diff --git a/docs/html/node16.html b/docs/html/node16.html index 8b62880f..3b79c094 100644 --- a/docs/html/node16.html +++ b/docs/html/node16.html @@ -145,6 +145,18 @@ Preconditioner types, corresponding strings and default choices. For any zero diagonal entry of the matrix to be preconditioned, the corresponding entry of the preconditioner is set to 1. +Gauss-Seidel +'GS' +Hybrid Gauss-Seidel (forward), that is, + global block Jacobi with + Gauss-Seidel as local solver. + +Symmetrized Gauss-Seidel +'FBGS' +Symmetrized hybrid Gauss-Seidel,that is, + forward Gauss-Seidel followed by + backward Gauss-Seidel. + Block Jacobi 'BJAC' Block-Jacobi with ILU(0) on the local blocks. diff --git a/docs/html/node31.html b/docs/html/node31.html index a3b9af7c..94842ed4 100644 --- a/docs/html/node31.html +++ b/docs/html/node31.html @@ -63,7 +63,7 @@ Mathematics Department, Macquarie University, Sydney. The command line arguments were:
latex2html -local_icons -noaddress -dir ../../html userhtml.tex

-The translation was initiated by Salvatore Filippone on 2017-09-18 +The translation was initiated by Salvatore Filippone on 2017-09-20

diff --git a/docs/mld2p4-2.1-guide.pdf b/docs/mld2p4-2.1-guide.pdf index cc4d9199..066527c2 100644 --- a/docs/mld2p4-2.1-guide.pdf +++ b/docs/mld2p4-2.1-guide.pdf @@ -179,7 +179,7 @@ BT 0 g 0 G [-792(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1280(17)]TJ + [-1280(18)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG /F44 10.9091 Tf -16.364 -24.459 Td [(6)-925(User)-383(In)32(terface)]TJ @@ -2222,7 +2222,7 @@ endstream endobj 402 0 obj << -/Length 9618 +/Length 9356 >> stream 0 g 0 G @@ -2246,174 +2246,232 @@ BT 0 g 0 G ET q -1 0 0 1 97.252 663.056 cm -[]0 d 0 J 0.398 w 0 0 m 405.148 0 l S +1 0 0 1 93.6 642.85 cm +[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S Q q -1 0 0 1 97.252 649.307 cm +1 0 0 1 93.6 629.102 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F42 10.9091 Tf 103.229 653.372 Td [(type)]TJ +/F42 10.9091 Tf 99.578 633.167 Td [(type)]TJ ET q -1 0 0 1 195.025 649.307 cm +1 0 0 1 231.54 629.102 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F42 10.9091 Tf 201.003 653.372 Td [(string)]TJ +/F42 10.9091 Tf 237.518 633.167 Td [(string)]TJ ET q -1 0 0 1 258.004 649.307 cm +1 0 0 1 294.519 629.102 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F42 10.9091 Tf 263.982 653.372 Td [(def)89(a)22(ul)67(t)-378(preconditioner)]TJ +/F42 10.9091 Tf 300.497 633.167 Td [(def)89(a)22(ul)67(t)-378(preconditioner)]TJ ET q -1 0 0 1 502.4 649.307 cm +1 0 0 1 538.915 629.102 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q q -1 0 0 1 97.252 649.108 cm -[]0 d 0 J 0.398 w 0 0 m 405.148 0 l S +1 0 0 1 93.6 628.903 cm +[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S Q q -1 0 0 1 97.252 621.81 cm +1 0 0 1 93.6 601.605 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 103.229 639.424 Td [(No)-333(preconditioner)]TJ +/F15 10.9091 Tf 99.578 619.219 Td [(No)-333(preconditioner)]TJ ET q -1 0 0 1 195.025 621.81 cm +1 0 0 1 231.54 601.605 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F45 10.9091 Tf 201.003 639.424 Td [('NOPREC')]TJ +/F45 10.9091 Tf 237.518 619.219 Td [('NOPREC')]TJ ET q -1 0 0 1 258.004 621.81 cm +1 0 0 1 294.519 601.605 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 263.982 639.424 Td [(Considered)-680(only)-681(to)-680(use)-680(the)-681(PSBLAS)-680(Krylo)28(v)]TJ 0 -13.549 Td [(solv)28(ers)-334(with)-333(no)-333(preconditioner.)]TJ +/F15 10.9091 Tf 300.497 619.219 Td [(Considered)-680(only)-681(to)-680(use)-681(th)1(e)-681(PSBLAS)-680(Krylo)28(v)]TJ 0 -13.549 Td [(solv)28(ers)-334(with)-333(no)-333(preconditioner.)]TJ ET q -1 0 0 1 502.4 621.81 cm +1 0 0 1 538.915 601.605 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q q -1 0 0 1 97.252 621.611 cm -[]0 d 0 J 0.398 w 0 0 m 405.148 0 l S +1 0 0 1 93.6 601.406 cm +[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S Q q -1 0 0 1 97.252 580.764 cm +1 0 0 1 93.6 560.559 cm []0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q BT -/F15 10.9091 Tf 103.229 611.927 Td [(Diagonal)]TJ +/F15 10.9091 Tf 99.578 591.722 Td [(Diagonal)]TJ ET q -1 0 0 1 195.025 580.764 cm +1 0 0 1 231.54 560.559 cm []0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q BT -/F45 10.9091 Tf 201.003 611.927 Td [('DIAG')]TJ/F15 10.9091 Tf 41.296 0 Td [(or)]TJ/F45 10.9091 Tf -41.296 -13.549 Td [('JACOBI')]TJ +/F45 10.9091 Tf 237.518 591.722 Td [('DIAG')]TJ/F15 10.9091 Tf 41.296 0 Td [(or)]TJ/F45 10.9091 Tf -41.296 -13.549 Td [('JACOBI')]TJ ET q -1 0 0 1 258.004 580.764 cm +1 0 0 1 294.519 560.559 cm []0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q BT -/F15 10.9091 Tf 263.982 611.927 Td [(Diagonal)-423(preconditioner.)-714(F)83(or)-423(an)28(y)-423(zero)-424(diagon)1(al)]TJ 0 -13.549 Td [(en)28(try)-275(of)-275(the)-275(matrix)-275(to)-276(b)-27(e)-276(p)1(rec)-1(on)1(ditioned,)-287(the)-275(cor-)]TJ 0 -13.549 Td [(resp)-28(onding)-278(en)28(try)-278(of)-278(the)-278(pr)1(e)-1(cond)1(itioner)-278(is)-278(set)-278(to)-278(1.)]TJ +/F15 10.9091 Tf 300.497 591.722 Td [(Diagonal)-423(preconditioner.)-714(F)83(or)-423(an)28(y)-423(zero)-424(diagon)1(al)]TJ 0 -13.549 Td [(en)28(try)-275(of)-275(the)-275(matrix)-276(to)-275(b)-27(e)-276(p)1(re)-1(cond)1(itioned,)-287(the)-275(cor-)]TJ 0 -13.549 Td [(resp)-28(onding)-278(en)28(try)-278(of)-278(the)-278(precondit)1(ioner)-278(is)-278(set)-278(to)-278(1.)]TJ ET q -1 0 0 1 502.4 580.764 cm +1 0 0 1 538.915 560.559 cm []0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q q -1 0 0 1 97.252 580.565 cm -[]0 d 0 J 0.398 w 0 0 m 405.148 0 l S +1 0 0 1 93.6 560.36 cm +[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S Q q -1 0 0 1 97.252 566.816 cm +1 0 0 1 93.6 533.062 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +Q +BT +/F15 10.9091 Tf 99.578 550.676 Td [(Gauss-Seidel)]TJ +ET +q +1 0 0 1 231.54 533.062 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +Q +BT +/F45 10.9091 Tf 237.518 550.676 Td [('GS')]TJ +ET +q +1 0 0 1 294.519 533.062 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +Q +BT +/F15 10.9091 Tf 300.497 550.676 Td [(Hybrid)-565(Gauss-Seidel)-565(\050forw)28(ard\051,)-623(that)-566(is,)-623(global)]TJ 0 -13.549 Td [(blo)-28(c)28(k)-333(Jacobi)-334(with)-333(Gauss-Seidel)-333(as)-334(lo)-27(cal)-334(solv)28(er.)]TJ +ET +q +1 0 0 1 538.915 533.062 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S +Q +q +1 0 0 1 93.6 532.863 cm +[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S +Q +q +1 0 0 1 93.6 492.016 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +BT +/F15 10.9091 Tf 99.578 523.179 Td [(Symmetrized)-333(Gauss-Seidel)]TJ +ET +q +1 0 0 1 231.54 492.016 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +BT +/F45 10.9091 Tf 237.518 523.179 Td [('FBGS')]TJ +ET +q +1 0 0 1 294.519 492.016 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +BT +/F15 10.9091 Tf 300.497 523.179 Td [(Symmetrized)-646(h)27(ybrid)-646(Gauss-Seidel,that)-646(is,)-725(for-)]TJ 0 -13.549 Td [(w)28(ard)-392(Gauss-Seidel)-392(follo)28(w)27(ed)-392(b)28(y)-392(bac)28(kw)28(ard)-392(Gauss-)]TJ 0 -13.549 Td [(Seidel.)]TJ +ET +q +1 0 0 1 538.915 492.016 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S +Q +q +1 0 0 1 93.6 491.817 cm +[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S +Q +q +1 0 0 1 93.6 478.068 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F15 10.9091 Tf 103.229 570.881 Td [(Blo)-28(c)28(k)-333(Jacobi)]TJ +/F15 10.9091 Tf 99.578 482.133 Td [(Blo)-28(c)28(k)-333(Jacobi)]TJ ET q -1 0 0 1 195.025 566.816 cm +1 0 0 1 231.54 478.068 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F45 10.9091 Tf 201.003 570.881 Td [('BJAC')]TJ +/F45 10.9091 Tf 237.518 482.133 Td [('BJAC')]TJ ET q -1 0 0 1 258.004 566.816 cm +1 0 0 1 294.519 478.068 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q BT -/F15 10.9091 Tf 263.982 570.881 Td [(Blo)-28(c)28(k-Jacobi)-333(with)-334(ILU\0500\051)-333(on)-333(the)-334(lo)-27(cal)-334(blo)-27(c)27(ks.)]TJ +/F15 10.9091 Tf 300.497 482.133 Td [(Blo)-28(c)28(k-Jacobi)-333(with)-334(ILU\0500\051)-333(on)-333(the)-334(lo)-27(cal)-334(blo)-27(c)27(ks.)]TJ ET q -1 0 0 1 502.4 566.816 cm +1 0 0 1 538.915 478.068 cm []0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q q -1 0 0 1 97.252 566.617 cm -[]0 d 0 J 0.398 w 0 0 m 405.148 0 l S +1 0 0 1 93.6 477.869 cm +[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S Q q -1 0 0 1 97.252 539.32 cm +1 0 0 1 93.6 450.571 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 103.229 556.934 Td [(Additiv)28(e)-333(Sc)27(h)28(w)28(arz)]TJ +/F15 10.9091 Tf 99.578 468.185 Td [(Additiv)28(e)-333(Sc)27(h)28(w)28(arz)]TJ ET q -1 0 0 1 195.025 539.32 cm +1 0 0 1 231.54 450.571 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F45 10.9091 Tf 201.003 556.934 Td [('AS')]TJ +/F45 10.9091 Tf 237.518 468.185 Td [('AS')]TJ ET q -1 0 0 1 258.004 539.32 cm +1 0 0 1 294.519 450.571 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q BT -/F15 10.9091 Tf 263.982 556.934 Td [(Restricted)-475(Additiv)28(e)-476(Sc)28(h)28(w)28(arz)-476(\050RAS\051,)-475(with)-475(o)28(v)27(er-)]TJ 0 -13.55 Td [(lap)-333(1)-334(and)-333(ILU\0500\051)-333(on)-333(the)-334(lo)-27(c)-1(al)-333(blo)-28(c)28(ks.)]TJ +/F15 10.9091 Tf 300.497 468.185 Td [(Restricted)-475(Additiv)28(e)-476(Sc)28(h)28(w)28(arz)-476(\050RAS\051,)-475(with)-475(o)28(v)27(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 1 502.4 539.32 cm +1 0 0 1 538.915 450.571 cm []0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q q -1 0 0 1 97.252 539.12 cm -[]0 d 0 J 0.398 w 0 0 m 405.148 0 l S +1 0 0 1 93.6 450.372 cm +[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S Q q -1 0 0 1 97.252 444.077 cm +1 0 0 1 93.6 355.328 cm []0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q BT -/F15 10.9091 Tf 103.229 529.437 Td [(Multilev)28(el)]TJ +/F15 10.9091 Tf 99.578 440.688 Td [(Multilev)28(el)]TJ ET q -1 0 0 1 195.025 444.077 cm +1 0 0 1 231.54 355.328 cm []0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q BT -/F45 10.9091 Tf 201.003 529.437 Td [('ML')]TJ +/F45 10.9091 Tf 237.518 440.688 Td [('ML')]TJ ET q -1 0 0 1 258.004 444.077 cm +1 0 0 1 294.519 355.328 cm []0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q BT -/F15 10.9091 Tf 263.982 529.437 Td [(V-cycle)-590(with)-589(one)-589(h)27(ybri)1(d)-590(forw)28(ard)-589(Gaus)-1(s-Seidel)]TJ 0 -13.55 Td [(\050GS\051)-245(s)-1(w)28(eep)-245(as)-246(pre-smo)-28(other)-246(and)-245(one)-246(h)28(ybrid)-246(bac)28(k-)]TJ 0 -13.549 Td [(w)28(ard)-249(GS)-249(sw)28(e)-1(ep)-249(as)-249(p)-27(ost-)-1(smo)-27(other,)-266(basic)-249(smo)-28(othed)]TJ 0 -13.549 Td [(aggregation)-645(as)-644(coarse)-1(n)1(ing)-645(algorithm,)-723(and)-644(LU)]TJ 0 -13.549 Td [(\050plus)-575(triangu)1(lar)-575(solv)28(e\051)-575(as)-575(coarsest-lev)28(el)-575(solv)28(er.)]TJ 0 -13.549 Td [(See)-449(the)-449(default)-449(v)55(alues)-449(in)-449(T)83(ables)]TJ +/F15 10.9091 Tf 300.497 440.688 Td [(V-cycle)-590(with)-589(one)-589(h)27(ybrid)-589(forw)28(ard)-590(Gau)1(s)-1(s-Seidel)]TJ 0 -13.549 Td [(\050GS\051)-246(sw)28(eep)-246(as)-245(pre-smo)-28(other)-246(and)-245(one)-246(h)28(ybrid)-246(bac)28(k-)]TJ 0 -13.549 Td [(w)28(ard)-249(GS)-249(sw)28(e)-1(ep)-249(as)-249(p)-27(os)-1(t-smo)-27(other,)-266(basic)-249(smo)-28(othed)]TJ 0 -13.549 Td [(aggregation)-645(as)-644(coarse)-1(n)1(ing)-645(algorithm,)-723(and)-644(LU)]TJ 0 -13.549 Td [(\050plus)-575(triangul)1(ar)-575(solv)28(e\051)-575(as)-575(coarsest-lev)28(el)-575(solv)28(er.)]TJ 0 -13.55 Td [(See)-449(the)-449(default)-449(v)55(alues)-449(in)-449(T)83(ables)]TJ 0 0 1 rg 0 0 1 RG [-449(2)]TJ 0 g 0 G @@ -2424,54 +2482,54 @@ BT [-449(for)-449(further)]TJ 0 -13.549 Td [(details)-333(of)-334(the)-333(preconditioner.)]TJ ET q -1 0 0 1 502.4 444.077 cm +1 0 0 1 538.915 355.328 cm []0 d 0 J 0.398 w 0 0 m 0 94.844 l S Q q -1 0 0 1 97.252 443.877 cm -[]0 d 0 J 0.398 w 0 0 m 405.148 0 l S +1 0 0 1 93.6 355.129 cm +[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S Q 0 g 0 G BT -/F15 10.9091 Tf 123.31 425.144 Td [(T)83(able)-333(1:)-444(Preconditioner)-334(t)28(yp)-28(es,)-333(corresp)-28(onding)-333(strings)-333(and)-334(d)1(e)-1(f)1(ault)-334(c)28(hoices.)]TJ +/F15 10.9091 Tf 123.31 336.395 Td [(T)83(able)-333(1:)-444(Preconditioner)-334(t)28(yp)-28(es,)-333(corresp)-28(onding)-333(strings)-333(and)-334(d)1(e)-1(f)1(ault)-334(c)28(hoices.)]TJ 0 g 0 G 0 g 0 G - -12.773 -37.167 Td [(Note)-266(that)-266(the)-266(mo)-27(dule)]TJ/F45 10.9091 Tf 104.329 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)-279(con)27(taini)1(ng)-266(the)-266(de\014nition)-266(of)-266(the)-266(pr)1(e)-1(cond)1(itioner)]TJ -189.992 -13.549 Td [(data)-319(t)28(yp)-28(e)-319(and)-319(the)-319(in)28(terfaces)-319(to)-319(the)-319(routines)-319(of)-319(MLD2P4,)-322(m)28(ust)-319(b)-28(e)-319(used)-319(in)-319(an)28(y)-320(p)1(rogram)]TJ 0 -13.549 Td [(calling)-358(suc)28(h)-359(routines.)-519(The)-358(mo)-28(dules)]TJ/F45 10.9091 Tf 172.419 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.727 0 Td [(,)-364(for)-359(the)-358(sparse)-358(matrix)-358(and)-359(comm)28(u-)]TJ -241.146 -13.549 Td [(nication)-404(descriptor)-403(data)-404(t)28(yp)-28(es,)-421(and)]TJ/F45 10.9091 Tf 174.817 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 80.181 0 Td [(,)-421(for)-404(in)28(terfacing)-404(with)-403(the)-404(Krylo)28(v)]TJ -254.998 -13.55 Td [(solv)28(ers,)-334(m)28(ust)-333(b)-28(e)-333(also)-334(used)-333(\050see)-333(Section)]TJ + -12.773 -56.375 Td [(Note)-266(that)-266(the)-266(mo)-27(dule)]TJ/F45 10.9091 Tf 104.329 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)-279(con)27(taini)1(ng)-266(the)-266(de\014nition)-266(of)-266(the)-266(pr)1(e)-1(cond)1(itioner)]TJ -189.992 -13.549 Td [(data)-319(t)28(yp)-28(e)-319(and)-319(the)-319(in)28(terfaces)-319(to)-319(the)-319(routines)-319(of)-319(MLD2P4,)-322(m)28(ust)-319(b)-28(e)-319(used)-319(in)-319(an)28(y)-320(p)1(rogram)]TJ 0 -13.549 Td [(calling)-358(suc)28(h)-359(routines.)-519(The)-358(mo)-28(dules)]TJ/F45 10.9091 Tf 172.419 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.727 0 Td [(,)-364(for)-359(the)-358(sparse)-358(matrix)-358(and)-359(comm)28(u-)]TJ -241.146 -13.55 Td [(nication)-404(descriptor)-403(data)-404(t)28(yp)-28(es,)-421(and)]TJ/F45 10.9091 Tf 174.817 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 80.181 0 Td [(,)-421(for)-404(in)28(terfacing)-404(with)-403(the)-404(Krylo)28(v)]TJ -254.998 -13.549 Td [(solv)28(ers,)-334(m)28(ust)-333(b)-28(e)-333(also)-334(used)-333(\050see)-333(Section)]TJ 0 0 1 rg 0 0 1 RG [-334(5.1)]TJ 0 g 0 G - [(\051.)]TJ/F44 10.9091 Tf 16.937 -27.098 Td [(Remark)-513(1.)]TJ/F15 10.9091 Tf 67.379 0 Td [(Coarsest-lev)28(el)-446(solv)28(ers)-446(based)-446(on)-446(the)-446(LU)-445(factorization,)-474(suc)28(h)-446(as)-446(those)]TJ -84.316 -13.549 Td [(implemen)28(ted)-437(in)-437(UMFP)83(A)28(CK,)-437(MUMPS,)-437(Sup)-28(erLU,)-437(an)1(d)-437(Sup)-28(erLU)]TJ + [(\051.)]TJ/F44 10.9091 Tf 16.937 -36.556 Td [(Remark)-513(1.)]TJ/F15 10.9091 Tf 67.379 0 Td [(Coarsest-lev)28(el)-446(solv)28(ers)-446(based)-446(on)-446(the)-446(LU)-445(factorization,)-474(suc)28(h)-446(as)-446(those)]TJ -84.316 -13.549 Td [(implemen)28(ted)-437(in)-437(UMFP)83(A)28(CK,)-437(MUMPS,)-437(Sup)-28(erLU,)-437(an)1(d)-437(Sup)-28(erLU)]TJ ET q -1 0 0 1 402.466 293.332 cm +1 0 0 1 402.466 175.917 cm []0 d 0 J 0.398 w 0 0 m 3.273 0 l S Q BT -/F15 10.9091 Tf 405.739 293.133 Td [(Dist,)-463(usually)-437(lead)-437(to)]TJ -312.139 -13.549 Td [(smaller)-462(n)28(um)28(b)-28(ers)-462(of)-462(preconditioned)-462(Krylo)28(v)-462(iterations)-462(than)-462(inexact)-462(solv)28(ers,)-495(when)-462(the)]TJ 0 -13.55 Td [(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 - [-262(2)]TJ -0 g 0 G - [-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 - [-371(1)]TJ -0 g 0 G - [(\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 +/F15 10.9091 Tf 405.739 175.718 Td [(Dist,)-463(usually)-437(lead)-437(to)]TJ -312.139 -13.55 Td [(smaller)-462(n)28(um)28(b)-28(ers)-462(of)-462(preconditioned)-462(Krylo)28(v)-462(iterations)-462(than)-462(inexact)-462(solv)28(ers,)-495(when)-462(the)]TJ 0 -13.549 Td [(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 0 g 0 G 0 g 0 G ET endstream endobj -415 0 obj +414 0 obj << -/Length 7095 +/Length 8728 >> 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 [(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 +/F17 11.9552 Tf -203.265 -35.866 Td [(5.1)-1125(Examples)]TJ/F15 10.9091 Tf 0 -20.594 Td [(The)-262(co)-28(de)-262(rep)-28(orted)-262(in)-262(Figure)]TJ +0 0 1 rg 0 0 1 RG + [-262(2)]TJ +0 g 0 G + [-263(sho)28(ws)-262(ho)28(w)-262(to)-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(ailabl)1(e)-372(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 + [-371(1)]TJ +0 g 0 G + [(\051.)