi)-297(sw)28(eeps,)-304(since)-297(this)-296(is)-297(the)-297(d)1(e)-1(f)1(ault)-297(asso)-28(ciated)-297(with)-296(blo)-28(c)28(k-Jacobi)-297(and)-296(set)-297(b)28(y)]TJ/F45 10.9091 Tf 375.057 0 Td [(P%init)]TJ/F15 10.9091 Tf 34.364 0 Td [(.)]TJ -409.421 -13.549 Td [(F)83(urthermore,)-347(s)-1(p)-27(ecifying)-345(blo)-28(c)28(k-Jacobi)-345(as)-345(coarsest-lev)27(el)-345(solv)28(er)-345(implies)-345(that)-345(the)-345(coarsest-)]TJ 0 -13.55 Td [(lev)28(el)-361(matrix)-360(is)-360(distributed)-361(among)-360(the)-360(pro)-28(cesses.)-526(Figure)]TJ 0 0 1 rg 0 0 1 RG - [-300(4)]TJ + [-360(4)]TJ 0 g 0 G - [-300(sho)28(ws)-300(ho)28(w)-300(to)-300(set)]TJ 0 -13.549 Td [(a)-315(W-cycle)-315(preconditioner)-315(whic)28(h)-315(applies)-315(2)-314(h)27(ybrid)-314(Gauss-)-1(S)1(e)-1(i)1(del)-315(sw)27(eeps)-315(as)-315(pre-)-315(an)1(d)-315(p)-28(ost-)]TJ 0 -13.549 Td [(smo)-28(other,)-400(and)-387(solv)28(es)-387(the)-387(coarsest-lev)27(el)-387(system)-387(with)-387(the)-387(m)28(ultifron)28(tal)-387(LU)-387(factorization)]TJ 0 -13.549 Td [(implemen)28(ted)-415(in)-414(MUMPS.)-414(It)-414(is)-415(sp)-28(eci\014ed)-414(that)-414(the)-415(coarsest-lev)28(el)-414(matrix)-415(is)-414(distributed,)]TJ 0 -13.549 Td [(since)-306(MUMPS)-306(can)-306(b)-28(e)-306(used)-307(on)-306(b)-27(oth)-307(repli)1(c)-1(ated)-306(and)-306(distributed)-306(matrices,)-312(an)1(d)-307(b)28(y)-306(default)]TJ 0 -13.55 Td [(it)-283(is)-282(used)-283(on)-282(replicated)-283(ones.)-427(The)-283(co)-28(de)-282(fragmen)27(ts)-282(sho)28(wn)-283(in)-283(F)1(igures)]TJ + 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[(...)-525(...)]TJ +/F45 9.9626 Tf -77.116 -65.676 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(build)-525(a)-525(W-cycle)-525(preconditioner)-525(with)-525(2)-525(hybrid)-525(Gauss-Seidel)-525(sweeps)]TJ 0 -11.955 Td [(!)-525(as)-525(pre-)-525(and)-525(post-smoother,)-525(a)-525(distributed)-525(coarsest)]TJ 0 -11.955 Td [(!)-525(matrix,)-525(and)-525(MUMPS)-525(as)-525(coarsest-level)-525(solver)]TJ 10.46 -11.956 Td [(call)-525(P%init\050'ML',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'ML_CYCLE','WCYCLE',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'SMOOTHER_TYPE','FBGS',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'SMOOTHER_SWEEPS',2,info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'COARSE_SOLVE','MUMPS',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'COARSE_MAT','DIST',info\051)]TJ 0 -11.956 Td [(call)-525(P%hierarchy_build\050A,desc_A,info\051)]TJ 0 -11.955 Td [(call)-525(P%smoothers_build\050A,desc_A,info\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ 0 