From 875443efe72e484b1ccd5cfd535a9bef5e8d2967 Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Mon, 9 May 2016 16:00:12 +0000 Subject: [PATCH 1/2] mld2p4-2: docs/src/userinterface.tex mlprec/impl/level/mld_c_base_onelev_cseti.f90 mlprec/impl/level/mld_c_base_onelev_seti.f90 mlprec/impl/level/mld_d_base_onelev_cseti.f90 mlprec/impl/level/mld_d_base_onelev_seti.f90 mlprec/impl/level/mld_s_base_onelev_cseti.f90 mlprec/impl/level/mld_s_base_onelev_seti.f90 mlprec/impl/level/mld_z_base_onelev_cseti.f90 mlprec/impl/level/mld_z_base_onelev_seti.f90 mlprec/impl/mld_c_dec_map_bld.f90 mlprec/impl/mld_caggrmap_bld.f90 mlprec/impl/mld_ccoarse_bld.f90 mlprec/impl/mld_ccprecset.F90 mlprec/impl/mld_cprecinit.F90 mlprec/impl/mld_cprecset.F90 mlprec/impl/mld_d_dec_map_bld.f90 mlprec/impl/mld_daggrmap_bld.f90 mlprec/impl/mld_dcoarse_bld.f90 mlprec/impl/mld_dcprecset.F90 mlprec/impl/mld_dprecinit.F90 mlprec/impl/mld_dprecset.F90 mlprec/impl/mld_s_dec_map_bld.f90 mlprec/impl/mld_saggrmap_bld.f90 mlprec/impl/mld_scoarse_bld.f90 mlprec/impl/mld_scprecset.F90 mlprec/impl/mld_sprecinit.F90 mlprec/impl/mld_sprecset.F90 mlprec/impl/mld_z_dec_map_bld.f90 mlprec/impl/mld_zaggrmap_bld.f90 mlprec/impl/mld_zcoarse_bld.f90 mlprec/impl/mld_zcprecset.F90 mlprec/impl/mld_zprecinit.F90 mlprec/impl/mld_zprecset.F90 mlprec/mld_base_prec_type.F90 mlprec/mld_c_inner_mod.f90 mlprec/mld_c_onelev_mod.f90 mlprec/mld_d_base_solver_mod.f90 mlprec/mld_d_inner_mod.f90 mlprec/mld_d_onelev_mod.f90 mlprec/mld_d_prec_type.f90 mlprec/mld_d_umf_solver.F90 mlprec/mld_s_inner_mod.f90 mlprec/mld_s_onelev_mod.f90 mlprec/mld_z_inner_mod.f90 mlprec/mld_z_onelev_mod.f90 tests/pdegen/ppde2d.f90 tests/pdegen/ppde3d.f90 tests/pdegen/runs/ppde.inp tests/pdegen/spde2d.f90 tests/pdegen/spde3d.f90 Added option to apply ordering while aggregating. --- docs/src/userinterface.tex | 8 +++ mlprec/impl/level/mld_c_base_onelev_cseti.f90 | 3 + mlprec/impl/level/mld_c_base_onelev_seti.f90 | 3 + mlprec/impl/level/mld_d_base_onelev_cseti.f90 | 3 + mlprec/impl/level/mld_d_base_onelev_seti.f90 | 3 + mlprec/impl/level/mld_s_base_onelev_cseti.f90 | 3 + mlprec/impl/level/mld_s_base_onelev_seti.f90 | 3 + mlprec/impl/level/mld_z_base_onelev_cseti.f90 | 3 + mlprec/impl/level/mld_z_base_onelev_seti.f90 | 3 + mlprec/impl/mld_c_dec_map_bld.f90 | 51 ++++++++++------ mlprec/impl/mld_caggrmap_bld.f90 | 9 +-- mlprec/impl/mld_ccoarse_bld.f90 | 7 ++- mlprec/impl/mld_ccprecset.F90 | 21 ++++--- mlprec/impl/mld_cprecinit.F90 | 22 +++---- mlprec/impl/mld_cprecset.F90 | 39 ++++++++---- mlprec/impl/mld_d_dec_map_bld.f90 | 51 ++++++++++------ mlprec/impl/mld_daggrmap_bld.f90 | 9 +-- mlprec/impl/mld_dcoarse_bld.f90 | 4 +- mlprec/impl/mld_dcprecset.F90 | 60 +++++++++--------- mlprec/impl/mld_dprecinit.F90 | 16 ++--- mlprec/impl/mld_dprecset.F90 | 13 ++-- mlprec/impl/mld_s_dec_map_bld.f90 | 51 ++++++++++------ mlprec/impl/mld_saggrmap_bld.f90 | 9 +-- mlprec/impl/mld_scoarse_bld.f90 | 5 +- mlprec/impl/mld_scprecset.F90 | 18 +++--- mlprec/impl/mld_sprecinit.F90 | 22 +++---- mlprec/impl/mld_sprecset.F90 | 38 +++++++----- mlprec/impl/mld_z_dec_map_bld.f90 | 51 ++++++++++------ mlprec/impl/mld_zaggrmap_bld.f90 | 9 +-- mlprec/impl/mld_zcoarse_bld.f90 | 8 ++- mlprec/impl/mld_zcprecset.F90 | 61 ++++++++++--------- mlprec/impl/mld_zprecinit.F90 | 15 ++--- mlprec/impl/mld_zprecset.F90 | 36 +++++++---- mlprec/mld_base_prec_type.F90 | 54 +++++++++++----- mlprec/mld_c_inner_mod.f90 | 6 +- mlprec/mld_c_onelev_mod.f90 | 1 + mlprec/mld_d_base_solver_mod.f90 | 1 + mlprec/mld_d_inner_mod.f90 | 6 +- mlprec/mld_d_onelev_mod.f90 | 10 +-- mlprec/mld_d_prec_type.f90 | 6 +- mlprec/mld_d_umf_solver.F90 | 4 +- mlprec/mld_s_inner_mod.f90 | 6 +- mlprec/mld_s_onelev_mod.f90 | 1 + mlprec/mld_z_inner_mod.f90 | 6 +- mlprec/mld_z_onelev_mod.f90 | 1 + tests/pdegen/ppde2d.f90 | 4 ++ tests/pdegen/ppde3d.f90 | 5 +- tests/pdegen/runs/ppde.inp | 9 +-- tests/pdegen/spde2d.f90 | 4 ++ tests/pdegen/spde3d.f90 | 4 ++ 50 files changed, 489 insertions(+), 296 deletions(-) diff --git a/docs/src/userinterface.tex b/docs/src/userinterface.tex index 7771bfcc..0d03c64e 100644 --- a/docs/src/userinterface.tex +++ b/docs/src/userinterface.tex @@ -305,6 +305,14 @@ according to their needs. & \texttt{'DEC'} & Aggregation algorithm. Currently, only the decoupled aggregation is available. \\ \hline +\verb|mld_aggr_ord_| \break \verb|AGGR_ORD| & \verb|character(len=*)| + & \texttt{'NAT'} + & \texttt{'DEGREE'} + & Initial ordering of indices for aggregation + algorithm: natural ordering or sorted by + descending degree of the node in the + matrix graph. Since aggregation is + heuristics, results will be different. \\ \hline \verb|mld_aggr_kind_| \break \verb|AGGR_KIND| & \verb|character(len=*)| & \texttt{'SMOOTHED'} \hspace{2.5cm} \texttt{'NONSMOOTHED'} & \texttt{'SMOOTHED'} diff --git a/mlprec/impl/level/mld_c_base_onelev_cseti.f90 b/mlprec/impl/level/mld_c_base_onelev_cseti.f90 index e84c84e8..ecb4e6c9 100644 --- a/mlprec/impl/level/mld_c_base_onelev_cseti.f90 +++ b/mlprec/impl/level/mld_c_base_onelev_cseti.f90 @@ -73,6 +73,9 @@ subroutine mld_c_base_onelev_cseti(lv,what,val,info) case ('AGGR_ALG') lv%parms%aggr_alg = val + case ('AGGR_ORD') + lv%parms%aggr_ord = val + case ('AGGR_KIND') lv%parms%aggr_kind = val diff --git a/mlprec/impl/level/mld_c_base_onelev_seti.f90 b/mlprec/impl/level/mld_c_base_onelev_seti.f90 index 56030073..859c1b5c 100644 --- a/mlprec/impl/level/mld_c_base_onelev_seti.f90 +++ b/mlprec/impl/level/mld_c_base_onelev_seti.f90 @@ -73,6 +73,9 @@ subroutine mld_c_base_onelev_seti(lv,what,val,info) case (mld_aggr_alg_) lv%parms%aggr_alg = val + case (mld_aggr_ord_) + lv%parms%aggr_ord = val + case (mld_aggr_kind_) lv%parms%aggr_kind = val diff --git a/mlprec/impl/level/mld_d_base_onelev_cseti.f90 b/mlprec/impl/level/mld_d_base_onelev_cseti.f90 index 39e32ae5..a2e3255b 100644 --- a/mlprec/impl/level/mld_d_base_onelev_cseti.f90 +++ b/mlprec/impl/level/mld_d_base_onelev_cseti.f90 @@ -73,6 +73,9 @@ subroutine mld_d_base_onelev_cseti(lv,what,val,info) case ('AGGR_ALG') lv%parms%aggr_alg = val + case ('AGGR_ORD') + lv%parms%aggr_ord = val + case ('AGGR_KIND') lv%parms%aggr_kind = val diff --git a/mlprec/impl/level/mld_d_base_onelev_seti.f90 b/mlprec/impl/level/mld_d_base_onelev_seti.f90 index 3ca46d90..4e27cbca 100644 --- a/mlprec/impl/level/mld_d_base_onelev_seti.f90 +++ b/mlprec/impl/level/mld_d_base_onelev_seti.f90 @@ -73,6 +73,9 @@ subroutine mld_d_base_onelev_seti(lv,what,val,info) case (mld_aggr_alg_) lv%parms%aggr_alg = val + case (mld_aggr_ord_) + lv%parms%aggr_ord = val + case (mld_aggr_kind_) lv%parms%aggr_kind = val diff --git a/mlprec/impl/level/mld_s_base_onelev_cseti.f90 b/mlprec/impl/level/mld_s_base_onelev_cseti.f90 index 6f4bb091..b35e92ba 100644 --- a/mlprec/impl/level/mld_s_base_onelev_cseti.f90 +++ b/mlprec/impl/level/mld_s_base_onelev_cseti.f90 @@ -73,6 +73,9 @@ subroutine mld_s_base_onelev_cseti(lv,what,val,info) case ('AGGR_ALG') lv%parms%aggr_alg = val + case ('AGGR_ORD') + lv%parms%aggr_ord = val + case ('AGGR_KIND') lv%parms%aggr_kind = val diff --git a/mlprec/impl/level/mld_s_base_onelev_seti.f90 b/mlprec/impl/level/mld_s_base_onelev_seti.f90 index 39acbdb0..ed687707 100644 --- a/mlprec/impl/level/mld_s_base_onelev_seti.f90 +++ b/mlprec/impl/level/mld_s_base_onelev_seti.f90 @@ -73,6 +73,9 @@ subroutine mld_s_base_onelev_seti(lv,what,val,info) case (mld_aggr_alg_) lv%parms%aggr_alg = val + case (mld_aggr_ord_) + lv%parms%aggr_ord = val + case (mld_aggr_kind_) lv%parms%aggr_kind = val diff --git a/mlprec/impl/level/mld_z_base_onelev_cseti.f90 b/mlprec/impl/level/mld_z_base_onelev_cseti.f90 index 3281f5ad..6352b4b9 100644 --- a/mlprec/impl/level/mld_z_base_onelev_cseti.f90 +++ b/mlprec/impl/level/mld_z_base_onelev_cseti.f90 @@ -73,6 +73,9 @@ subroutine mld_z_base_onelev_cseti(lv,what,val,info) case ('AGGR_ALG') lv%parms%aggr_alg = val + case ('AGGR_ORD') + lv%parms%aggr_ord = val + case ('AGGR_KIND') lv%parms%aggr_kind = val diff --git a/mlprec/impl/level/mld_z_base_onelev_seti.f90 b/mlprec/impl/level/mld_z_base_onelev_seti.f90 index 61014f13..2d0a36a1 100644 --- a/mlprec/impl/level/mld_z_base_onelev_seti.f90 +++ b/mlprec/impl/level/mld_z_base_onelev_seti.f90 @@ -73,6 +73,9 @@ subroutine mld_z_base_onelev_seti(lv,what,val,info) case (mld_aggr_alg_) lv%parms%aggr_alg = val + case (mld_aggr_ord_) + lv%parms%aggr_ord = val + case (mld_aggr_kind_) lv%parms%aggr_kind = val diff --git a/mlprec/impl/mld_c_dec_map_bld.f90 b/mlprec/impl/mld_c_dec_map_bld.f90 index 687f7161..7d0c5f94 100644 --- a/mlprec/impl/mld_c_dec_map_bld.f90 +++ b/mlprec/impl/mld_c_dec_map_bld.f90 @@ -37,7 +37,7 @@ !!$ !!$ -subroutine mld_c_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) +subroutine mld_c_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) use psb_base_mod use mld_c_inner_mod, mld_protect_name => mld_c_dec_map_bld @@ -45,6 +45,7 @@ subroutine mld_c_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) implicit none ! Arguments + integer(psb_ipk_), intent(in) :: iorder type(psb_cspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a real(psb_spk_), intent(in) :: theta @@ -52,9 +53,11 @@ subroutine mld_c_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) integer(psb_ipk_), intent(out) :: info ! Local variables - integer(psb_ipk_), allocatable :: ils(:), neigh(:), irow(:), icol(:) + integer(psb_ipk_), allocatable :: ils(:), neigh(:), irow(:), icol(:),& + & ideg(:), idxs(:) complex(psb_spk_), allocatable :: val(:), diag(:) - integer(psb_ipk_) :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m, nz, ilg + integer(psb_ipk_) :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m, nz, ilg, ii + type(psb_c_csr_sparse_mat) :: acsr real(psb_spk_) :: cpling, tcl logical :: recovery integer(psb_ipk_) :: debug_level, debug_unit,err_act @@ -75,7 +78,7 @@ subroutine mld_c_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) ncol = desc_a%get_local_cols() nr = a%get_nrows() - allocate(ilaggr(nr),neigh(nr),stat=info) + allocate(ilaggr(nr),neigh(nr),ideg(nr),idxs(nr),stat=info) if(info /= psb_success_) then info=psb_err_alloc_request_ call psb_errpush(info,name,i_err=(/2*nr,izero,izero,izero,izero/),& @@ -90,11 +93,20 @@ subroutine mld_c_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) goto 9999 end if - do i=1, nr - ilaggr(i) = -(nr+1) - end do - - + if (iorder == mld_aggr_ord_nat_) then + do i=1, nr + ilaggr(i) = -(nr+1) + idxs(i) = i + end do + else + call a%cp_to(acsr) + do i=1, nr + ilaggr(i) = -(nr+1) + ideg(i) = acsr%irp(i+1) - acsr%irp(i) + end do + call acsr%free() + call psb_msort(ideg,ix=idxs,dir=psb_sort_down_) + end if ! Note: -(nr+1) Untouched as yet ! -i 1<=i<=nr Adjacent to aggregate i ! i 1<=i<=nr Belonging to aggregate i @@ -106,7 +118,8 @@ subroutine mld_c_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) nlp = 0 do icnt = 0 - do i=1, nr + do ii=1, nr + i = idxs(ii) if (ilaggr(i) == -(nr+1)) then ! ! 1. Untouched nodes are marked >0 together @@ -124,14 +137,16 @@ subroutine mld_c_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) end if do k=1, nz - j = icol(k) - ilg = ilaggr(j) - if ((ilg<0).and.(1<=j).and.(j<=nr).and.(i /= j)) then - if (abs(val(k)) > theta*sqrt(abs(diag(i)*diag(j)))) then - ilaggr(j) = naggr - else - ilaggr(j) = -naggr - endif + j = icol(k) + if ((1<=j).and.(j<=nr)) then + ilg = ilaggr(j) + if ((ilg<0).and.(i /= j)) then + if (abs(val(k)) > theta*sqrt(abs(diag(i)*diag(j)))) then + ilaggr(j) = naggr + else + ilaggr(j) = -naggr + endif + end if end if enddo diff --git a/mlprec/impl/mld_caggrmap_bld.f90 b/mlprec/impl/mld_caggrmap_bld.f90 index 81e8be11..e2ed909b 100644 --- a/mlprec/impl/mld_caggrmap_bld.f90 +++ b/mlprec/impl/mld_caggrmap_bld.f90 @@ -79,7 +79,7 @@ ! info - integer, output. ! Error code. ! -subroutine mld_caggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) +subroutine mld_caggrmap_bld(aggr_type,iorder,theta,a,desc_a,ilaggr,nlaggr,info) use psb_base_mod use mld_c_inner_mod, mld_protect_name => mld_caggrmap_bld @@ -87,6 +87,7 @@ subroutine mld_caggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) implicit none ! Arguments + integer(psb_ipk_), intent(in) :: iorder integer(psb_ipk_), intent(in) :: aggr_type real(psb_spk_), intent(in) :: theta type(psb_cspmat_type), intent(in) :: a @@ -118,7 +119,7 @@ subroutine mld_caggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) select case (aggr_type) case (mld_dec_aggr_) - call mld_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) + call mld_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) case (mld_sym_dec_aggr_) nr = a%get_nrows() @@ -126,14 +127,14 @@ subroutine mld_caggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) & rscale=.false.,cscale=.false.) call atmp%set_nrows(nr) call atmp%set_ncols(nr) - if (info == psb_success_) call atrans%transp(atmp) + if (info == psb_success_) call atmp%transp(atrans) if (info == psb_success_) call atrans%cscnv(info,type='COO') if (info == psb_success_) call psb_rwextd(nr,atmp,info,b=atrans,rowscale=.false.) call atmp%set_nrows(nr) call atmp%set_ncols(nr) if (info == psb_success_) call atrans%free() if (info == psb_success_) call atmp%cscnv(info,type='CSR') - if (info == psb_success_) call mld_dec_map_bld(theta,atmp,desc_a,nlaggr,ilaggr,info) + if (info == psb_success_) call mld_dec_map_bld(iorder,theta,atmp,desc_a,nlaggr,ilaggr,info) if (info == psb_success_) call atmp%free() case default diff --git a/mlprec/impl/mld_ccoarse_bld.f90 b/mlprec/impl/mld_ccoarse_bld.f90 index 9f184722..ab9fc56d 100644 --- a/mlprec/impl/mld_ccoarse_bld.f90 +++ b/mlprec/impl/mld_ccoarse_bld.f90 @@ -39,7 +39,7 @@ ! File: mld_ccoarse_bld.f90 ! ! Subroutine: mld_ccoarse_bld -! Version: complex +! Version: real ! ! This routine builds the matrix associated to the current level of the ! multilevel preconditioner from the matrix associated to the previous level, @@ -95,6 +95,8 @@ subroutine mld_ccoarse_bld(a,desc_a,p,info) & mld_mult_ml_,is_legal_ml_type) call mld_check_def(p%parms%aggr_alg,'Aggregation',& & mld_dec_aggr_,is_legal_ml_aggr_alg) + call mld_check_def(p%parms%aggr_ord,'Ordering',& + & mld_aggr_ord_nat_,is_legal_ml_aggr_ord) call mld_check_def(p%parms%aggr_kind,'Smoother',& & mld_smooth_prol_,is_legal_ml_aggr_kind) call mld_check_def(p%parms%coarse_mat,'Coarse matrix',& @@ -117,7 +119,7 @@ subroutine mld_ccoarse_bld(a,desc_a,p,info) ! aggregation algorithm. This also defines a tentative prolongator from ! the coarse to the fine level. ! - call mld_aggrmap_bld(p%parms%aggr_alg,p%parms%aggr_thresh,& + call mld_aggrmap_bld(p%parms%aggr_alg,p%parms%aggr_ord,p%parms%aggr_thresh,& & a,desc_a,ilaggr,nlaggr,info) if (info /= psb_success_) then @@ -136,6 +138,7 @@ subroutine mld_ccoarse_bld(a,desc_a,p,info) call psb_errpush(psb_err_from_subroutine_,name,a_err='mld_aggrmat_asb') goto 9999 end if + ! ! Fix the base_a and base_desc pointers for handling of residuals. ! This is correct because this routine is only called at levels >=2. diff --git a/mlprec/impl/mld_ccprecset.F90 b/mlprec/impl/mld_ccprecset.F90 index 29235f51..e4858649 100644 --- a/mlprec/impl/mld_ccprecset.F90 +++ b/mlprec/impl/mld_ccprecset.F90 @@ -93,6 +93,7 @@ subroutine mld_ccprecseti(p,what,val,info,ilev) use mld_c_mumps_solver #endif + implicit none ! Arguments @@ -148,9 +149,10 @@ subroutine mld_ccprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case('SUB_SOLVE') call onelev_set_solver(p%precv(ilev_),val,info) - case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_KIND',& - & 'SMOOTHER_POS','AGGR_OMEGA_ALG','AGGR_EIG',& - & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& + case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_ORD',& + & 'AGGR_KIND','SMOOTHER_POS','AGGR_OMEGA_ALG',& + & 'AGGR_EIG','SMOOTHER_SWEEPS_PRE',& + & 'SMOOTHER_SWEEPS_POST',& & 'SUB_RESTR','SUB_PROL', & & 'SUB_REN','SUB_OVR','SUB_FILLIN') call p%precv(ilev_)%set(what,val,info) @@ -166,9 +168,10 @@ subroutine mld_ccprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case('SUB_SOLVE') call onelev_set_solver(p%precv(ilev_),val,info) - case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_KIND',& - & 'SMOOTHER_POS','AGGR_OMEGA_ALG','AGGR_EIG',& - & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& + case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_ORD',& + & 'AGGR_KIND','SMOOTHER_POS','AGGR_OMEGA_ALG',& + & 'AGGR_EIG','SMOOTHER_SWEEPS_PRE',& + & 'SMOOTHER_SWEEPS_POST',& & 'SUB_RESTR','SUB_PROL', & & 'SUB_REN','SUB_OVR','SUB_FILLIN',& & 'COARSE_MAT') @@ -214,7 +217,7 @@ subroutine mld_ccprecseti(p,what,val,info,ilev) case(mld_mumps_) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),val,info) - call p%precv(nlev_)%set('COARSE_MAT',mld_distr_mat_,info) + call p%precv(nlev_)%set('COARSE_MAT',mld_distr_mat_,info) case(mld_jac_) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),mld_diag_scale_,info) @@ -280,7 +283,7 @@ subroutine mld_ccprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) end do - case('ML_TYPE','AGGR_ALG','AGGR_KIND',& + case('ML_TYPE','AGGR_ALG','AGGR_ORD','AGGR_KIND',& & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& & 'SMOOTHER_POS','AGGR_OMEGA_ALG',& & 'AGGR_EIG','AGGR_FILTER') @@ -302,7 +305,6 @@ subroutine mld_ccprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) #if defined(HAVE_SLU_) call onelev_set_solver(p%precv(nlev_),mld_slu_,info) - call onelev_set_solver(p%precv(nlev_),mld_slu_,info) #elif defined(HAVE_MUMPS_) call onelev_set_solver(p%precv(nlev_),mld_mumps_,info) #else @@ -321,7 +323,6 @@ subroutine mld_ccprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),val,info) call p%precv(nlev_)%set('COARSE_MAT',mld_distr_mat_,info) - case(mld_jac_) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),mld_diag_scale_,info) diff --git a/mlprec/impl/mld_cprecinit.F90 b/mlprec/impl/mld_cprecinit.F90 index a5f6ffd2..b1347ea7 100644 --- a/mlprec/impl/mld_cprecinit.F90 +++ b/mlprec/impl/mld_cprecinit.F90 @@ -2,9 +2,9 @@ !!$ !!$ MLD2P4 version 2.0 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package -!!$ based on PSBLAS (Parallel Sparse BLAS version 3.0) +!!$ based on PSBLAS (Parallel Sparse BLAS version 3.3) !!$ -!!$ (C) Copyright 2008,2009,2010,2012,2013 +!!$ (C) Copyright 2008, 2010, 2012, 2015 !!$ !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari CNRS-IRIT, Toulouse @@ -61,7 +61,7 @@ ! ! 'ML' - Multilevel hybrid preconditioner (additive on the ! same level and multiplicative through the levels), -! with 2 levels and post-smoothing only. RAS with +! with 2 levels, pre and post-smoothing, RAS with ! overlap 1 and ILU(0) on the local blocks is ! applied as post-smoother at each level, but the ! coarsest one; four sweeps of the block-Jacobi solver, @@ -97,9 +97,6 @@ subroutine mld_cprecinit(p,ptype,info,nlev) use mld_c_id_solver use mld_c_diag_solver use mld_c_ilu_solver -#if defined(HAVE_UMF_) && 0 - use mld_c_umf_solver -#endif #if defined(HAVE_SLU_) use mld_c_slu_solver #endif @@ -115,7 +112,7 @@ subroutine mld_cprecinit(p,ptype,info,nlev) ! Local variables integer(psb_ipk_) :: nlev_, ilev_ - real(psb_spk_) :: thr + real(psb_spk_) :: thr, scale character(len=*), parameter :: name='mld_precinit' info = psb_success_ @@ -191,10 +188,8 @@ subroutine mld_cprecinit(p,ptype,info,nlev) ilev_ = nlev_ allocate(mld_c_jac_smoother_type :: p%precv(ilev_)%sm, stat=info) if (info /= psb_success_) return -#if defined(HAVE_UMF_) && 0 - allocate(mld_c_umf_solver_type :: p%precv(ilev_)%sm%sv, stat=info) -#elif defined(HAVE_SLU_) - allocate(mld_c_slu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) +#if defined(HAVE_SLU_) + allocate(mld_c_slu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #else allocate(mld_c_ilu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #endif @@ -205,10 +200,11 @@ subroutine mld_cprecinit(p,ptype,info,nlev) call p%precv(ilev_)%set(mld_sub_prol_,psb_none_,info) call p%precv(ilev_)%set(mld_sub_ovr_,izero,info) - thr = 0.16d0 + thr = 0.05 + scale = 1.0 do ilev_=1,nlev_ call p%precv(ilev_)%set(mld_aggr_thresh_,thr,info) - thr = thr/2 + call p%precv(ilev_)%set(mld_aggr_scale_,scale,info) end do case default diff --git a/mlprec/impl/mld_cprecset.F90 b/mlprec/impl/mld_cprecset.F90 index 7e16077d..6728ca12 100644 --- a/mlprec/impl/mld_cprecset.F90 +++ b/mlprec/impl/mld_cprecset.F90 @@ -92,6 +92,7 @@ subroutine mld_cprecseti(p,what,val,info,ilev) #if defined(HAVE_MUMPS_) use mld_c_mumps_solver #endif + implicit none ! Arguments @@ -148,8 +149,8 @@ subroutine mld_cprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case(mld_sub_solve_) call onelev_set_solver(p%precv(ilev_),val,info) - case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& - & mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& + case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,& + & mld_aggr_kind_,mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_sub_restr_,mld_sub_prol_, & & mld_sub_ren_,mld_sub_ovr_,mld_sub_fillin_) @@ -166,8 +167,8 @@ subroutine mld_cprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case(mld_sub_solve_) call onelev_set_solver(p%precv(ilev_),val,info) - case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& - & mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& + case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,& + & mld_aggr_kind_,mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_sub_restr_,mld_sub_prol_, & & mld_sub_ren_,mld_sub_ovr_,mld_sub_fillin_,& @@ -207,7 +208,7 @@ subroutine mld_cprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),val,info) call p%precv(nlev_)%set(mld_coarse_mat_,mld_repl_mat_,info) - case(mld_sludist_, mld_mumps_) + case(mld_sludist_,mld_mumps_) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),val,info) call p%precv(nlev_)%set(mld_coarse_mat_,mld_distr_mat_,info) @@ -276,7 +277,7 @@ subroutine mld_cprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) end do - case(mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& + case(mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,mld_aggr_kind_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_smoother_pos_,mld_aggr_omega_alg_,& & mld_aggr_eig_,mld_aggr_filter_) @@ -298,8 +299,8 @@ subroutine mld_cprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) #if defined(HAVE_SLU_) call onelev_set_solver(p%precv(nlev_),mld_slu_,info) -#elif defined(HAVE_MUMPS_) - call onelev_set_solver(p%precv(nlev_),mld_mumps_,info) +#elif defined(HAVE_SLU_) + call onelev_set_solver(p%precv(nlev_),mld_slu_,info) #else call onelev_set_solver(p%precv(nlev_),mld_ilu_n_,info) #endif @@ -599,7 +600,6 @@ contains end if end if #endif - case default ! ! Do nothing and hope for the best :) @@ -723,13 +723,26 @@ subroutine mld_cprecsetsv(p,val,info,ilev) do ilev_ = ilmin, ilmax if (allocated(p%precv(ilev_)%sm)) then - if (allocated(p%precv(ilev_)%sm%sv)) & - & deallocate(p%precv(ilev_)%sm%sv) + if (allocated(p%precv(ilev_)%sm%sv)) then + if (.not.same_type_as(p%precv(ilev_)%sm%sv,val)) then + deallocate(p%precv(ilev_)%sm%sv,stat=info) + if (info /= 0) then + info = 3111 + return + end if + end if + if (.not.allocated(p%precv(ilev_)%sm%sv)) then #ifdef HAVE_MOLD - allocate(p%precv(ilev_)%sm%sv,mold=val) + allocate(p%precv(ilev_)%sm%sv,mold=val,stat=info) #else - allocate(p%precv(ilev_)%sm%sv,source=val) + allocate(p%precv(ilev_)%sm%sv,source=val,stat=info) #endif + if (info /= 0) then + info = 3111 + return + end if + end if + end if call p%precv(ilev_)%sm%sv%default() else info = 3111 diff --git a/mlprec/impl/mld_d_dec_map_bld.f90 b/mlprec/impl/mld_d_dec_map_bld.f90 index bc0d40bf..67e4437b 100644 --- a/mlprec/impl/mld_d_dec_map_bld.f90 +++ b/mlprec/impl/mld_d_dec_map_bld.f90 @@ -37,7 +37,7 @@ !!$ !!$ -subroutine mld_d_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) +subroutine mld_d_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) use psb_base_mod use mld_d_inner_mod, mld_protect_name => mld_d_dec_map_bld @@ -45,6 +45,7 @@ subroutine mld_d_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) implicit none ! Arguments + integer(psb_ipk_), intent(in) :: iorder type(psb_dspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a real(psb_dpk_), intent(in) :: theta @@ -52,9 +53,11 @@ subroutine mld_d_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) integer(psb_ipk_), intent(out) :: info ! Local variables - integer(psb_ipk_), allocatable :: ils(:), neigh(:), irow(:), icol(:) + integer(psb_ipk_), allocatable :: ils(:), neigh(:), irow(:), icol(:),& + & ideg(:), idxs(:) real(psb_dpk_), allocatable :: val(:), diag(:) - integer(psb_ipk_) :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m, nz, ilg + integer(psb_ipk_) :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m, nz, ilg, ii + type(psb_d_csr_sparse_mat) :: acsr real(psb_dpk_) :: cpling, tcl logical :: recovery integer(psb_ipk_) :: debug_level, debug_unit,err_act @@ -75,7 +78,7 @@ subroutine mld_d_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) ncol = desc_a%get_local_cols() nr = a%get_nrows() - allocate(ilaggr(nr),neigh(nr),stat=info) + allocate(ilaggr(nr),neigh(nr),ideg(nr),idxs(nr),stat=info) if(info /= psb_success_) then info=psb_err_alloc_request_ call psb_errpush(info,name,i_err=(/2*nr,izero,izero,izero,izero/),& @@ -90,11 +93,20 @@ subroutine mld_d_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) goto 9999 end if - do i=1, nr - ilaggr(i) = -(nr+1) - end do - - + if (iorder == mld_aggr_ord_nat_) then + do i=1, nr + ilaggr(i) = -(nr+1) + idxs(i) = i + end do + else + call a%cp_to(acsr) + do i=1, nr + ilaggr(i) = -(nr+1) + ideg(i) = acsr%irp(i+1) - acsr%irp(i) + end do + call acsr%free() + call psb_msort(ideg,ix=idxs,dir=psb_sort_down_) + end if ! Note: -(nr+1) Untouched as yet ! -i 1<=i<=nr Adjacent to aggregate i ! i 1<=i<=nr Belonging to aggregate i @@ -106,7 +118,8 @@ subroutine mld_d_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) nlp = 0 do icnt = 0 - do i=1, nr + do ii=1, nr + i = idxs(ii) if (ilaggr(i) == -(nr+1)) then ! ! 1. Untouched nodes are marked >0 together @@ -124,14 +137,16 @@ subroutine mld_d_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) end if do k=1, nz - j = icol(k) - ilg = ilaggr(j) - if ((ilg<0).and.(1<=j).and.(j<=nr).and.(i /= j)) then - if (abs(val(k)) > theta*sqrt(abs(diag(i)*diag(j)))) then - ilaggr(j) = naggr - else - ilaggr(j) = -naggr - endif + j = icol(k) + if ((1<=j).and.(j<=nr)) then + ilg = ilaggr(j) + if ((ilg<0).and.(i /= j)) then + if (abs(val(k)) > theta*sqrt(abs(diag(i)*diag(j)))) then + ilaggr(j) = naggr + else + ilaggr(j) = -naggr + endif + end if end if enddo diff --git a/mlprec/impl/mld_daggrmap_bld.f90 b/mlprec/impl/mld_daggrmap_bld.f90 index 025622f3..c652983a 100644 --- a/mlprec/impl/mld_daggrmap_bld.f90 +++ b/mlprec/impl/mld_daggrmap_bld.f90 @@ -79,7 +79,7 @@ ! info - integer, output. ! Error code. ! -subroutine mld_daggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) +subroutine mld_daggrmap_bld(aggr_type,iorder,theta,a,desc_a,ilaggr,nlaggr,info) use psb_base_mod use mld_d_inner_mod, mld_protect_name => mld_daggrmap_bld @@ -87,6 +87,7 @@ subroutine mld_daggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) implicit none ! Arguments + integer(psb_ipk_), intent(in) :: iorder integer(psb_ipk_), intent(in) :: aggr_type real(psb_dpk_), intent(in) :: theta type(psb_dspmat_type), intent(in) :: a @@ -118,7 +119,7 @@ subroutine mld_daggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) select case (aggr_type) case (mld_dec_aggr_) - call mld_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) + call mld_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) case (mld_sym_dec_aggr_) nr = a%get_nrows() @@ -126,14 +127,14 @@ subroutine mld_daggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) & rscale=.false.,cscale=.false.) call atmp%set_nrows(nr) call atmp%set_ncols(nr) - if (info == psb_success_) call atrans%transp(atmp) + if (info == psb_success_) call atmp%transp(atrans) if (info == psb_success_) call atrans%cscnv(info,type='COO') if (info == psb_success_) call psb_rwextd(nr,atmp,info,b=atrans,rowscale=.false.) call atmp%set_nrows(nr) call atmp%set_ncols(nr) if (info == psb_success_) call atrans%free() if (info == psb_success_) call atmp%cscnv(info,type='CSR') - if (info == psb_success_) call mld_dec_map_bld(theta,atmp,desc_a,nlaggr,ilaggr,info) + if (info == psb_success_) call mld_dec_map_bld(iorder,theta,atmp,desc_a,nlaggr,ilaggr,info) if (info == psb_success_) call atmp%free() case default diff --git a/mlprec/impl/mld_dcoarse_bld.f90 b/mlprec/impl/mld_dcoarse_bld.f90 index 8d8b5e86..b52c4215 100644 --- a/mlprec/impl/mld_dcoarse_bld.f90 +++ b/mlprec/impl/mld_dcoarse_bld.f90 @@ -95,6 +95,8 @@ subroutine mld_dcoarse_bld(a,desc_a,p,info) & mld_mult_ml_,is_legal_ml_type) call mld_check_def(p%parms%aggr_alg,'Aggregation',& & mld_dec_aggr_,is_legal_ml_aggr_alg) + call mld_check_def(p%parms%aggr_ord,'Ordering',& + & mld_aggr_ord_nat_,is_legal_ml_aggr_ord) call mld_check_def(p%parms%aggr_kind,'Smoother',& & mld_smooth_prol_,is_legal_ml_aggr_kind) call mld_check_def(p%parms%coarse_mat,'Coarse matrix',& @@ -117,7 +119,7 @@ subroutine mld_dcoarse_bld(a,desc_a,p,info) ! aggregation algorithm. This also defines a tentative prolongator from ! the coarse to the fine level. ! - call mld_aggrmap_bld(p%parms%aggr_alg,p%parms%aggr_thresh,& + call mld_aggrmap_bld(p%parms%aggr_alg,p%parms%aggr_ord,p%parms%aggr_thresh,& & a,desc_a,ilaggr,nlaggr,info) if (info /= psb_success_) then diff --git a/mlprec/impl/mld_dcprecset.F90 b/mlprec/impl/mld_dcprecset.F90 index 13d18ff6..47782d44 100644 --- a/mlprec/impl/mld_dcprecset.F90 +++ b/mlprec/impl/mld_dcprecset.F90 @@ -99,6 +99,7 @@ subroutine mld_dcprecseti(p,what,val,info,ilev) use mld_d_mumps_solver #endif + implicit none ! Arguments @@ -113,6 +114,7 @@ subroutine mld_dcprecseti(p,what,val,info,ilev) character(len=*), parameter :: name='mld_precseti' info = psb_success_ + if (.not.allocated(p%precv)) then info = 3111 write(psb_err_unit,*) name,& @@ -153,9 +155,10 @@ subroutine mld_dcprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case('SUB_SOLVE') call onelev_set_solver(p%precv(ilev_),val,info) - case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_KIND',& - & 'SMOOTHER_POS','AGGR_OMEGA_ALG','AGGR_EIG',& - & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& + case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_ORD',& + & 'AGGR_KIND','SMOOTHER_POS','AGGR_OMEGA_ALG',& + & 'AGGR_EIG','SMOOTHER_SWEEPS_PRE',& + & 'SMOOTHER_SWEEPS_POST',& & 'SUB_RESTR','SUB_PROL', & & 'SUB_REN','SUB_OVR','SUB_FILLIN') call p%precv(ilev_)%set(what,val,info) @@ -171,9 +174,10 @@ subroutine mld_dcprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case('SUB_SOLVE') call onelev_set_solver(p%precv(ilev_),val,info) - case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_KIND',& - & 'SMOOTHER_POS','AGGR_OMEGA_ALG','AGGR_EIG',& - & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& + case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_ORD',& + & 'AGGR_KIND','SMOOTHER_POS','AGGR_OMEGA_ALG',& + & 'AGGR_EIG','SMOOTHER_SWEEPS_PRE',& + & 'SMOOTHER_SWEEPS_POST',& & 'SUB_RESTR','SUB_PROL', & & 'SUB_REN','SUB_OVR','SUB_FILLIN',& & 'COARSE_MAT') @@ -287,7 +291,7 @@ subroutine mld_dcprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) end do - case('ML_TYPE','AGGR_ALG','AGGR_KIND',& + case('ML_TYPE','AGGR_ALG','AGGR_ORD','AGGR_KIND',& & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& & 'SMOOTHER_POS','AGGR_OMEGA_ALG',& & 'AGGR_EIG','AGGR_FILTER') @@ -592,6 +596,27 @@ contains info = -5 end if #endif +#ifdef HAVE_MUMPS_ + case (mld_mumps_) + if (allocated(level%sm%sv)) then + select type (sv => level%sm%sv) + class is (mld_d_mumps_solver_type) + ! do nothing + class default + call level%sm%sv%free(info) + if (info == 0) deallocate(level%sm%sv) + if (info == 0) allocate(mld_d_mumps_solver_type ::& + & level%sm%sv, stat=info) + end select + else + allocate(mld_d_mumps_solver_type :: level%sm%sv, stat=info) + endif + if (allocated(level%sm)) then + if (allocated(level%sm%sv)) & + & call level%sm%sv%default() + end if +#endif + #ifdef HAVE_UMF_ case (mld_umf_) if (allocated(level%sm)) then @@ -642,27 +667,6 @@ contains info = -5 end if #endif - -#ifdef HAVE_MUMPS_ - case (mld_mumps_) - if (allocated(level%sm%sv)) then - select type (sv => level%sm%sv) - class is (mld_d_mumps_solver_type) - ! do nothing - class default - call level%sm%sv%free(info) - if (info == 0) deallocate(level%sm%sv) - if (info == 0) allocate(mld_d_mumps_solver_type ::& - & level%sm%sv, stat=info) - end select - else - allocate(mld_d_mumps_solver_type :: level%sm%sv, stat=info) - endif - if (allocated(level%sm)) then - if (allocated(level%sm%sv)) & - & call level%sm%sv%default() - end if -#endif case default ! ! Do nothing and hope for the best :) diff --git a/mlprec/impl/mld_dprecinit.F90 b/mlprec/impl/mld_dprecinit.F90 index bc8e6ced..86be5b05 100644 --- a/mlprec/impl/mld_dprecinit.F90 +++ b/mlprec/impl/mld_dprecinit.F90 @@ -2,9 +2,9 @@ !!$ !!$ MLD2P4 version 2.0 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package -!!$ based on PSBLAS (Parallel Sparse BLAS version 3.0) +!!$ based on PSBLAS (Parallel Sparse BLAS version 3.3) !!$ -!!$ (C) Copyright 2008,2009,2010,2012,2013 +!!$ (C) Copyright 2008, 2010, 2012, 2015 !!$ !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari CNRS-IRIT, Toulouse @@ -61,7 +61,7 @@ ! ! 'ML' - Multilevel hybrid preconditioner (additive on the ! same level and multiplicative through the levels), -! with 2 levels and post-smoothing only. RAS with +! with 2 levels, pre and post-smoothing, RAS with ! overlap 1 and ILU(0) on the local blocks is ! applied as post-smoother at each level, but the ! coarsest one; four sweeps of the block-Jacobi solver, @@ -104,6 +104,7 @@ subroutine mld_dprecinit(p,ptype,info,nlev) use mld_d_slu_solver #endif + implicit none ! Arguments @@ -114,7 +115,7 @@ subroutine mld_dprecinit(p,ptype,info,nlev) ! Local variables integer(psb_ipk_) :: nlev_, ilev_ - real(psb_dpk_) :: thr + real(psb_dpk_) :: thr, scale character(len=*), parameter :: name='mld_precinit' info = psb_success_ @@ -193,7 +194,7 @@ subroutine mld_dprecinit(p,ptype,info,nlev) #if defined(HAVE_UMF_) allocate(mld_d_umf_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #elif defined(HAVE_SLU_) - allocate(mld_d_slu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) + allocate(mld_d_slu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #else allocate(mld_d_ilu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #endif @@ -204,10 +205,11 @@ subroutine mld_dprecinit(p,ptype,info,nlev) call p%precv(ilev_)%set(mld_sub_prol_,psb_none_,info) call p%precv(ilev_)%set(mld_sub_ovr_,izero,info) - thr = 0.16d0 + thr = 0.05 + scale = 1.0 do ilev_=1,nlev_ call p%precv(ilev_)%set(mld_aggr_thresh_,thr,info) - thr = thr/2 + call p%precv(ilev_)%set(mld_aggr_scale_,scale,info) end do case default diff --git a/mlprec/impl/mld_dprecset.F90 b/mlprec/impl/mld_dprecset.F90 index 2f328351..1a5fe0ef 100644 --- a/mlprec/impl/mld_dprecset.F90 +++ b/mlprec/impl/mld_dprecset.F90 @@ -155,8 +155,8 @@ subroutine mld_dprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case(mld_sub_solve_) call onelev_set_solver(p%precv(ilev_),val,info) - case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& - & mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& + case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,& + & mld_aggr_kind_,mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_sub_restr_,mld_sub_prol_, & & mld_sub_ren_,mld_sub_ovr_,mld_sub_fillin_) @@ -173,8 +173,8 @@ subroutine mld_dprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case(mld_sub_solve_) call onelev_set_solver(p%precv(ilev_),val,info) - case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& - & mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& + case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,& + & mld_aggr_kind_,mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_sub_restr_,mld_sub_prol_, & & mld_sub_ren_,mld_sub_ovr_,mld_sub_fillin_,& @@ -285,7 +285,7 @@ subroutine mld_dprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) end do - case(mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& + case(mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,mld_aggr_kind_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_smoother_pos_,mld_aggr_omega_alg_,& & mld_aggr_eig_,mld_aggr_filter_) @@ -309,8 +309,6 @@ subroutine mld_dprecseti(p,what,val,info,ilev) call onelev_set_solver(p%precv(nlev_),mld_umf_,info) #elif defined(HAVE_SLU_) call onelev_set_solver(p%precv(nlev_),mld_slu_,info) -#elif defined(HAVE_MUMPS_) - call onelev_set_solver(p%precv(nlev_),mld_mumps_,info) #else call onelev_set_solver(p%precv(nlev_),mld_ilu_n_,info) #endif @@ -1002,6 +1000,7 @@ subroutine mld_dprecsetr(p,what,val,info,ilev) case(mld_coarse_iluthrs_) ilev_=nlev_ call p%precv(ilev_)%set(mld_sub_iluthrs_,val,info) + case(mld_aggr_thresh_) thr = val do ilev_ = 2, nlev_ diff --git a/mlprec/impl/mld_s_dec_map_bld.f90 b/mlprec/impl/mld_s_dec_map_bld.f90 index 2fa3a6c3..e980ecf8 100644 --- a/mlprec/impl/mld_s_dec_map_bld.f90 +++ b/mlprec/impl/mld_s_dec_map_bld.f90 @@ -37,7 +37,7 @@ !!$ !!$ -subroutine mld_s_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) +subroutine mld_s_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) use psb_base_mod use mld_s_inner_mod, mld_protect_name => mld_s_dec_map_bld @@ -45,6 +45,7 @@ subroutine mld_s_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) implicit none ! Arguments + integer(psb_ipk_), intent(in) :: iorder type(psb_sspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a real(psb_spk_), intent(in) :: theta @@ -52,9 +53,11 @@ subroutine mld_s_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) integer(psb_ipk_), intent(out) :: info ! Local variables - integer(psb_ipk_), allocatable :: ils(:), neigh(:), irow(:), icol(:) + integer(psb_ipk_), allocatable :: ils(:), neigh(:), irow(:), icol(:),& + & ideg(:), idxs(:) real(psb_spk_), allocatable :: val(:), diag(:) - integer(psb_ipk_) :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m, nz, ilg + integer(psb_ipk_) :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m, nz, ilg, ii + type(psb_s_csr_sparse_mat) :: acsr real(psb_spk_) :: cpling, tcl logical :: recovery integer(psb_ipk_) :: debug_level, debug_unit,err_act @@ -75,7 +78,7 @@ subroutine mld_s_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) ncol = desc_a%get_local_cols() nr = a%get_nrows() - allocate(ilaggr(nr),neigh(nr),stat=info) + allocate(ilaggr(nr),neigh(nr),ideg(nr),idxs(nr),stat=info) if(info /= psb_success_) then info=psb_err_alloc_request_ call psb_errpush(info,name,i_err=(/2*nr,izero,izero,izero,izero/),& @@ -90,11 +93,20 @@ subroutine mld_s_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) goto 9999 end if - do i=1, nr - ilaggr(i) = -(nr+1) - end do - - + if (iorder == mld_aggr_ord_nat_) then + do i=1, nr + ilaggr(i) = -(nr+1) + idxs(i) = i + end do + else + call a%cp_to(acsr) + do i=1, nr + ilaggr(i) = -(nr+1) + ideg(i) = acsr%irp(i+1) - acsr%irp(i) + end do + call acsr%free() + call psb_msort(ideg,ix=idxs,dir=psb_sort_down_) + end if ! Note: -(nr+1) Untouched as yet ! -i 1<=i<=nr Adjacent to aggregate i ! i 1<=i<=nr Belonging to aggregate i @@ -106,7 +118,8 @@ subroutine mld_s_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) nlp = 0 do icnt = 0 - do i=1, nr + do ii=1, nr + i = idxs(ii) if (ilaggr(i) == -(nr+1)) then ! ! 1. Untouched nodes are marked >0 together @@ -124,14 +137,16 @@ subroutine mld_s_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) end if do k=1, nz - j = icol(k) - ilg = ilaggr(j) - if ((ilg<0).and.(1<=j).and.(j<=nr).and.(i /= j)) then - if (abs(val(k)) > theta*sqrt(abs(diag(i)*diag(j)))) then - ilaggr(j) = naggr - else - ilaggr(j) = -naggr - endif + j = icol(k) + if ((1<=j).and.(j<=nr)) then + ilg = ilaggr(j) + if ((ilg<0).and.(i /= j)) then + if (abs(val(k)) > theta*sqrt(abs(diag(i)*diag(j)))) then + ilaggr(j) = naggr + else + ilaggr(j) = -naggr + endif + end if end if enddo diff --git a/mlprec/impl/mld_saggrmap_bld.f90 b/mlprec/impl/mld_saggrmap_bld.f90 index 4bc55695..b46bb98a 100644 --- a/mlprec/impl/mld_saggrmap_bld.f90 +++ b/mlprec/impl/mld_saggrmap_bld.f90 @@ -79,7 +79,7 @@ ! info - integer, output. ! Error code. ! -subroutine mld_saggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) +subroutine mld_saggrmap_bld(aggr_type,iorder,theta,a,desc_a,ilaggr,nlaggr,info) use psb_base_mod use mld_s_inner_mod, mld_protect_name => mld_saggrmap_bld @@ -87,6 +87,7 @@ subroutine mld_saggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) implicit none ! Arguments + integer(psb_ipk_), intent(in) :: iorder integer(psb_ipk_), intent(in) :: aggr_type real(psb_spk_), intent(in) :: theta type(psb_sspmat_type), intent(in) :: a @@ -118,7 +119,7 @@ subroutine mld_saggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) select case (aggr_type) case (mld_dec_aggr_) - call mld_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) + call mld_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) case (mld_sym_dec_aggr_) nr = a%get_nrows() @@ -126,14 +127,14 @@ subroutine mld_saggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) & rscale=.false.,cscale=.false.) call atmp%set_nrows(nr) call atmp%set_ncols(nr) - if (info == psb_success_) call atrans%transp(atmp) + if (info == psb_success_) call atmp%transp(atrans) if (info == psb_success_) call atrans%cscnv(info,type='COO') if (info == psb_success_) call psb_rwextd(nr,atmp,info,b=atrans,rowscale=.false.) call atmp%set_nrows(nr) call atmp%set_ncols(nr) if (info == psb_success_) call atrans%free() if (info == psb_success_) call atmp%cscnv(info,type='CSR') - if (info == psb_success_) call mld_dec_map_bld(theta,atmp,desc_a,nlaggr,ilaggr,info) + if (info == psb_success_) call mld_dec_map_bld(iorder,theta,atmp,desc_a,nlaggr,ilaggr,info) if (info == psb_success_) call atmp%free() case default diff --git a/mlprec/impl/mld_scoarse_bld.f90 b/mlprec/impl/mld_scoarse_bld.f90 index 344bfc18..acc85154 100644 --- a/mlprec/impl/mld_scoarse_bld.f90 +++ b/mlprec/impl/mld_scoarse_bld.f90 @@ -95,6 +95,8 @@ subroutine mld_scoarse_bld(a,desc_a,p,info) & mld_mult_ml_,is_legal_ml_type) call mld_check_def(p%parms%aggr_alg,'Aggregation',& & mld_dec_aggr_,is_legal_ml_aggr_alg) + call mld_check_def(p%parms%aggr_ord,'Ordering',& + & mld_aggr_ord_nat_,is_legal_ml_aggr_ord) call mld_check_def(p%parms%aggr_kind,'Smoother',& & mld_smooth_prol_,is_legal_ml_aggr_kind) call mld_check_def(p%parms%coarse_mat,'Coarse matrix',& @@ -117,7 +119,7 @@ subroutine mld_scoarse_bld(a,desc_a,p,info) ! aggregation algorithm. This also defines a tentative prolongator from ! the coarse to the fine level. ! - call mld_aggrmap_bld(p%parms%aggr_alg,p%parms%aggr_thresh,& + call mld_aggrmap_bld(p%parms%aggr_alg,p%parms%aggr_ord,p%parms%aggr_thresh,& & a,desc_a,ilaggr,nlaggr,info) if (info /= psb_success_) then @@ -136,6 +138,7 @@ subroutine mld_scoarse_bld(a,desc_a,p,info) call psb_errpush(psb_err_from_subroutine_,name,a_err='mld_aggrmat_asb') goto 9999 end if + ! ! Fix the base_a and base_desc pointers for handling of residuals. ! This is correct because this routine is only called at levels >=2. diff --git a/mlprec/impl/mld_scprecset.F90 b/mlprec/impl/mld_scprecset.F90 index d1c651f6..5b80da49 100644 --- a/mlprec/impl/mld_scprecset.F90 +++ b/mlprec/impl/mld_scprecset.F90 @@ -93,6 +93,7 @@ subroutine mld_scprecseti(p,what,val,info,ilev) use mld_s_mumps_solver #endif + implicit none ! Arguments @@ -148,9 +149,10 @@ subroutine mld_scprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case('SUB_SOLVE') call onelev_set_solver(p%precv(ilev_),val,info) - case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_KIND',& - & 'SMOOTHER_POS','AGGR_OMEGA_ALG','AGGR_EIG',& - & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& + case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_ORD',& + & 'AGGR_KIND','SMOOTHER_POS','AGGR_OMEGA_ALG',& + & 'AGGR_EIG','SMOOTHER_SWEEPS_PRE',& + & 'SMOOTHER_SWEEPS_POST',& & 'SUB_RESTR','SUB_PROL', & & 'SUB_REN','SUB_OVR','SUB_FILLIN') call p%precv(ilev_)%set(what,val,info) @@ -166,9 +168,10 @@ subroutine mld_scprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case('SUB_SOLVE') call onelev_set_solver(p%precv(ilev_),val,info) - case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_KIND',& - & 'SMOOTHER_POS','AGGR_OMEGA_ALG','AGGR_EIG',& - & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& + case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_ORD',& + & 'AGGR_KIND','SMOOTHER_POS','AGGR_OMEGA_ALG',& + & 'AGGR_EIG','SMOOTHER_SWEEPS_PRE',& + & 'SMOOTHER_SWEEPS_POST',& & 'SUB_RESTR','SUB_PROL', & & 'SUB_REN','SUB_OVR','SUB_FILLIN',& & 'COARSE_MAT') @@ -280,7 +283,7 @@ subroutine mld_scprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) end do - case('ML_TYPE','AGGR_ALG','AGGR_KIND',& + case('ML_TYPE','AGGR_ALG','AGGR_ORD','AGGR_KIND',& & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& & 'SMOOTHER_POS','AGGR_OMEGA_ALG',& & 'AGGR_EIG','AGGR_FILTER') @@ -583,7 +586,6 @@ contains info = -5 end if #endif - #ifdef HAVE_MUMPS_ case (mld_mumps_) if (allocated(level%sm%sv)) then diff --git a/mlprec/impl/mld_sprecinit.F90 b/mlprec/impl/mld_sprecinit.F90 index 3ff111ba..24021e6d 100644 --- a/mlprec/impl/mld_sprecinit.F90 +++ b/mlprec/impl/mld_sprecinit.F90 @@ -2,9 +2,9 @@ !!$ !!$ MLD2P4 version 2.0 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package -!!$ based on PSBLAS (Parallel Sparse BLAS version 3.0) +!!$ based on PSBLAS (Parallel Sparse BLAS version 3.3) !!$ -!!$ (C) Copyright 2008,2009,2010,2012,2013 +!!$ (C) Copyright 2008, 2010, 2012, 2015 !!$ !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari CNRS-IRIT, Toulouse @@ -61,7 +61,7 @@ ! ! 'ML' - Multilevel hybrid preconditioner (additive on the ! same level and multiplicative through the levels), -! with 2 levels and post-smoothing only. RAS with +! with 2 levels, pre and post-smoothing, RAS with ! overlap 1 and ILU(0) on the local blocks is ! applied as post-smoother at each level, but the ! coarsest one; four sweeps of the block-Jacobi solver, @@ -97,9 +97,6 @@ subroutine mld_sprecinit(p,ptype,info,nlev) use mld_s_id_solver use mld_s_diag_solver use mld_s_ilu_solver -#if defined(HAVE_UMF_) && 0 - use mld_s_umf_solver -#endif #if defined(HAVE_SLU_) use mld_s_slu_solver #endif @@ -115,7 +112,7 @@ subroutine mld_sprecinit(p,ptype,info,nlev) ! Local variables integer(psb_ipk_) :: nlev_, ilev_ - real(psb_spk_) :: thr + real(psb_spk_) :: thr, scale character(len=*), parameter :: name='mld_precinit' info = psb_success_ @@ -191,10 +188,8 @@ subroutine mld_sprecinit(p,ptype,info,nlev) ilev_ = nlev_ allocate(mld_s_jac_smoother_type :: p%precv(ilev_)%sm, stat=info) if (info /= psb_success_) return -#if defined(HAVE_UMF_) && 0 - allocate(mld_s_umf_solver_type :: p%precv(ilev_)%sm%sv, stat=info) -#elif defined(HAVE_SLU_) - allocate(mld_s_slu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) +#if defined(HAVE_SLU_) + allocate(mld_s_slu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #else allocate(mld_s_ilu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #endif @@ -205,10 +200,11 @@ subroutine mld_sprecinit(p,ptype,info,nlev) call p%precv(ilev_)%set(mld_sub_prol_,psb_none_,info) call p%precv(ilev_)%set(mld_sub_ovr_,izero,info) - thr = 0.16d0 + thr = 0.05 + scale = 1.0 do ilev_=1,nlev_ call p%precv(ilev_)%set(mld_aggr_thresh_,thr,info) - thr = thr/2 + call p%precv(ilev_)%set(mld_aggr_scale_,scale,info) end do case default diff --git a/mlprec/impl/mld_sprecset.F90 b/mlprec/impl/mld_sprecset.F90 index c7d277d9..822e1ea2 100644 --- a/mlprec/impl/mld_sprecset.F90 +++ b/mlprec/impl/mld_sprecset.F90 @@ -149,8 +149,8 @@ subroutine mld_sprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case(mld_sub_solve_) call onelev_set_solver(p%precv(ilev_),val,info) - case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& - & mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& + case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,& + & mld_aggr_kind_,mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_sub_restr_,mld_sub_prol_, & & mld_sub_ren_,mld_sub_ovr_,mld_sub_fillin_) @@ -167,8 +167,8 @@ subroutine mld_sprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case(mld_sub_solve_) call onelev_set_solver(p%precv(ilev_),val,info) - case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& - & mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& + case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,& + & mld_aggr_kind_,mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_sub_restr_,mld_sub_prol_, & & mld_sub_ren_,mld_sub_ovr_,mld_sub_fillin_,& @@ -277,7 +277,7 @@ subroutine mld_sprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) end do - case(mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& + case(mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,mld_aggr_kind_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_smoother_pos_,mld_aggr_omega_alg_,& & mld_aggr_eig_,mld_aggr_filter_) @@ -299,8 +299,8 @@ subroutine mld_sprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) #if defined(HAVE_SLU_) call onelev_set_solver(p%precv(nlev_),mld_slu_,info) -#elif defined(HAVE_MUMPS_) - call onelev_set_solver(p%precv(nlev_),mld_mumps_,info) +#elif defined(HAVE_SLU_) + call onelev_set_solver(p%precv(nlev_),mld_slu_,info) #else call onelev_set_solver(p%precv(nlev_),mld_ilu_n_,info) #endif @@ -579,7 +579,6 @@ contains info = -5 end if #endif - #ifdef HAVE_MUMPS_ case (mld_mumps_) if (allocated(level%sm%sv)) then @@ -601,8 +600,6 @@ contains end if end if #endif - - case default ! ! Do nothing and hope for the best :) @@ -726,13 +723,26 @@ subroutine mld_sprecsetsv(p,val,info,ilev) do ilev_ = ilmin, ilmax if (allocated(p%precv(ilev_)%sm)) then - if (allocated(p%precv(ilev_)%sm%sv)) & - & deallocate(p%precv(ilev_)%sm%sv) + if (allocated(p%precv(ilev_)%sm%sv)) then + if (.not.same_type_as(p%precv(ilev_)%sm%sv,val)) then + deallocate(p%precv(ilev_)%sm%sv,stat=info) + if (info /= 0) then + info = 3111 + return + end if + end if + if (.not.allocated(p%precv(ilev_)%sm%sv)) then #ifdef HAVE_MOLD - allocate(p%precv(ilev_)%sm%sv,mold=val) + allocate(p%precv(ilev_)%sm%sv,mold=val,stat=info) #else - allocate(p%precv(ilev_)%sm%sv,source=val) + allocate(p%precv(ilev_)%sm%sv,source=val,stat=info) #endif + if (info /= 0) then + info = 3111 + return + end if + end if + end if call p%precv(ilev_)%sm%sv%default() else info = 3111 diff --git a/mlprec/impl/mld_z_dec_map_bld.f90 b/mlprec/impl/mld_z_dec_map_bld.f90 index b578cc78..718856aa 100644 --- a/mlprec/impl/mld_z_dec_map_bld.f90 +++ b/mlprec/impl/mld_z_dec_map_bld.f90 @@ -37,7 +37,7 @@ !!$ !!$ -subroutine mld_z_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) +subroutine mld_z_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) use psb_base_mod use mld_z_inner_mod, mld_protect_name => mld_z_dec_map_bld @@ -45,6 +45,7 @@ subroutine mld_z_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) implicit none ! Arguments + integer(psb_ipk_), intent(in) :: iorder type(psb_zspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a real(psb_dpk_), intent(in) :: theta @@ -52,9 +53,11 @@ subroutine mld_z_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) integer(psb_ipk_), intent(out) :: info ! Local variables - integer(psb_ipk_), allocatable :: ils(:), neigh(:), irow(:), icol(:) + integer(psb_ipk_), allocatable :: ils(:), neigh(:), irow(:), icol(:),& + & ideg(:), idxs(:) complex(psb_dpk_), allocatable :: val(:), diag(:) - integer(psb_ipk_) :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m, nz, ilg + integer(psb_ipk_) :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m, nz, ilg, ii + type(psb_z_csr_sparse_mat) :: acsr real(psb_dpk_) :: cpling, tcl logical :: recovery integer(psb_ipk_) :: debug_level, debug_unit,err_act @@ -75,7 +78,7 @@ subroutine mld_z_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) ncol = desc_a%get_local_cols() nr = a%get_nrows() - allocate(ilaggr(nr),neigh(nr),stat=info) + allocate(ilaggr(nr),neigh(nr),ideg(nr),idxs(nr),stat=info) if(info /= psb_success_) then info=psb_err_alloc_request_ call psb_errpush(info,name,i_err=(/2*nr,izero,izero,izero,izero/),& @@ -90,11 +93,20 @@ subroutine mld_z_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) goto 9999 end if - do i=1, nr - ilaggr(i) = -(nr+1) - end do - - + if (iorder == mld_aggr_ord_nat_) then + do i=1, nr + ilaggr(i) = -(nr+1) + idxs(i) = i + end do + else + call a%cp_to(acsr) + do i=1, nr + ilaggr(i) = -(nr+1) + ideg(i) = acsr%irp(i+1) - acsr%irp(i) + end do + call acsr%free() + call psb_msort(ideg,ix=idxs,dir=psb_sort_down_) + end if ! Note: -(nr+1) Untouched as yet ! -i 1<=i<=nr Adjacent to aggregate i ! i 1<=i<=nr Belonging to aggregate i @@ -106,7 +118,8 @@ subroutine mld_z_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) nlp = 0 do icnt = 0 - do i=1, nr + do ii=1, nr + i = idxs(ii) if (ilaggr(i) == -(nr+1)) then ! ! 1. Untouched nodes are marked >0 together @@ -124,14 +137,16 @@ subroutine mld_z_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) end if do k=1, nz - j = icol(k) - ilg = ilaggr(j) - if ((ilg<0).and.(1<=j).and.(j<=nr).and.(i /= j)) then - if (abs(val(k)) > theta*sqrt(abs(diag(i)*diag(j)))) then - ilaggr(j) = naggr - else - ilaggr(j) = -naggr - endif + j = icol(k) + if ((1<=j).and.(j<=nr)) then + ilg = ilaggr(j) + if ((ilg<0).and.(i /= j)) then + if (abs(val(k)) > theta*sqrt(abs(diag(i)*diag(j)))) then + ilaggr(j) = naggr + else + ilaggr(j) = -naggr + endif + end if end if enddo diff --git a/mlprec/impl/mld_zaggrmap_bld.f90 b/mlprec/impl/mld_zaggrmap_bld.f90 index 41e6f677..2058fd66 100644 --- a/mlprec/impl/mld_zaggrmap_bld.f90 +++ b/mlprec/impl/mld_zaggrmap_bld.f90 @@ -79,7 +79,7 @@ ! info - integer, output. ! Error code. ! -subroutine mld_zaggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) +subroutine mld_zaggrmap_bld(aggr_type,iorder,theta,a,desc_a,ilaggr,nlaggr,info) use psb_base_mod use mld_z_inner_mod, mld_protect_name => mld_zaggrmap_bld @@ -87,6 +87,7 @@ subroutine mld_zaggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) implicit none ! Arguments + integer(psb_ipk_), intent(in) :: iorder integer(psb_ipk_), intent(in) :: aggr_type real(psb_dpk_), intent(in) :: theta type(psb_zspmat_type), intent(in) :: a @@ -118,7 +119,7 @@ subroutine mld_zaggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) select case (aggr_type) case (mld_dec_aggr_) - call mld_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) + call mld_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) case (mld_sym_dec_aggr_) nr = a%get_nrows() @@ -126,14 +127,14 @@ subroutine mld_zaggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) & rscale=.false.,cscale=.false.) call atmp%set_nrows(nr) call atmp%set_ncols(nr) - if (info == psb_success_) call atrans%transp(atmp) + if (info == psb_success_) call atmp%transp(atrans) if (info == psb_success_) call atrans%cscnv(info,type='COO') if (info == psb_success_) call psb_rwextd(nr,atmp,info,b=atrans,rowscale=.false.) call atmp%set_nrows(nr) call atmp%set_ncols(nr) if (info == psb_success_) call atrans%free() if (info == psb_success_) call atmp%cscnv(info,type='CSR') - if (info == psb_success_) call mld_dec_map_bld(theta,atmp,desc_a,nlaggr,ilaggr,info) + if (info == psb_success_) call mld_dec_map_bld(iorder,theta,atmp,desc_a,nlaggr,ilaggr,info) if (info == psb_success_) call atmp%free() case default diff --git a/mlprec/impl/mld_zcoarse_bld.f90 b/mlprec/impl/mld_zcoarse_bld.f90 index dc67d86f..644284de 100644 --- a/mlprec/impl/mld_zcoarse_bld.f90 +++ b/mlprec/impl/mld_zcoarse_bld.f90 @@ -39,7 +39,7 @@ ! File: mld_zcoarse_bld.f90 ! ! Subroutine: mld_zcoarse_bld -! Version: complex +! Version: real ! ! This routine builds the matrix associated to the current level of the ! multilevel preconditioner from the matrix associated to the previous level, @@ -95,6 +95,8 @@ subroutine mld_zcoarse_bld(a,desc_a,p,info) & mld_mult_ml_,is_legal_ml_type) call mld_check_def(p%parms%aggr_alg,'Aggregation',& & mld_dec_aggr_,is_legal_ml_aggr_alg) + call mld_check_def(p%parms%aggr_ord,'Ordering',& + & mld_aggr_ord_nat_,is_legal_ml_aggr_ord) call mld_check_def(p%parms%aggr_kind,'Smoother',& & mld_smooth_prol_,is_legal_ml_aggr_kind) call mld_check_def(p%parms%coarse_mat,'Coarse matrix',& @@ -117,7 +119,7 @@ subroutine mld_zcoarse_bld(a,desc_a,p,info) ! aggregation algorithm. This also defines a tentative prolongator from ! the coarse to the fine level. ! - call mld_aggrmap_bld(p%parms%aggr_alg,p%parms%aggr_thresh,& + call mld_aggrmap_bld(p%parms%aggr_alg,p%parms%aggr_ord,p%parms%aggr_thresh,& & a,desc_a,ilaggr,nlaggr,info) if (info /= psb_success_) then @@ -136,6 +138,7 @@ subroutine mld_zcoarse_bld(a,desc_a,p,info) call psb_errpush(psb_err_from_subroutine_,name,a_err='mld_aggrmat_asb') goto 9999 end if + ! ! Fix the base_a and base_desc pointers for handling of residuals. ! This is correct because this routine is only called at levels >=2. @@ -147,7 +150,6 @@ subroutine mld_zcoarse_bld(a,desc_a,p,info) return 9999 call psb_error_handler(err_act) - return end subroutine mld_zcoarse_bld diff --git a/mlprec/impl/mld_zcprecset.F90 b/mlprec/impl/mld_zcprecset.F90 index 0c16e732..c75b80ce 100644 --- a/mlprec/impl/mld_zcprecset.F90 +++ b/mlprec/impl/mld_zcprecset.F90 @@ -99,6 +99,7 @@ subroutine mld_zcprecseti(p,what,val,info,ilev) use mld_z_mumps_solver #endif + implicit none ! Arguments @@ -154,9 +155,10 @@ subroutine mld_zcprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case('SUB_SOLVE') call onelev_set_solver(p%precv(ilev_),val,info) - case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_KIND',& - & 'SMOOTHER_POS','AGGR_OMEGA_ALG','AGGR_EIG',& - & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& + case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_ORD',& + & 'AGGR_KIND','SMOOTHER_POS','AGGR_OMEGA_ALG',& + & 'AGGR_EIG','SMOOTHER_SWEEPS_PRE',& + & 'SMOOTHER_SWEEPS_POST',& & 'SUB_RESTR','SUB_PROL', & & 'SUB_REN','SUB_OVR','SUB_FILLIN') call p%precv(ilev_)%set(what,val,info) @@ -172,9 +174,10 @@ subroutine mld_zcprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case('SUB_SOLVE') call onelev_set_solver(p%precv(ilev_),val,info) - case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_KIND',& - & 'SMOOTHER_POS','AGGR_OMEGA_ALG','AGGR_EIG',& - & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& + case('SMOOTHER_SWEEPS','ML_TYPE','AGGR_ALG','AGGR_ORD',& + & 'AGGR_KIND','SMOOTHER_POS','AGGR_OMEGA_ALG',& + & 'AGGR_EIG','SMOOTHER_SWEEPS_PRE',& + & 'SMOOTHER_SWEEPS_POST',& & 'SUB_RESTR','SUB_PROL', & & 'SUB_REN','SUB_OVR','SUB_FILLIN',& & 'COARSE_MAT') @@ -288,7 +291,7 @@ subroutine mld_zcprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) end do - case('ML_TYPE','AGGR_ALG','AGGR_KIND',& + case('ML_TYPE','AGGR_ALG','AGGR_ORD','AGGR_KIND',& & 'SMOOTHER_SWEEPS_PRE','SMOOTHER_SWEEPS_POST',& & 'SMOOTHER_POS','AGGR_OMEGA_ALG',& & 'AGGR_EIG','AGGR_FILTER') @@ -330,7 +333,6 @@ subroutine mld_zcprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),val,info) call p%precv(nlev_)%set('COARSE_MAT',mld_distr_mat_,info) - case(mld_jac_) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),mld_diag_scale_,info) @@ -594,6 +596,27 @@ contains info = -5 end if #endif +#ifdef HAVE_MUMPS_ + case (mld_mumps_) + if (allocated(level%sm%sv)) then + select type (sv => level%sm%sv) + class is (mld_z_mumps_solver_type) + ! do nothing + class default + call level%sm%sv%free(info) + if (info == 0) deallocate(level%sm%sv) + if (info == 0) allocate(mld_z_mumps_solver_type ::& + & level%sm%sv, stat=info) + end select + else + allocate(mld_z_mumps_solver_type :: level%sm%sv, stat=info) + endif + if (allocated(level%sm)) then + if (allocated(level%sm%sv)) & + & call level%sm%sv%default() + end if +#endif + #ifdef HAVE_UMF_ case (mld_umf_) if (allocated(level%sm)) then @@ -644,28 +667,6 @@ contains info = -5 end if #endif - -#ifdef HAVE_MUMPS_ - case (mld_mumps_) - if (allocated(level%sm%sv)) then - select type (sv => level%sm%sv) - class is (mld_z_mumps_solver_type) - ! do nothing - class default - call level%sm%sv%free(info) - if (info == 0) deallocate(level%sm%sv) - if (info == 0) allocate(mld_z_mumps_solver_type ::& - & level%sm%sv, stat=info) - end select - else - allocate(mld_z_mumps_solver_type :: level%sm%sv, stat=info) - endif - if (allocated(level%sm)) then - if (allocated(level%sm%sv)) & - & call level%sm%sv%default() - end if -#endif - case default ! ! Do nothing and hope for the best :) diff --git a/mlprec/impl/mld_zprecinit.F90 b/mlprec/impl/mld_zprecinit.F90 index 2b04946e..fa0f9337 100644 --- a/mlprec/impl/mld_zprecinit.F90 +++ b/mlprec/impl/mld_zprecinit.F90 @@ -2,9 +2,9 @@ !!