-558(This)]TJ 0 -13.55 Td [(preconditioner)-365(is)-364(c)27(hosen)-364(b)27(y)-364(sim)-1(p)1(ly)-365(sp)-28(ecifying)]TJ/F45 10.9091 Tf 220.847 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 130.353 0 Td [(P%init)]TJ/F15 10.9091 Tf -378.088 -13.549 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)-305(w)-1(i)1(th)-306(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(assumed)-395(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 68.726 0 Td [(,)]TJ/F45 10.9091 Tf 6.507 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf 72.164 0 Td [(and)]TJ/F45 10.9091 Tf 21.012 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 83.618 0 Td [(m)28(ust)]TJ -389.057 -13.549 Td [(b)-28(e)-333(used)-333(b)27(y)-333(the)-333(example)-334(program.)]TJ 16.936 -13.55 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 -13.549 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 -13.55 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 0 0 1 rg 0 0 1 RG [-358(3.5)]TJ 0 g 0 G @@ -2479,19 +2537,19 @@ BT 1 0 0 rg 1 0 0 RG [(13)]TJ 0 g 0 G - [(].)]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 + [(].)]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 -13.549 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(obtain)1(e)-1(d)-494(with)]TJ 0 -13.55 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)-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 + [-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(c)-1(o)-27(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(precondit)1(ioner)-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(c)-1(o)-27(de)-358(rep)-27(orted)-358(in)-357(Figure)]TJ 0 0 1 rg 0 0 1 RG [-357(3)]TJ 0 g 0 G - [-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 + [-357(sho)27(ws)]TJ 0 -13.549 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)-440(as)-439(pre-)-439(and)]TJ 0 -13.55 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 -13.549 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 [-360(4)]TJ 0 g 0 G - [-361(sho)28(ws)-360(ho)27(w)-360(to)-360(set)-361(a)-360(W-cycle)]TJ 0 -13.549 Td [(preconditioner)-346(whic)27(h)-346(applies)-346(2)-347(h)28(ybrid)-346(Gauss)-1(-Seid)1(e)-1(l)-346(sw)28(eeps)-347(as)-346(pre-)-347(and)-346(p)-28(ost-smo)-28(other,)]TJ 0 -13.549 Td [(and)-261(solv)28(e)-1(s)-261(the)-261(coarsest-lev)27(el)-261(system)-262(with)-261(the)-261(m)28(ultifron)28(tal)-262(LU)-261(factorization)-261(implemen)27(ted)]TJ 0 -13.549 Td [(in)-350(MUMPS.)-350(It)-350(is)-350(sp)-28(eci\014ed)-350(that)-350(the)-350(coarsest-lev)28(e)-1(l)-350(matrix)-350(is)-350(distributed,)-354(since)-350(MUMPS)]TJ 0 -13.549 Td 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For any zero diagonal entry of the matrix to be preconditioned, the corresponding entry of the preconditioner is set to~1.\\ \hline +Gauss-Seidel & \verb|'GS'| & Hybrid Gauss-Seidel (forward), that is, + global block Jacobi with + Gauss-Seidel as local solver.\\ \hline +Symmetrized Gauss-Seidel & \verb|'FBGS'| & Symmetrized hybrid Gauss-Seidel,that is, + forward Gauss-Seidel followed by + backward Gauss-Seidel.\\ \hline Block Jacobi & \verb|'BJAC'| & Block-Jacobi with ILU(0) on the local blocks.\\ \hline Additive Schwarz & \verb|'AS'| & Restricted Additive Schwarz (RAS), with overlap~1 and ILU(0) on the local blocks. \\ \hline