g 0 G -/F15 10.9091 Tf 75.298 -18.535 Td [(Figure)-333(4:)-445(setup)-333(of)-333(a)-334(m)28(ulti-lev)28(el)-333(preconditioner)]TJ +/F15 10.9091 Tf 77.116 -18.535 Td [(Figure)-333(4:)-445(setup)-333(of)-333(a)-334(m)28(ultilev)28(el)-333(preconditioner)]TJ 0 g 0 G 0 g 0 G 0 g 0 G @@ -3258,7 +3261,7 @@ BT 0 g 0 G 0 g 0 G 0 g 0 G -/F45 9.9626 Tf -75.298 -65.675 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(set)-525(RAS)-525(with)-525(overlap)-525(2)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(local)-525(blocks)]TJ 10.46 -11.956 Td [(call)-525(P%init\050'AS',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'SUB_OVR',2,info\051)]TJ 0 -11.955 Td [(call)-525(P%bld\050A,desc_A,info\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(solve)-525(Ax=b)-525(with)-525(preconditioned)-525(BiCGSTAB)]TJ 10.46 -11.955 Td [(call)-525(psb_krylov\050'BICGSTAB',A,P,b,x,tol,desc_A,info\051)]TJ +/F45 9.9626 Tf -77.116 -65.675 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(set)-525(RAS)-525(with)-525(overlap)-525(2)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(local)-525(blocks)]TJ 10.46 -11.956 Td [(call)-525(P%init\050'AS',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'SUB_OVR',2,info\051)]TJ 0 -11.955 Td [(call)-525(P%bld\050A,desc_A,info\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(solve)-525(Ax=b)-525(with)-525(preconditioned)-525(BiCGSTAB)]TJ 10.46 -11.955 Td [(call)-525(psb_krylov\050'BICGSTAB',A,P,b,x,tol,desc_A,info\051)]TJ 0 g 0 G /F15 10.9091 Tf 46.641 -20.749 Td [(Figure)-333(5:)-445(setup)-333(of)-333(a)-334(one-lev)28(el)-333(Sc)28(h)27(w)28(arz)-333(preconditioner.)]TJ 0 g 0 G @@ -3271,7 +3274,7 @@ endstream endobj 435 0 obj << -/Length 6206 +/Length 6211 >> stream 0 g 0 G @@ -3281,7 +3284,7 @@ BT 0 g 0 G [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(21)]TJ 0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(6)-1125(User)-375(In)31(terface)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)-352(basic)-352(user)-352(in)28(terface)-352(of)-351(MLD2P4)-352(consists)-352(of)-352(eigh)28(t)-352(routines.)-500(The)-352(six)-351(routines)]TJ/F45 10.9091 Tf 386.512 0 Td [(init)]TJ/F15 10.9091 Tf 22.909 0 Td [(,)]TJ/F45 10.9091 Tf -409.421 -13.549 Td [(set)]TJ/F15 10.9091 Tf 17.182 0 Td [(,)]TJ/F45 10.9091 Tf 5.75 0 Td [(hierarchy_build)]TJ/F15 10.9091 Tf 85.908 0 Td [(,)]TJ/F45 10.9091 Tf 5.75 0 Td [(smoothers_build)]TJ/F15 10.9091 Tf 85.908 0 Td [(,)]TJ/F45 10.9091 Tf 5.75 0 Td [(bld)]TJ/F15 10.9091 Tf 17.182 0 Td [(,)-249(and)]TJ/F45 10.9091 Tf 25.816 0 Td [(apply)]TJ/F15 10.9091 Tf 31.127 0 Td [(encapsulate)-228(all)-229(the)-228(function-)]TJ -280.373 -13.549 Td [(alities)-323(for)-322(the)-323(setup)-323(and)-322(the)-323(application)-322(of)-323(an)28(y)-323(m)28(ulti-lev)28(el)-323(and)-322(one-lev)27(el)-322(preconditioner)]TJ 0 -13.549 Td [(implemen)28(ted)-466(i)1(n)-466(the)-465(pac)28(k)55(age.)