$ !!$ MLD2P4 version 2.0 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package -!!$ based on PSBLAS (Parallel Sparse BLAS version 3.0) +!!$ based on PSBLAS (Parallel Sparse BLAS version 3.3) !!$ -!!$ (C) Copyright 2008,2009,2010,2012,2013 +!!$ (C) Copyright 2008, 2010, 2012, 2015 !!$ !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari CNRS-IRIT, Toulouse @@ -61,7 +61,7 @@ ! ! 'ML' - Multilevel hybrid preconditioner (additive on the ! same level and multiplicative through the levels), -! with 2 levels and post-smoothing only. RAS with +! with 2 levels, pre and post-smoothing, RAS with ! overlap 1 and ILU(0) on the local blocks is ! applied as post-smoother at each level, but the ! coarsest one; four sweeps of the block-Jacobi solver, @@ -115,7 +115,7 @@ subroutine mld_zprecinit(p,ptype,info,nlev) ! Local variables integer(psb_ipk_) :: nlev_, ilev_ - real(psb_dpk_) :: thr + real(psb_dpk_) :: thr, scale character(len=*), parameter :: name='mld_precinit' info = psb_success_ @@ -194,7 +194,7 @@ subroutine mld_zprecinit(p,ptype,info,nlev) #if defined(HAVE_UMF_) allocate(mld_z_umf_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #elif defined(HAVE_SLU_) - allocate(mld_z_slu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) + allocate(mld_z_slu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #else allocate(mld_z_ilu_solver_type :: p%precv(ilev_)%sm%sv, stat=info) #endif @@ -205,10 +205,11 @@ subroutine mld_zprecinit(p,ptype,info,nlev) call p%precv(ilev_)%set(mld_sub_prol_,psb_none_,info) call p%precv(ilev_)%set(mld_sub_ovr_,izero,info) - thr = 0.16d0 + thr = 0.05 + scale = 1.0 do ilev_=1,nlev_ call p%precv(ilev_)%set(mld_aggr_thresh_,thr,info) - thr = thr/2 + call p%precv(ilev_)%set(mld_aggr_scale_,scale,info) end do case default diff --git a/mlprec/impl/mld_zprecset.F90 b/mlprec/impl/mld_zprecset.F90 index f0bdfd51..7b46a90c 100644 --- a/mlprec/impl/mld_zprecset.F90 +++ b/mlprec/impl/mld_zprecset.F90 @@ -98,6 +98,7 @@ subroutine mld_zprecseti(p,what,val,info,ilev) #if defined(HAVE_MUMPS_) use mld_z_mumps_solver #endif + implicit none ! Arguments @@ -154,8 +155,8 @@ subroutine mld_zprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case(mld_sub_solve_) call onelev_set_solver(p%precv(ilev_),val,info) - case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& - & mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& + case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,& + & mld_aggr_kind_,mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_sub_restr_,mld_sub_prol_, & & mld_sub_ren_,mld_sub_ovr_,mld_sub_fillin_) @@ -172,8 +173,8 @@ subroutine mld_zprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) case(mld_sub_solve_) call onelev_set_solver(p%precv(ilev_),val,info) - case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& - & mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& + case(mld_smoother_sweeps_,mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,& + & mld_aggr_kind_,mld_smoother_pos_,mld_aggr_omega_alg_,mld_aggr_eig_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_sub_restr_,mld_sub_prol_, & & mld_sub_ren_,mld_sub_ovr_,mld_sub_fillin_,& @@ -215,7 +216,7 @@ subroutine mld_zprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),val,info) call p%precv(nlev_)%set(mld_coarse_mat_,mld_repl_mat_,info) - case(mld_sludist_, mld_mumps_) + case(mld_sludist_,mld_mumps_) call onelev_set_smoother(p%precv(nlev_),mld_bjac_,info) call onelev_set_solver(p%precv(nlev_),val,info) call p%precv(nlev_)%set(mld_coarse_mat_,mld_distr_mat_,info) @@ -284,7 +285,7 @@ subroutine mld_zprecseti(p,what,val,info,ilev) call onelev_set_smoother(p%precv(ilev_),val,info) end do - case(mld_ml_type_,mld_aggr_alg_,mld_aggr_kind_,& + case(mld_ml_type_,mld_aggr_alg_,mld_aggr_ord_,mld_aggr_kind_,& & mld_smoother_sweeps_pre_,mld_smoother_sweeps_post_,& & mld_smoother_pos_,mld_aggr_omega_alg_,& & mld_aggr_eig_,mld_aggr_filter_) @@ -308,8 +309,6 @@ subroutine mld_zprecseti(p,what,val,info,ilev) call onelev_set_solver(p%precv(nlev_),mld_umf_,info) #elif defined(HAVE_SLU_) call onelev_set_solver(p%precv(nlev_),mld_slu_,info) -#elif defined(HAVE_MUMPS_) - call onelev_set_solver(p%precv(nlev_),mld_mumps_,info) #else call onelev_set_solver(p%precv(nlev_),mld_ilu_n_,info) #endif @@ -782,13 +781,26 @@ subroutine mld_zprecsetsv(p,val,info,ilev) do ilev_ = ilmin, ilmax if (allocated(p%precv(ilev_)%sm)) then - if (allocated(p%precv(ilev_)%sm%sv)) & - & deallocate(p%precv(ilev_)%sm%sv) + if (allocated(p%precv(ilev_)%sm%sv)) then + if (.not.same_type_as(p%precv(ilev_)%sm%sv,val)) then + deallocate(p%precv(ilev_)%sm%sv,stat=info) + if (info /= 0) then + info = 3111 + return + end if + end if + if (.not.allocated(p%precv(ilev_)%sm%sv)) then #ifdef HAVE_MOLD - allocate(p%precv(ilev_)%sm%sv,mold=val) + allocate(p%precv(ilev_)%sm%sv,mold=val,stat=info) #else - allocate(p%precv(ilev_)%sm%sv,source=val) + allocate(p%precv(ilev_)%sm%sv,source=val,stat=info) #endif + if (info /= 0) then + info = 3111 + return + end if + end if + end if call p%precv(ilev_)%sm%sv%default() else info = 3111 diff --git a/mlprec/mld_base_prec_type.F90 b/mlprec/mld_base_prec_type.F90 index d3e07fbb..142c10a1 100644 --- a/mlprec/mld_base_prec_type.F90 +++ b/mlprec/mld_base_prec_type.F90 @@ -98,7 +98,7 @@ module mld_base_prec_type type mld_ml_parms integer(psb_ipk_) :: sweeps, sweeps_pre, sweeps_post integer(psb_ipk_) :: ml_type, smoother_pos - integer(psb_ipk_) :: aggr_alg, aggr_kind + integer(psb_ipk_) :: aggr_alg, aggr_ord, aggr_kind integer(psb_ipk_) :: aggr_omega_alg, aggr_eig, aggr_filter integer(psb_ipk_) :: coarse_mat, coarse_solve logical :: clean_zeros=.true. @@ -151,18 +151,19 @@ module mld_base_prec_type integer(psb_ipk_), parameter :: mld_smoother_pos_ = 23 integer(psb_ipk_), parameter :: mld_aggr_kind_ = 24 integer(psb_ipk_), parameter :: mld_aggr_alg_ = 25 - integer(psb_ipk_), parameter :: mld_aggr_omega_alg_ = 26 - integer(psb_ipk_), parameter :: mld_aggr_eig_ = 27 - integer(psb_ipk_), parameter :: mld_aggr_filter_ = 28 - integer(psb_ipk_), parameter :: mld_coarse_mat_ = 29 - integer(psb_ipk_), parameter :: mld_coarse_solve_ = 30 - integer(psb_ipk_), parameter :: mld_coarse_sweeps_ = 31 - integer(psb_ipk_), parameter :: mld_coarse_fillin_ = 32 - integer(psb_ipk_), parameter :: mld_coarse_subsolve_ = 33 - integer(psb_ipk_), parameter :: mld_smoother_sweeps_ = 34 - integer(psb_ipk_), parameter :: mld_coarse_aggr_size_ = 35 - integer(psb_ipk_), parameter :: mld_solver_sweeps_ = 36 - integer(psb_ipk_), parameter :: mld_ifpsz_ = 37 + integer(psb_ipk_), parameter :: mld_aggr_ord_ = 26 + integer(psb_ipk_), parameter :: mld_aggr_omega_alg_ = 27 + integer(psb_ipk_), parameter :: mld_aggr_eig_ = 28 + integer(psb_ipk_), parameter :: mld_aggr_filter_ = 29 + integer(psb_ipk_), parameter :: mld_coarse_mat_ = 30 + integer(psb_ipk_), parameter :: mld_coarse_solve_ = 31 + integer(psb_ipk_), parameter :: mld_coarse_sweeps_ = 32 + integer(psb_ipk_), parameter :: mld_coarse_fillin_ = 33 + integer(psb_ipk_), parameter :: mld_coarse_subsolve_ = 34 + integer(psb_ipk_), parameter :: mld_smoother_sweeps_ = 35 + integer(psb_ipk_), parameter :: mld_coarse_aggr_size_ = 36 + integer(psb_ipk_), parameter :: mld_solver_sweeps_ = 37 + integer(psb_ipk_), parameter :: mld_ifpsz_ = 38 ! ! Legal values for entry: mld_smoother_type_ @@ -249,8 +250,13 @@ module mld_base_prec_type integer(psb_ipk_), parameter :: mld_glb_aggr_=2 integer(psb_ipk_), parameter :: mld_new_dec_aggr_=3 integer(psb_ipk_), parameter :: mld_new_glb_aggr_=4 - integer(psb_ipk_), parameter :: mld_max_aggr_alg_=mld_dec_aggr_ - + integer(psb_ipk_), parameter :: mld_max_aggr_alg_=mld_sym_dec_aggr_ + ! + ! Legal values for entry: mld_aggr_ord_ + ! + integer(psb_ipk_), parameter :: mld_aggr_ord_nat_ = 0 + integer(psb_ipk_), parameter :: mld_aggr_ord_desc_deg_ = 1 + integer(psb_ipk_), parameter :: mld_max_aggr_ord_ = mld_aggr_ord_desc_deg_ ! ! Legal values for entry: mld_aggr_omega_alg_ ! @@ -320,6 +326,8 @@ module mld_base_prec_type character(len=18), parameter, private :: & & aggr_names(0:4)=(/'local aggregation ','sym. local aggr. ',& & 'global aggregation', 'new local aggr. ','new global aggr. '/) + character(len=18), parameter, private :: & + & ord_names(0:1)=(/'Natural ordering ','Desc. degree ord. '/) character(len=6), parameter, private :: & & restrict_names(0:4)=(/'none ','halo ',' ',' ',' '/) character(len=12), parameter, private :: & @@ -411,6 +419,10 @@ contains val = mld_dec_aggr_ case('SYMDEC') val = mld_sym_dec_aggr_ + case('NAT','NATURAL') + val = mld_aggr_ord_nat_ + case('DESC','RDEGREE','DEGREE') + val = mld_aggr_ord_desc_deg_ case('GLB') val = mld_glb_aggr_ case('REPL') @@ -467,7 +479,7 @@ contains write(iout,*) 'Sweeps: ',pm%sweeps,pm%sweeps_pre,pm%sweeps_post write(iout,*) 'ML : ',pm%ml_type,pm%smoother_pos - write(iout,*) 'AGGR : ',pm%aggr_alg,pm%aggr_kind + write(iout,*) 'AGGR : ',pm%aggr_alg,pm%aggr_kind, pm%aggr_ord write(iout,*) ' : ',pm%aggr_omega_alg,pm%aggr_eig,pm%aggr_filter write(iout,*) 'COARSE: ',pm%coarse_mat,pm%coarse_solve end subroutine ml_parms_printout @@ -533,6 +545,8 @@ contains end if write(iout,*) ' Aggregation: ', & & aggr_names(pm%aggr_alg) + write(iout,*) ' with initial ordering: ',& + & ord_names(pm%aggr_ord) write(iout,*) ' Aggregation type: ', & & aggr_kinds(pm%aggr_kind) if (pm%aggr_kind /= mld_no_smooth_) then @@ -720,6 +734,14 @@ contains is_legal_ml_aggr_alg = ((ip>=mld_dec_aggr_).and.(ip<=mld_max_aggr_alg_)) return end function is_legal_ml_aggr_alg + function is_legal_ml_aggr_ord(ip) + implicit none + integer(psb_ipk_), intent(in) :: ip + logical :: is_legal_ml_aggr_ord + + is_legal_ml_aggr_ord = ((mld_aggr_ord_nat_<=ip).and.(ip<=mld_max_aggr_ord_)) + return + end function is_legal_ml_aggr_ord function is_legal_ml_aggr_omega_alg(ip) implicit none integer(psb_ipk_), intent(in) :: ip diff --git a/mlprec/mld_c_inner_mod.f90 b/mlprec/mld_c_inner_mod.f90 index f0840043..a1aa0253 100644 --- a/mlprec/mld_c_inner_mod.f90 +++ b/mlprec/mld_c_inner_mod.f90 @@ -109,9 +109,10 @@ module mld_c_inner_mod end interface mld_coarse_bld interface mld_aggrmap_bld - subroutine mld_caggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) + subroutine mld_caggrmap_bld(aggr_type,iorder,theta,a,desc_a,ilaggr,nlaggr,info) use psb_base_mod, only : psb_cspmat_type, psb_desc_type, psb_spk_, psb_ipk_ implicit none + integer(psb_ipk_), intent(in) :: iorder integer(psb_ipk_), intent(in) :: aggr_type real(psb_spk_), intent(in) :: theta type(psb_cspmat_type), intent(in) :: a @@ -123,9 +124,10 @@ module mld_c_inner_mod interface mld_dec_map_bld - subroutine mld_c_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) + subroutine mld_c_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) use psb_base_mod, only : psb_cspmat_type, psb_desc_type, psb_spk_, psb_ipk_ implicit none + integer(psb_ipk_), intent(in) :: iorder type(psb_cspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a real(psb_spk_), intent(in) :: theta diff --git a/mlprec/mld_c_onelev_mod.f90 b/mlprec/mld_c_onelev_mod.f90 index ddc0266a..e0115610 100644 --- a/mlprec/mld_c_onelev_mod.f90 +++ b/mlprec/mld_c_onelev_mod.f90 @@ -379,6 +379,7 @@ contains lv%parms%sweeps_post = 1 lv%parms%ml_type = mld_mult_ml_ lv%parms%aggr_alg = mld_dec_aggr_ + lv%parms%aggr_ord = mld_aggr_ord_nat_ lv%parms%aggr_kind = mld_smooth_prol_ lv%parms%coarse_mat = mld_distr_mat_ lv%parms%smoother_pos = mld_twoside_smooth_ diff --git a/mlprec/mld_d_base_solver_mod.f90 b/mlprec/mld_d_base_solver_mod.f90 index 6971fed1..89f6cd3c 100644 --- a/mlprec/mld_d_base_solver_mod.f90 +++ b/mlprec/mld_d_base_solver_mod.f90 @@ -360,6 +360,7 @@ contains integer(psb_long_int_k_) :: val integer(psb_ipk_) :: i val = 0 + return end function d_base_solver_sizeof diff --git a/mlprec/mld_d_inner_mod.f90 b/mlprec/mld_d_inner_mod.f90 index 3c6b8bea..84bf1fc5 100644 --- a/mlprec/mld_d_inner_mod.f90 +++ b/mlprec/mld_d_inner_mod.f90 @@ -109,9 +109,10 @@ module mld_d_inner_mod end interface mld_coarse_bld interface mld_aggrmap_bld - subroutine mld_daggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) + subroutine mld_daggrmap_bld(aggr_type,iorder,theta,a,desc_a,ilaggr,nlaggr,info) use psb_base_mod, only : psb_dspmat_type, psb_desc_type, psb_dpk_, psb_ipk_ implicit none + integer(psb_ipk_), intent(in) :: iorder integer(psb_ipk_), intent(in) :: aggr_type real(psb_dpk_), intent(in) :: theta type(psb_dspmat_type), intent(in) :: a @@ -123,9 +124,10 @@ module mld_d_inner_mod interface mld_dec_map_bld - subroutine mld_d_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) + subroutine mld_d_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) use psb_base_mod, only : psb_dspmat_type, psb_desc_type, psb_dpk_, psb_ipk_ implicit none + integer(psb_ipk_), intent(in) :: iorder type(psb_dspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a real(psb_dpk_), intent(in) :: theta diff --git a/mlprec/mld_d_onelev_mod.f90 b/mlprec/mld_d_onelev_mod.f90 index 3401115b..ee3b1b7f 100644 --- a/mlprec/mld_d_onelev_mod.f90 +++ b/mlprec/mld_d_onelev_mod.f90 @@ -338,6 +338,7 @@ contains class(mld_d_onelev_type), intent(in) :: lv integer(psb_long_int_k_) :: val integer(psb_ipk_) :: i + val = 0 val = val + lv%desc_ac%sizeof() val = val + lv%ac%sizeof() @@ -378,6 +379,7 @@ contains lv%parms%sweeps_post = 1 lv%parms%ml_type = mld_mult_ml_ lv%parms%aggr_alg = mld_dec_aggr_ + lv%parms%aggr_ord = mld_aggr_ord_nat_ lv%parms%aggr_kind = mld_smooth_prol_ lv%parms%coarse_mat = mld_distr_mat_ lv%parms%smoother_pos = mld_twoside_smooth_ @@ -386,7 +388,7 @@ contains lv%parms%aggr_filter = mld_no_filter_mat_ lv%parms%aggr_omega_val = dzero lv%parms%aggr_thresh = dzero - + if (allocated(lv%sm)) call lv%sm%default() return @@ -402,8 +404,8 @@ contains ! Arguments class(mld_d_onelev_type), target, intent(inout) :: lv class(mld_d_onelev_type), intent(inout) :: lvout - integer(psb_ipk_), intent(out) :: info - + integer(psb_ipk_), intent(out) :: info + info = psb_success_ if (allocated(lv%sm)) then call lv%sm%clone(lvout%sm,info) @@ -430,7 +432,7 @@ contains implicit none type(mld_d_onelev_type), intent(inout) :: a, b integer(psb_ipk_), intent(out) :: info - + call b%free(info) b%parms = a%parms call move_alloc(a%sm,b%sm) diff --git a/mlprec/mld_d_prec_type.f90 b/mlprec/mld_d_prec_type.f90 index 765f6999..134baa15 100644 --- a/mlprec/mld_d_prec_type.f90 +++ b/mlprec/mld_d_prec_type.f90 @@ -262,7 +262,7 @@ contains integer(psb_ipk_), optional :: ilev class(mld_d_base_smoother_type), pointer :: val integer(psb_ipk_) :: ilev_ - + val => null() if (present(ilev)) then ilev_ = ilev @@ -327,7 +327,6 @@ contains class(mld_dprec_type), intent(in) :: prec integer(psb_long_int_k_) :: val integer(psb_ipk_) :: i - val = 0 val = val + psb_sizeof_int if (allocated(prec%precv)) then @@ -530,6 +529,7 @@ contains ! Local variables integer(psb_ipk_) :: me,err_act,i character(len=20) :: name + if(psb_get_errstatus().ne.0) return info=psb_success_ name = 'mld_dprecfree' @@ -799,7 +799,7 @@ contains type(mld_dprec_type), intent(inout), target :: b integer(psb_ipk_), intent(out) :: info integer(psb_ipk_) :: i - + if (allocated(b%precv)) then ! This might not be required if FINAL procedures are available. call mld_precfree(b,info) diff --git a/mlprec/mld_d_umf_solver.F90 b/mlprec/mld_d_umf_solver.F90 index 0f7d76da..e76afb51 100644 --- a/mlprec/mld_d_umf_solver.F90 +++ b/mlprec/mld_d_umf_solver.F90 @@ -133,6 +133,7 @@ contains integer :: ictxt,np,me,i, err_act character :: trans_ character(len=20) :: name='d_umf_solver_apply' + call psb_erractionsave(err_act) info = psb_success_ @@ -216,7 +217,6 @@ contains integer :: err_act character(len=20) :: name='d_umf_solver_apply_vect' - call psb_erractionsave(err_act) call psb_erractionsave(err_act) info = psb_success_ @@ -257,8 +257,6 @@ contains integer :: n_row,n_col, nrow_a, nztota integer :: ictxt,np,me,i, err_act, debug_unit, debug_level character(len=20) :: name='d_umf_solver_bld', ch_err - - call psb_erractionsave(err_act) info=psb_success_ call psb_erractionsave(err_act) diff --git a/mlprec/mld_s_inner_mod.f90 b/mlprec/mld_s_inner_mod.f90 index e79453bc..74cbcdfb 100644 --- a/mlprec/mld_s_inner_mod.f90 +++ b/mlprec/mld_s_inner_mod.f90 @@ -109,9 +109,10 @@ module mld_s_inner_mod end interface mld_coarse_bld interface mld_aggrmap_bld - subroutine mld_saggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) + subroutine mld_saggrmap_bld(aggr_type,iorder,theta,a,desc_a,ilaggr,nlaggr,info) use psb_base_mod, only : psb_sspmat_type, psb_desc_type, psb_spk_, psb_ipk_ implicit none + integer(psb_ipk_), intent(in) :: iorder integer(psb_ipk_), intent(in) :: aggr_type real(psb_spk_), intent(in) :: theta type(psb_sspmat_type), intent(in) :: a @@ -123,9 +124,10 @@ module mld_s_inner_mod interface mld_dec_map_bld - subroutine mld_s_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) + subroutine mld_s_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) use psb_base_mod, only : psb_sspmat_type, psb_desc_type, psb_spk_, psb_ipk_ implicit none + integer(psb_ipk_), intent(in) :: iorder type(psb_sspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a real(psb_spk_), intent(in) :: theta diff --git a/mlprec/mld_s_onelev_mod.f90 b/mlprec/mld_s_onelev_mod.f90 index f8e89935..7122f167 100644 --- a/mlprec/mld_s_onelev_mod.f90 +++ b/mlprec/mld_s_onelev_mod.f90 @@ -379,6 +379,7 @@ contains lv%parms%sweeps_post = 1 lv%parms%ml_type = mld_mult_ml_ lv%parms%aggr_alg = mld_dec_aggr_ + lv%parms%aggr_ord = mld_aggr_ord_nat_ lv%parms%aggr_kind = mld_smooth_prol_ lv%parms%coarse_mat = mld_distr_mat_ lv%parms%smoother_pos = mld_twoside_smooth_ diff --git a/mlprec/mld_z_inner_mod.f90 b/mlprec/mld_z_inner_mod.f90 index d14123ec..e9c3d360 100644 --- a/mlprec/mld_z_inner_mod.f90 +++ b/mlprec/mld_z_inner_mod.f90 @@ -109,9 +109,10 @@ module mld_z_inner_mod end interface mld_coarse_bld interface mld_aggrmap_bld - subroutine mld_zaggrmap_bld(aggr_type,theta,a,desc_a,ilaggr,nlaggr,info) + subroutine mld_zaggrmap_bld(aggr_type,iorder,theta,a,desc_a,ilaggr,nlaggr,info) use psb_base_mod, only : psb_zspmat_type, psb_desc_type, psb_dpk_, psb_ipk_ implicit none + integer(psb_ipk_), intent(in) :: iorder integer(psb_ipk_), intent(in) :: aggr_type real(psb_dpk_), intent(in) :: theta type(psb_zspmat_type), intent(in) :: a @@ -123,9 +124,10 @@ module mld_z_inner_mod interface mld_dec_map_bld - subroutine mld_z_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info) + subroutine mld_z_dec_map_bld(iorder,theta,a,desc_a,nlaggr,ilaggr,info) use psb_base_mod, only : psb_zspmat_type, psb_desc_type, psb_dpk_, psb_ipk_ implicit none + integer(psb_ipk_), intent(in) :: iorder type(psb_zspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a real(psb_dpk_), intent(in) :: theta diff --git a/mlprec/mld_z_onelev_mod.f90 b/mlprec/mld_z_onelev_mod.f90 index 4f60dccb..e94a7d5c 100644 --- a/mlprec/mld_z_onelev_mod.f90 +++ b/mlprec/mld_z_onelev_mod.f90 @@ -379,6 +379,7 @@ contains lv%parms%sweeps_post = 1 lv%parms%ml_type = mld_mult_ml_ lv%parms%aggr_alg = mld_dec_aggr_ + lv%parms%aggr_ord = mld_aggr_ord_nat_ lv%parms%aggr_kind = mld_smooth_prol_ lv%parms%coarse_mat = mld_distr_mat_ lv%parms%smoother_pos = mld_twoside_smooth_ diff --git a/tests/pdegen/ppde2d.f90 b/tests/pdegen/ppde2d.f90 index 907a29e8..c96d4eae 100644 --- a/tests/pdegen/ppde2d.f90 +++ b/tests/pdegen/ppde2d.f90 @@ -159,6 +159,7 @@ program ppde2d integer(psb_ipk_) :: nlev ! Number of levels in multilevel prec. character(len=16) :: aggrkind ! smoothed/raw aggregatin character(len=16) :: aggr_alg ! local or global aggregation + character(len=16) :: aggr_ord ! Ordering for aggregation character(len=16) :: mltype ! additive or multiplicative 2nd level prec character(len=16) :: smthpos ! side: pre, post, both smoothing integer(psb_ipk_) :: csize ! aggregation size at which to stop. @@ -241,6 +242,7 @@ program ppde2d call mld_precset(prec,'sub_iluthrs', prectype%thr1, info) call mld_precset(prec,'aggr_kind', prectype%aggrkind,info) call mld_precset(prec,'aggr_alg', prectype%aggr_alg,info) + call mld_precset(prec,'aggr_ord', prectype%aggr_ord,info) call mld_precset(prec,'ml_type', prectype%mltype, info) call mld_precset(prec,'smoother_pos', prectype%smthpos, info) if (prectype%athres >= dzero) & @@ -383,6 +385,7 @@ contains call read_data(prectype%nlev,psb_inp_unit) ! Number of levels in multilevel prec. call read_data(prectype%aggrkind,psb_inp_unit) ! smoothed/raw aggregatin call read_data(prectype%aggr_alg,psb_inp_unit) ! local or global aggregation + call read_data(prectype%aggr_ord,psb_inp_unit) ! aggregation ordering call read_data(prectype%mltype,psb_inp_unit) ! additive or multiplicative 2nd level prec call read_data(prectype%smthpos,psb_inp_unit) ! side: pre, post, both smoothing call read_data(prectype%cmat,psb_inp_unit) ! coarse mat @@ -422,6 +425,7 @@ contains call psb_bcast(ictxt,prectype%nlev) ! Number of levels in multilevel prec. call psb_bcast(ictxt,prectype%aggrkind) ! smoothed/raw aggregatin call psb_bcast(ictxt,prectype%aggr_alg) ! local or global aggregation + call psb_bcast(ictxt,prectype%aggr_ord) ! aggregation ordering call psb_bcast(ictxt,prectype%mltype) ! additive or multiplicative 2nd level prec call psb_bcast(ictxt,prectype%smthpos) ! side: pre, post, both smoothing call psb_bcast(ictxt,prectype%cmat) ! coarse mat diff --git a/tests/pdegen/ppde3d.f90 b/tests/pdegen/ppde3d.f90 index b8730ce2..47a28a2e 100644 --- a/tests/pdegen/ppde3d.f90 +++ b/tests/pdegen/ppde3d.f90 @@ -171,6 +171,7 @@ program ppde3d integer(psb_ipk_) :: nlev ! Number of levels in multilevel prec. character(len=16) :: aggrkind ! smoothed/raw aggregatin character(len=16) :: aggr_alg ! local or global aggregation + character(len=16) :: aggr_ord ! Ordering for aggregation character(len=16) :: mltype ! additive or multiplicative 2nd level prec character(len=16) :: smthpos ! side: pre, post, both smoothing integer(psb_ipk_) :: csize ! aggregation size at which to stop. @@ -253,6 +254,7 @@ program ppde3d call mld_precset(prec,'sub_iluthrs', prectype%thr1, info) call mld_precset(prec,'aggr_kind', prectype%aggrkind,info) call mld_precset(prec,'aggr_alg', prectype%aggr_alg,info) + call mld_precset(prec,'aggr_ord', prectype%aggr_ord,info) call mld_precset(prec,'ml_type', prectype%mltype, info) call mld_precset(prec,'smoother_pos', prectype%smthpos, info) if (prectype%athres >= dzero) & @@ -396,6 +398,7 @@ contains call read_data(prectype%nlev,psb_inp_unit) ! Number of levels in multilevel prec. call read_data(prectype%aggrkind,psb_inp_unit) ! smoothed/raw aggregatin call read_data(prectype%aggr_alg,psb_inp_unit) ! local or global aggregation + call read_data(prectype%aggr_ord,psb_inp_unit) ! aggregation ordering call read_data(prectype%mltype,psb_inp_unit) ! additive or multiplicative 2nd level prec call read_data(prectype%smthpos,psb_inp_unit) ! side: pre, post, both smoothing call read_data(prectype%cmat,psb_inp_unit) ! coarse mat @@ -435,6 +438,7 @@ contains call psb_bcast(ictxt,prectype%nlev) ! Number of levels in multilevel prec. call psb_bcast(ictxt,prectype%aggrkind) ! smoothed/raw aggregatin call psb_bcast(ictxt,prectype%aggr_alg) ! local or global aggregation + call psb_bcast(ictxt,prectype%aggr_ord) ! aggregation ordering call psb_bcast(ictxt,prectype%mltype) ! additive or multiplicative 2nd level prec call psb_bcast(ictxt,prectype%smthpos) ! side: pre, post, both smoothing call psb_bcast(ictxt,prectype%cmat) ! coarse mat @@ -482,4 +486,3 @@ contains end subroutine pr_usage end program ppde3d - diff --git a/tests/pdegen/runs/ppde.inp b/tests/pdegen/runs/ppde.inp index 7e9993c4..c77e56c6 100644 --- a/tests/pdegen/runs/ppde.inp +++ b/tests/pdegen/runs/ppde.inp @@ -3,15 +3,15 @@ CSR ! Storage format CSR COO JAD 0100 ! IDIM; domain size is idim**3 2 ! ISTOPC 0100 ! ITMAX -1 ! ITRACE +10 ! ITRACE 30 ! IRST (restart for RGMRES and BiCGSTABL) 1.d-6 ! EPS 3L-MUL-RAS-BJAC4-ILU ! Descriptive name for preconditioner (up to 40 chars) -ML ! Preconditioner NONE JACOBI BJAC AS ML +ML ! Preconditioner NONE JACOBI BJAC AS ML 1 ! Number of overlap layers for AS preconditioner at finest level HALO ! Restriction operator NONE HALO NONE ! Prolongation operator NONE SUM AVG -GS ! Subdomain solver DSCALE ILU MILU ILUT UMF SLU +GS ! Subdomain solver DSCALE ILU MILU ILUT UMF SLU 1 ! sweeps for GS 0 ! Level-set N for ILU(N), and P for ILUT 1.d-4 ! Threshold T for ILU(T,P) @@ -20,11 +20,12 @@ BJAC ! Smoother type JACOBI BJAC AS; ignored for non-ML 2 ! Number of levels in a multilevel preconditioner SMOOTHED ! Kind of aggregation: SMOOTHED, NONSMOOTHED, MINENERGY DEC ! Type of aggregation DEC SYMDEC GLB +DEGREE ! Ordering of aggregation NATURAL DEGREE MULT ! Type of multilevel correction: ADD MULT TWOSIDE ! Side of correction PRE POST TWOSIDE (ignored for ADD) REPL ! Coarse level: matrix distribution DIST REPL BJAC ! Coarse level: solver JACOBI BJAC UMF SLU SLUDIST MUMPS -MUMPS ! Coarse level: subsolver DSCALE ILU UMF SLU SLUDIST MUMPS +MUMPS ! Coarse level: subsolver DSCALE ILU UMF SLU SLUDIST MUMPS 1 ! Coarse level: Level-set N for ILU(N) 1.d-4 ! Coarse level: Threshold T for ILU(T,P) 4 ! Coarse level: Number of Jacobi sweeps diff --git a/tests/pdegen/spde2d.f90 b/tests/pdegen/spde2d.f90 index b6decae2..ccff4dd4 100644 --- a/tests/pdegen/spde2d.f90 +++ b/tests/pdegen/spde2d.f90 @@ -159,6 +159,7 @@ program spde2d integer(psb_ipk_) :: nlev ! Number of levels in multilevel prec. character(len=16) :: aggrkind ! smoothed/raw aggregatin character(len=16) :: aggr_alg ! local or global aggregation + character(len=16) :: aggr_ord ! Ordering for aggregation character(len=16) :: mltype ! additive or multiplicative 2nd level prec character(len=16) :: smthpos ! side: pre, post, both smoothing integer(psb_ipk_) :: csize ! aggregation size at which to stop. @@ -241,6 +242,7 @@ program spde2d call mld_precset(prec,'sub_iluthrs', prectype%thr1, info) call mld_precset(prec,'aggr_kind', prectype%aggrkind,info) call mld_precset(prec,'aggr_alg', prectype%aggr_alg,info) + call mld_precset(prec,'aggr_ord', prectype%aggr_ord,info) call mld_precset(prec,'ml_type', prectype%mltype, info) call mld_precset(prec,'smoother_pos', prectype%smthpos, info) if (prectype%athres >= dzero) & @@ -384,6 +386,7 @@ contains call read_data(prectype%nlev,psb_inp_unit) ! Number of levels in multilevel prec. call read_data(prectype%aggrkind,psb_inp_unit) ! smoothed/raw aggregatin call read_data(prectype%aggr_alg,psb_inp_unit) ! local or global aggregation + call read_data(prectype%aggr_ord,psb_inp_unit) ! aggregation ordering call read_data(prectype%mltype,psb_inp_unit) ! additive or multiplicative 2nd level prec call read_data(prectype%smthpos,psb_inp_unit) ! side: pre, post, both smoothing call read_data(prectype%cmat,psb_inp_unit) ! coarse mat @@ -423,6 +426,7 @@ contains call psb_bcast(ictxt,prectype%nlev) ! Number of levels in multilevel prec. call psb_bcast(ictxt,prectype%aggrkind) ! smoothed/raw aggregatin call psb_bcast(ictxt,prectype%aggr_alg) ! local or global aggregation + call psb_bcast(ictxt,prectype%aggr_ord) ! aggregation ordering call psb_bcast(ictxt,prectype%mltype) ! additive or multiplicative 2nd level prec call psb_bcast(ictxt,prectype%smthpos) ! side: pre, post, both smoothing call psb_bcast(ictxt,prectype%cmat) ! coarse mat diff --git a/tests/pdegen/spde3d.f90 b/tests/pdegen/spde3d.f90 index ce397f94..308cd03b 100644 --- a/tests/pdegen/spde3d.f90 +++ b/tests/pdegen/spde3d.f90 @@ -171,6 +171,7 @@ program spde3d integer(psb_ipk_) :: nlev ! Number of levels in multilevel prec. character(len=16) :: aggrkind ! smoothed/raw aggregatin character(len=16) :: aggr_alg ! local or global aggregation + character(len=16) :: aggr_ord ! Ordering for aggregation character(len=16) :: mltype ! additive or multiplicative 2nd level prec character(len=16) :: smthpos ! side: pre, post, both smoothing integer(psb_ipk_) :: csize ! aggregation size at which to stop. @@ -254,6 +255,7 @@ program spde3d call mld_precset(prec,'sub_iluthrs', prectype%thr1, info) call mld_precset(prec,'aggr_kind', prectype%aggrkind,info) call mld_precset(prec,'aggr_alg', prectype%aggr_alg,info) + call mld_precset(prec,'aggr_ord', prectype%aggr_ord,info) call mld_precset(prec,'ml_type', prectype%mltype, info) call mld_precset(prec,'smoother_pos', prectype%smthpos, info) if (prectype%athres >= dzero) & @@ -397,6 +399,7 @@ contains call read_data(prectype%nlev,psb_inp_unit) ! Number of levels in multilevel prec. call read_data(prectype%aggrkind,psb_inp_unit) ! smoothed/raw aggregatin call read_data(prectype%aggr_alg,psb_inp_unit) ! local or global aggregation + call read_data(prectype%aggr_ord,psb_inp_unit) ! aggregation ordering call read_data(prectype%mltype,psb_inp_unit) ! additive or multiplicative 2nd level prec call read_data(prectype%smthpos,psb_inp_unit) ! side: pre, post, both smoothing call read_data(prectype%cmat,psb_inp_unit) ! coarse mat @@ -436,6 +439,7 @@ contains call psb_bcast(ictxt,prectype%nlev) ! Number of levels in multilevel prec. call psb_bcast(ictxt,prectype%aggrkind) ! smoothed/raw aggregatin call psb_bcast(ictxt,prectype%aggr_alg) ! local or global aggregation + call psb_bcast(ictxt,prectype%aggr_ord) ! aggregation ordering call psb_bcast(ictxt,prectype%mltype) ! additive or multiplicative 2nd level prec call psb_bcast(ictxt,prectype%smthpos) ! side: pre, post, both smoothing call psb_bcast(ictxt,prectype%cmat) ! coarse mat From c592733a8ef53437de4a925b36bc10e7dc452ea9 Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Mon, 9 May 2016 16:04:33 +0000 Subject: [PATCH 2/2] mld2p4-2: docs/html/img100.png docs/html/img101.png docs/html/img102.png docs/html/img103.png docs/html/img104.png docs/html/img105.png docs/html/img92.png docs/html/img93.png docs/html/img95.png docs/html/img96.png docs/html/img97.png docs/html/img98.png docs/html/img99.png docs/html/index.html docs/html/node1.html docs/html/node10.html docs/html/node11.html docs/html/node12.html 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- Next: Next: Abstract -   Contents
-
+
-MLD2P4 +MLD2P4