-840(The)-465(routine)]TJ/F45 10.9091 Tf 212.452 0 Td [(free)]TJ/F15 10.9091 Tf 27.985 0 Td [(deallo)-28(cates)-465(the)-465(preconditioner)-465(data)]TJ -240.437 -13.55 Td [(structure,)-333(while)]TJ/F45 10.9091 Tf 78.303 0 Td [(descr)]TJ/F15 10.9091 Tf 32.273 0 Td [(prin)28(ts)-333(a)-334(description)-333(of)-333(the)-334(preconditi)1(oner)-334(setup)-333(b)28(y)-334(the)-333(user.)]TJ -93.639 -13.549 Td [(All)-434(the)-433(routines)-434(are)-434(a)28(v)56(ailable)-434(as)-434(metho)-28(ds)-433(of)-434(the)-434(preconditioner)-433(ob)-56(ject.)-745(F)83(or)-434(eac)28(h)]TJ -16.937 -13.549 Td [(routine,)-418(the)-402(same)-401(user)-402(in)28(terface)-401(is)-402(o)28(v)28(erloaded)-402(with)-401(resp)-28(ect)-401(to)-402(the)-401(real/)-402(complex)-401(case)]TJ 0 -13.549 Td [(and)-274(the)-274(single/double)-274(precision;)-294(argumen)28(ts)-275(with)-274(appropriate)-274(data)-274(t)28(yp)-28(es)-274(m)28(ust)-275(b)-27(e)-274(pass)-1(ed)]TJ 0 -13.549 Td [(to)-333(the)-334(routine,)-333(i.e.,)]TJ +/F17 14.3462 Tf -401.542 -35.866 Td [(6)-1125(User)-375(In)31(terface)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)-352(basic)-352(user)-352(in)28(terface)-352(of)-351(MLD2P4)-352(consists)-352(of)-352(eigh)28(t)-352(routines.)-500(The)-352(six)-351(routines)]TJ/F45 10.9091 Tf 386.512 0 Td [(init)]TJ/F15 10.9091 Tf 22.909 0 Td [(,)]TJ/F45 10.9091 Tf -409.421 -13.549 Td [(set)]TJ/F15 10.9091 Tf 17.182 0 Td [(,)]TJ/F45 10.9091 Tf 5.75 0 Td [(hierarchy_build)]TJ/F15 10.9091 Tf 85.908 0 Td [(,)]TJ/F45 10.9091 Tf 5.75 0 Td [(smoothers_build)]TJ/F15 10.9091 Tf 85.908 0 Td [(,)]TJ/F45 10.9091 Tf 5.75 0 Td [(bld)]TJ/F15 10.9091 Tf 17.182 0 Td [(,)-249(and)]TJ/F45 10.9091 Tf 25.816 0 Td [(apply)]TJ/F15 10.9091 Tf 31.127 0 Td [(encapsulate)-228(all)-229(the)-228(function-)]TJ -280.373 -13.549 Td [(alities)-350(for)-351(the)-350(setup)-351(and)-350(the)-350(application)-351(of)-350(an)28(y)-351(m)28(ultilev)28(el)-351(an)1(d)-351(one-lev)28(el)-351(precondit)1(ioner)]TJ 0 -13.549 Td [(implemen)28(ted)-466(i)1(n)-466(the)-465(pac)28(k)55(age.)-840(The)-465(routine)]TJ/F45 10.9091 Tf 212.452 0 Td [(free)]TJ/F15 10.9091 Tf 27.985 0 Td [(deallo)-28(cates)-465(the)-465(preconditioner)-465(data)]TJ -240.437 -13.55 Td [(structure,)-333(while)]TJ/F45 10.9091 Tf 78.303 0 Td [(descr)]TJ/F15 10.9091 Tf 32.273 0 Td [(prin)28(ts)-333(a)-334(description)-333(of)-333(the)-334(preconditi)1(oner)-334(setup)-333(b)28(y)-334(the)-333(user.)]TJ -93.639 -13.549 Td [(All)-434(the)-433(routines)-434(are)-434(a)28(v)56(ailable)-434(as)-434(metho)-28(ds)-433(of)-434(the)-434(preconditioner)-433(ob)-56(ject.)-745(F)83(or)-434(eac)28(h)]TJ -16.937 -13.549 Td [(routine,)-418(the)-402(same)-401(user)-402(in)28(terface)-401(is)-402(o)28(v)28(erloaded)-402(with)-401(resp)-28(ect)-401(to)-402(the)-401(real/)-402(complex)-401(case)]TJ 0 -13.549 Td [(and)-274(the)-274(single/double)-274(precision;)-294(argumen)28(ts)-275(with)-274(appropriate)-274(data)-274(t)28(yp)-28(es)-274(m)28(ust)-275(b)-27(e)-274(pass)-1(ed)]TJ 0 -13.549 Td [(to)-333(the)-334(routine,)-333(i.e.,)]TJ 0 g 0 G /F25 10.9091 Tf 16.364 -22.516 Td [(\017)]TJ 0 g 0 G @@ -3340,7 +3343,7 @@ endstream endobj 453 0 obj << -/Length 7087 +/Length 7098 >> stream 0 g 0 G @@ -3373,7 +3376,7 @@ BT 0 0 1 rg 0 0 1 RG [-333(8)]TJ 0 g 0 G - [-333(for)-334(details.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(ilev)-2114(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(F)83(or)-306(the)-307(m)28(ulti-lev)28(el)-307(preconditioner,)-311(the)-307(lev)28(el)-307(at)-306(whic)27(h)-306(the)-307(preconditioner)]TJ 0 -13.549 Td [(parameter)-404(has)-404(to)-404(b)-27(e)-404(set.)-656(T)-1(h)1(e)-404(lev)27(els)-404(are)-403(n)27(um)28(b)-28(ered)-403(in)-404(increasing)-404(order)]TJ 0 -13.55 Td 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[(parameter)-404(has)-404(to)-404(b)-27(e)-404(set.)-656(T)-1(h)1(e)-404(lev)27(els)-404(are)-403(n)27(um)28(b)-28(ered)-403(in)-404(increasing)-404(order)]TJ 0 -13.55 Td [(starting)-307(from)-307(the)-306(\014nest)-307(one,)-312(i.e.,)-313(lev)28(el)-307(1)-307(i)1(s)-307(the)-307(\014nest)-307(lev)28(el.)-436(If)]TJ/F45 10.9091 Tf 287.463 0 Td [(ilev)]TJ/F15 10.9091 Tf 26.256 0 Td [(is)-307(not)]TJ -313.719 -13.549 Td [(presen)28(t,)-419(the)-402(parameter)-402(iden)27(ti\014ed)-402(b)28(y)]TJ/F45 10.9091 Tf 178.631 0 Td [(what)]TJ/F15 10.9091 Tf 27.295 0 Td [(is)-402(set)-402(at)-402(all)-402(the)-402(appropriate)]TJ -205.926 -13.549 Td [(lev)28(els)-334(\050see)-333(T)83(ables)]TJ 0 0 1 rg 0 0 1 RG [-333(2)]TJ 0 g 0 G @@ -3381,7 +3384,7 @@ BT 0 0 1 rg 0 0 1 RG [(8)]TJ 0 g 0 G - [(\051.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(ilmax)-1589(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(F)83(or)-572(the)-572(m)28(ulti-lev)28(el)-572(preconditioner,)-632(when)-572(b)-28(oth)]TJ/F45 10.9091 Tf 237.737 0 Td [(ilev)]TJ/F15 10.9091 Tf 29.15 0 Td [(and)]TJ/F45 10.9091 Tf 23.817 0 Td [(ilmax)]TJ/F15 10.9091 Tf 34.878 0 Td [(are)]TJ -325.582 -13.549 Td [(presen)28(t,)-393(the)-381(settings)-380(are)-381(applied)-381(at)-381(all)-380(lev)27(els)]TJ/F45 10.9091 Tf 218.209 0 Td [(ilev:ilmax)]TJ/F15 10.9091 Tf 57.272 0 Td [(.)