-User's and Reference Guide -
A guide for the Multi-Level Domain Decomposition +User's and Reference Guide +
A guide for the Multi-Level Domain Decomposition Parallel Preconditioners Package -based on PSBLAS +based on PSBLAS


@@ -62,9 +61,9 @@ University of Rome ``Tor Vergata'', Italy


-Software version: 2.0 +Software version: 2.1
-Oct. 12, 2015 +Mar. 31, 2016
@@ -77,70 +76,70 @@ Oct. 12, 2015 -
    -
  • Abstract + diff --git a/docs/html/node1.html b/docs/html/node1.html index 76ffc87b..2bbddf2a 100644 --- a/docs/html/node1.html +++ b/docs/html/node1.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
    - Next: Next: Contents - Up: Up: userhtml - Previous: Previous: userhtml -   Contents
    -
    +

    @@ -87,30 +86,29 @@ the user interface of MLD2P4.

    - -

    +
    -     next - up - previous - contents
    - Next: Next: Contents - Up: Up: userhtml - Previous: Previous: userhtml -   Contents
    +   Contents diff --git a/docs/html/node10.html b/docs/html/node10.html index fc859cc1..e8ca4162 100644 --- a/docs/html/node10.html +++ b/docs/html/node10.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
    - Next: Next: Multi-level Domain Decomposition Background - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Bug reporting -   Contents
    -
    +

    diff --git a/docs/html/node11.html b/docs/html/node11.html index 17913cc1..2809e7ed 100644 --- a/docs/html/node11.html +++ b/docs/html/node11.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
    - Next: Next: Multi-level Schwarz Preconditioners - Up: Up: userhtml - Previous: Previous: Example and test programs -   Contents
    -
    +

    @@ -58,7 +57,7 @@ Multi-level Domain Decomposition Background

    -Domain Decomposition (DD) preconditioners, coupled with Krylov iterative +Domain Decomposition (DD) preconditioners, coupled with Krylov iterative solvers, are widely used in the parallel solution of large and sparse linear systems. These preconditioners are based on the divide and conquer technique: the matrix to be preconditioned is divided into submatrices, a ``local'' linear system @@ -71,13 +70,13 @@ solution of the original problem from the local solutions [6,7,22]. + HREF="node25.html#dd2_96">23].

    -Additive Schwarz preconditioners are DD preconditioners using overlapping +Additive Schwarz preconditioners are DD preconditioners using overlapping submatrices, i.e. with some common rows, to couple the local information related to the submatrices (see, e.g., [22]). + HREF="node25.html#dd2_96">23]). The main motivation for choosing Additive Schwarz preconditioners is their intrinsic parallelism. A drawback of these preconditioners is that the number of iterations of the preconditioned solvers @@ -90,15 +89,15 @@ in a coarse space, which globally couples the information related to the single submatrices.

    -Two-level Schwarz preconditioners are obtained +Two-level Schwarz preconditioners are obtained by combining basic (one-level) Schwarz preconditioners with a coarse-level correction. In this context, the one-level preconditioner is often called `smoother'. Different two-level preconditioners are obtained by varying the choice of the smoother and of the coarse-level correction, and the way they are combined [22]. The same reasoning can be applied starting + HREF="node25.html#dd2_96">23]. The same reasoning can be applied starting from the coarse-level system, i.e. a coarse-space correction can be built -from this system, thus obtaining multi-level preconditioners. +from this system, thus obtaining multi-level preconditioners.

    It is worth noting that optimal preconditioners do not necessarily correspond @@ -120,17 +119,17 @@ are considered. The algebraic approach builds coarse-space corrections using onl information. It performs a fully automatic coarsening and enforces the interplay between the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine interpolation [24]. + HREF="node25.html#StubenGMD69_99">25].

    MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices -starting from the original matrix. The algebraic approach is based on the smoothed -aggregation algorithm [smoothed +aggregation algorithm [1,26]. A decoupled version + HREF="node25.html#VANEK_MANDEL_BREZINA">27]. A decoupled version of this algorithm is implemented, where the smoothed aggregation is applied locally to each submatrix [25]. In the next two subsections we provide + HREF="node25.html#TUMINARO_TONG">26]. In the next two subsections we provide a brief description of the multi-level Schwarz preconditioners and of the smoothed aggregation technique as implemented in MLD2P4. For further details the reader is referred to [3,4,8,22]. + HREF="node25.html#dd2_96">23].