-587(When)]TJ/F45 10.9091 Tf 41.768 0 Td [(ilev)]TJ/F15 10.9091 Tf -317.249 -13.55 Td [(is)-341(presen)28(t)-341(but)]TJ/F45 10.9091 Tf 69.19 0 Td [(ilmax)]TJ/F15 10.9091 Tf 32.355 0 Td [(is)-341(not,)-343(then)-341(the)-341(default)-341(is)]TJ/F45 10.9091 Tf 125.189 0 Td [(ilmax=ilev)]TJ/F15 10.9091 Tf 57.272 0 Td [(.)-467(The)-341(lev)27(els)]TJ -284.006 -13.549 Td [(are)-331(n)28(um)27(b)-27(ered)-332(in)-331(increasing)-331(order)-331(starting)-332(from)-331(the)-331(\014nest)-331(one,)-332(i.e.,)-332(lev)28(el)]TJ 0 -13.549 Td [(1)-333(is)-334(the)-333(\014nest)-333(lev)27(el.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(pos)-2639(charater\050len=*\051,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 257.878 0 Td [(.)]TJ -211.907 -13.549 Td [(Whether)-256(the)-255(other)-256(argumen)28(ts)-256(app)1(ly)-256(only)-256(to)-255(the)-256(pre-smo)-28(other)-255(\050)]TJ/F45 10.9091 Tf 294.764 0 Td [('PRE')]TJ/F15 10.9091 Tf 28.636 0 Td [(\051)-256(or)]TJ -323.4 -13.55 Td [(to)-223(the)-223(p)-27(ost-smo)-28(other)-223(\050)]TJ/F45 10.9091 Tf 104.413 0 Td [('POST')]TJ/F15 10.9091 Tf 34.363 0 Td [(\051.)-223(If)]TJ/F45 10.9091 Tf 19.406 0 Td [(pos)]TJ/F15 10.9091 Tf 19.612 0 Td [(is)-223(not)-223(presen)28(t,)-245(the)-222(other)-223(argumen)28(ts)]TJ -177.794 -13.549 Td [(are)-349(applied)-349(to)-349(b)-28(oth)-349(smo)-28(others.)-492(If)-349(the)-349(preconditioner)-349(is)-350(one-lev)28(el)-349(or)-349(the)]TJ 0 -13.549 Td [(parameter)-447(iden)28(ti\014ed)-448(b)28(y)]TJ/F45 10.9091 Tf 118.636 0 Td [(what)]TJ/F15 10.9091 Tf 27.788 0 Td [(do)-28(es)-447(not)-447(concern)-447(the)-448(smo)-27(others,)]TJ/F45 10.9091 Tf 164.34 0 Td [(pos)]TJ/F15 10.9091 Tf 22.06 0 Td [(is)]TJ -332.824 -13.549 Td [(ignored.)]TJ -51.948 -32.961 Td [(F)83(or)-380(compatibilit)28(y)-381(with)-380(the)-381(pr)1(e)-1(viou)1(s)-381(v)28(ersions)-381(of)-380(MLD2P4,)-392(this)-381(routine)-380(can)-381(b)-27(e)-381(also)]TJ -16.937 -13.549 Td [(in)28(v)28(ok)27(ed)-333(as)-333(follo)28(ws:)]TJ + [(\051.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(ilmax)-1589(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(F)83(or)-608(the)-608(m)28(ultilev)28(el)-609(p)1(rec)-1(on)1(ditioner,)-677(when)-608(b)-28(oth)]TJ/F45 10.9091 Tf 236.557 0 Td [(ilev)]TJ/F15 10.9091 Tf 29.544 0 Td [(and)]TJ/F45 10.9091 Tf 24.21 0 Td [(ilmax)]TJ/F15 10.9091 Tf 35.271 0 Td [(are)]TJ -325.582 -13.549 Td 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