    Subsections -
      -
    • Multi-level Schwarz Preconditioners + - -
      +
      - next - up - previous - contents
      - Next: Next: Multi-level Schwarz Preconditioners - Up: Up: userhtml - Previous: Previous: Example and test programs -   Contents
      +   Contents diff --git a/docs/html/node12.html b/docs/html/node12.html index 2e128b41..d7166530 100644 --- a/docs/html/node12.html +++ b/docs/html/node12.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
      - Next: Next: Smoothed Aggregation - Up: Up: Multi-level Domain Decomposition Background - Previous: Previous: Multi-level Domain Decomposition Background -   Contents

      @@ -295,7 +295,7 @@ ILU($p,t$) [21, Chapter 10]. + HREF="node25.html#Saad_book">22, Chapter 10].

      A variant of the classical AS preconditioner that outperforms it @@ -303,7 +303,7 @@ in terms of convergence rate and of computation and communication time on parallel distributed-memory computers is the so-called Restricted AS (RAS) preconditioner [5,14]. It + HREF="node25.html#EFSTATHIOU">15]. It is obtained by zeroing the components of $W$ increases [7,22]. To reduce the dependency + HREF="node25.html#dd2_96">23]. To reduce the dependency of the number of iterations on the degree of parallelism we may introduce a global coupling among the overlapping partitions by defining a coarse-space approximation multi-level preconditioners, can significantly reduce the computational cost of preconditioning with respect to the two-level case (see [22, Chapter 3]). + HREF="node25.html#dd2_96">23, Chapter 3]). Additive and hybrid multilevel preconditioners are obtained as direct extensions of the two-level counterparts. For a detailed descrition of them, the reader is referred to [22, Chapter 3]. + HREF="node25.html#dd2_96">23, Chapter 3]. The algorithm for the application of a multi-level hybrid post-smoothed preconditioner $R_l$. -

      +
      @@ -726,7 +726,7 @@ $w = y_1$; \begin{tabbing} \quad \=\quad... ...= y_l+r_l$\\ -\textbf{endfor} [1mm] +\textbf{endfor} \\ [1mm] $w = y_1$; \end{tabbing}} \end{minipage}}"> @@ -738,26 +738,26 @@ $w = y_1$;

      - next - up - previous - contents
      - Next: Next: Smoothed Aggregation - Up: Up: Multi-level Domain Decomposition Background - Previous: Previous: Multi-level Domain Decomposition Background -   Contents diff --git a/docs/html/node13.html b/docs/html/node13.html index 856d6b39..08f9f8e4 100644 --- a/docs/html/node13.html +++ b/docs/html/node13.html @@ -25,26 +25,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
      - Next: Next: Getting Started - Up: Up: Multi-level Domain Decomposition Background - Previous: Previous: Multi-level Schwarz Preconditioners -   Contents

      @@ -66,7 +66,7 @@ the coarse-level matrix $A_C$, MLD2P4 uses the smoothed aggregation algorithm described in [1,26]. + HREF="node25.html#VANEK_MANDEL_BREZINA">27]. The basic idea of this algorithm is to build a coarse set of vertices 4]. According to [26], a modification of + HREF="node25.html#VANEK_MANDEL_BREZINA">27], a modification of this algorithm has been actually considered, in which each aggregate 3,4,25]. + HREF="node25.html#TUMINARO_TONG">26].

      The prolongator 1,24]. + HREF="node25.html#StubenGMD69_99">25]. A simple choice for

      - next - up - previous - contents
      - Next: Next: Getting Started - Up: Up: Multi-level Domain Decomposition Background - Previous: Previous: Multi-level Schwarz Preconditioners -   Contents diff --git a/docs/html/node14.html b/docs/html/node14.html index 3b579598..cc900beb 100644 --- a/docs/html/node14.html +++ b/docs/html/node14.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
      - Next: Next: Examples - Up: Up: userhtml - Previous: Previous: Smoothed Aggregation -   Contents

      @@ -59,7 +59,7 @@ Getting Started

      We describe the basics for building and applying MLD2P4 one-level and multi-level Schwarz preconditioners with the Krylov solvers included in PSBLAS [15]. + HREF="node25.html#PSBLASGUIDE">16]. The following steps are required:

        @@ -131,7 +131,7 @@ for the coarsest-level solvers available in MLD2P4).


        -
        +
      Figure 1: Application of the multi-level hybrid post-smoothed preconditioner.
      Table 1: Preconditioner types, corresponding strings and default choices. @@ -197,32 +197,32 @@ Preconditioner types, corresponding strings and default choices. Subsections
      - next - up - previous - contents
      - Next: Next: Examples - Up: Up: userhtml - Previous: Previous: Smoothed Aggregation -   Contents diff --git a/docs/html/node15.html b/docs/html/node15.html index 9ff0610b..f7a2ff60 100644 --- a/docs/html/node15.html +++ b/docs/html/node15.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
      - Next: Next: User Interface - Up: Up: Getting Started - Previous: Previous: Getting Started -   Contents
      -
      +

      @@ -76,7 +75,7 @@ in the directory examples/fileread of the MLD2P4 tree (see Section 3.5). For details on the use of the PSBLAS routines, see the PSBLAS User's Guide [15]. + HREF="node25.html#PSBLASGUIDE">16].

      The setup and application of the default multi-level @@ -87,7 +86,7 @@ the corresponding Fortran 95 codes are available in examples/fileread/ -

      +
      Figure 2: Setup and application of the default multi-level Schwarz preconditioner. @@ -164,6 +163,10 @@ preconditioner, which uses block Jacobi with ILU(0) on the local blocks as post-smoother, has a coarsest matrix replicated on the processors, and solves the coarsest-level system with the LU factorization from UMFPACK [9]. +Figure 4 shows how to set a three-level preconditioner similar to the one of 3, but the coarsest-level systems is solved with the multifrontal factorization from MUMPS [9]. +Note that MUMPS can be used on both replicated and distributed coarsest level matrices, +as a global and local solver respectively. The number of levels is specified by using mld_precinit; the other preconditioner parameters are set by calling mld_precset. Note that the type of multilevel framework (i.e. multiplicative among the levels @@ -171,7 +174,7 @@ with post-smoothing only) is not specified since it is the default set by mld_precinit.

      -Figure 4 shows how to +Figure 5 shows how to set a three-level additive Schwarz preconditioner, which uses RAS, with overlap 1 and ILU(0) on the blocks, as pre- and post-smoother, and applies five block-Jacobi sweeps, with @@ -180,11 +183,11 @@ solver. Again, mld_precset is used only to set non-default values of the parameters (see Tables 2-5). In both cases, the construction and the application of the preconditioner are carried out as for the default multi-level preconditioner. -The code fragments shown in in Figures 3-4 are +The code fragments shown in in Figures 3 4-5 are included in the example program file mld_dexample_ml.f90 too.

      -Finally, Figure 5 shows the setup of a one-level +Finally, Figure 6 shows the setup of a one-level additive Schwarz preconditioner, i.e. RAS with overlap 2. The corresponding example program is available in mld_dexample_ 1lev.f90. @@ -195,7 +198,7 @@ boundary conditions are also available in the directory examples/pdegen -

      +
      @@ -228,9 +231,43 @@ Setup of a hybrid three-level Schwarz preconditioner.

      -

      +
      Figure 3: Setup of a hybrid three-level Schwarz preconditioner.
      + +
      Figure 4: +Setup of a hybrid three-level Schwarz preconditioner.
      +
      +
      + +
      +
      +... ...
+! set a three-level hybrid Schwarz preconditioner, which uses
+! block Jacobi (with ILU(0) on the blocks) as post-smoother,
+! a coarsest matrix replicated on the processors, and the
+! multifrontal solver in MUMPS as coarse-level solver
+
+  call mld_precinit(P,'ML',info,nlev=3)
+  call mld_precset(P,mld_smoother_type_,'BJAC',info)
+  call mld_precset(P,mld_coarse_mat_,'REPL',info)
+  call mld_precset(P,mld_coarse_solve_,'MUMPS',info)
+
+... ...
+
      +
      +
      +
      +

      +

      +
      +
      + +

      + +

      + +
      Figure 5: Setup of an additive three-level Schwarz preconditioner.
      @@ -260,9 +297,9 @@ Setup of an additive three-level Schwarz preconditioner.

      -

      +
      -
      Figure 5: +Figure 6: Setup of a one-level Schwarz preconditioner.
      @@ -284,30 +321,29 @@ Setup of a one-level Schwarz preconditioner.

      - -

      +
      - next - up - previous - contents
      - Next: Next: User Interface - Up: Up: Getting Started - Previous: Previous: Getting Started -   Contents
      +   Contents diff --git a/docs/html/node16.html b/docs/html/node16.html index 668fa510..d749e818 100644 --- a/docs/html/node16.html +++ b/docs/html/node16.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
      - Next: Next: Subroutine mld_precinit - Up: Up: userhtml - Previous: Previous: Examples -   Contents
      -
      +

      @@ -73,28 +72,28 @@ i.e.
      • the sparse matrix data structure, containing the matrix to be - preconditioned, must be of type psb_xspmat_type - with x = s for real single precision, x = d - for real double precision, x = c for complex single precision, - x = z for complex double precision; + preconditioned, must be of type psb_xspmat_type + with x = s for real single precision, x = d + for real double precision, x = c for complex single precision, + x = z for complex double precision;
      • the preconditioner data structure must be of type - mld_xprec_type, with x = + mld_xprec_type, with x = s, d, c, z, according to the sparse matrix data structure;
        • -
      • the arrays containing the vectors the arrays containing the vectors $v$ and $v$ and $w$ involved in - the preconditioner application $w$ involved in + the preconditioner application $w=M^{-1}v$ must be of type - psb_xvect_type with x = + ALT="$w=M^{-1}v$"> must be of type + psb_xvect_type with x = s, d, c, z, in a manner completely analogous to the sparse matrix type;
        • @@ -112,45 +111,44 @@ A description of each routine is given in the remainder of this section. Subsections -
          -
        • Subroutine mld_precinit + - -
          +
          - next - up - previous - contents
          - Next: Next: Subroutine mld_precinit - Up: Up: userhtml - Previous: Previous: Examples -   Contents
          +   Contents diff --git a/docs/html/node17.html b/docs/html/node17.html index 2cb07691..d45e31c2 100644 --- a/docs/html/node17.html +++ b/docs/html/node17.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Subroutine mld_precset - Up: Up: User Interface - Previous: Previous: User Interface -   Contents
          -
          +

          @@ -69,15 +68,15 @@ This routine allocates and initializes the preconditioner data structure, according to the preconditioner type chosen by the user.

          -Arguments +Arguments

          - + - @@ -110,30 +109,29 @@ according to the preconditioner type chosen by the user.

          - -

          +
          - next - up - previous - contents
          - Next: Next: Subroutine mld_precset - Up: Up: User Interface - Previous: Previous: User Interface -   Contents
          +   Contents diff --git a/docs/html/node18.html b/docs/html/node18.html index 24f46470..90842249 100644 --- a/docs/html/node18.html +++ b/docs/html/node18.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Subroutine mld_precbld - Up: Up: User Interface - Previous: Previous: Subroutine mld_precinit -   Contents
          -
          +

          @@ -89,25 +88,25 @@ the new smoother/solver variable to the setup routine as follows:
          call p%set(solver,info [,ilev]) -In this way, the variable will act as a mold to which the +In this way, the variable will act as a mold to which the preconditioner will conform, even though the MLD2P4 library is not modified, and thus has no direct knowledge about the new type.

          -Arguments +Arguments

          ptype(mld_xprec_type), intent(inout).type(mld_xprec_type), intent(inout).
           The preconditioner data structure. Note that x +The preconditioner data structure. Note that x must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
          - + - - + - @@ -180,7 +179,7 @@ object is specified its defaults are also set, overriding in both cases any previous settings even if explicitly specified. Therefore if the user sets a new smoother, and wishes to use a solver different from the default one, the call to set the solver must come -after the call to set the smoother. +after the call to set the smoother.

          The combination of a Jacobi smoother with a Diagonal Scaling local solver is equivalent to the strategy called Point Jacobi in the @@ -203,7 +202,7 @@ according to their needs.


          -
          +
          ptype(mld_xprec_type), intent(inout).type(mld_xprec_type), intent(inout).
           The preconditioner data structure. Note that x must +The preconditioner data structure. Note that x must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
          whatinteger, intent(in) or character(len=*).integer, intent(in) or character(len=*).
            The parameter to be set. It can be specified by @@ -116,8 +115,8 @@ modified, and thus has no direct knowledge about the new type. Tables 2-5.
          val integer or character(len=*) or - real(psb_spk_) or real(psb_dpk_), +integer or character(len=*) or + real(psb_spk_) or real(psb_dpk_), intent(in).
           

          - -

          +
          - next - up - previous - contents
          - Next: Next: Subroutine mld_precbld - Up: Up: User Interface - Previous: Previous: Subroutine mld_precinit -   Contents
          +   Contents diff --git a/docs/html/node19.html b/docs/html/node19.html index e5cdd86a..e87714b9 100644 --- a/docs/html/node19.html +++ b/docs/html/node19.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Subroutine mld_precaply - Up: Up: User Interface - Previous: Previous: Subroutine mld_precset -   Contents
          -
          +

          @@ -68,20 +67,20 @@ This routine builds the preconditioner according to the requirements made by the user through the routines mld_precinit and mld_precset.

          -Arguments +Arguments

          Table 2: Parameters defining the type of multi-level preconditioner. @@ -247,7 +246,7 @@ Parameters defining the type of multi-level preconditioner.


          -
          +
          - + ALT="$\ge 0$"> @@ -311,30 +310,30 @@ Parameters defining the one-level preconditioner used as smoother. - + ALT="$\ge 0$"> - + ALT="$p$"> of the incomplete LU factorizations. - - + + ALT="$\ge 0$"> - + ALT="$p,t$">) factorization. @@ -347,7 +346,7 @@ Parameters defining the one-level preconditioner used as smoother. @@ -363,7 +362,7 @@ Parameters defining the one-level preconditioner used as smoother.


          -
          +
          Table 3: Parameters defining the one-level preconditioner used as smoother. @@ -263,10 +262,10 @@ Parameters defining the one-level preconditioner used as smoother.
          mld_sub_ovr_
          SUB_OVR          		 integerany int. num. any int. num. $\ge 0$ 1 Number of overlap layers.
          mld_sub_fillin_
          SUB_FILLIN          		 integerAny int. num. Any int. num. $\ge 0$ 0Fill-in level Fill-in level $p$ of the incomplete LU factorizations.
          mld_sub_iluthrs_
          SUB_ILUTHRS          		real(kind_parameter)Any real num. real(kind_parameter)Any real num. $\ge 0$ 0Drop tolerance Drop tolerance $t$ in the ILU($t$ in the ILU($p,t$) factorization.
          mld_sub_ren_
          SUB_REN          		 character(len=*)
          mld_solver_sweeps_
          SOLVER_SWEEPS          		 integer Any int. num. $\ge 1$ 1
          + + + + + + @@ -404,16 +413,16 @@ Parameters defining the aggregation algorithm. (i.e. using the tentative prolongator). - - + + ALT="$\in [0, 1]$"> + ALT="$\theta$"> in the aggregation algorithm. @@ -435,55 +444,55 @@ Parameters defining the aggregation algorithm. - - - + - + + ALT="$D^{-1}A$">.
          Table 4: Parameters defining the aggregation algorithm. @@ -396,6 +395,16 @@ Parameters defining the aggregation algorithm.
          Aggregation algorithm. Currently, only the decoupled aggregation is available.
          mld_aggr_ord_
          AGGR_ORD          		character(len=*)'NAT''DEGREE'Initial ordering of indices for aggregation + algorithm: natural ordering or sorted by + descending degree of the node in the + matrix graph. Since aggregation is + heuristics, results will be different.
          mld_aggr_kind_
          AGGR_KIND          		 character(len=*) 'SMOOTHED' 'NONSMOOTHED'
          mld_aggr_thresh_
          AGGR_THRESH          		real(kind_parameter)Any real num. 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)character(len=*) 'EIG_EST' 'USER_CHOICE' 'EIG_EST'How the damping parameter How the damping parameter $\omega$ in the + ALT="$\omega$"> in the smoothed aggregation should be computed: either via an estimate of the spectral radius of - $D^{-1}A$, or explicily + ALT="$D^{-1}A$">, or explicily specified by the user.
          mld_aggr_eig_
          AGGR_EIG          		 character(len=*) 'A_NORMI' 'A_NORMI'How to estimate the spectral radius of How to estimate the spectral radius of $D^{-1}A$. + ALT="$D^{-1}A$">. Currently only the infinity norm estimate is available.
          mld_aggr_omega_val_
          AGGR_OMEGA_VAL          		real(kind_parameter)real(kind_parameter) Any nonnegative real num. -$4/(3\rho(D^{-1}A))$Damping parameter $4/(3\rho(D^{-1}A))$Damping parameter $\omega$ in the smoothed aggregation algorithm. + ALT="$\omega$"> in the smoothed aggregation algorithm. It must be set by the user if USER_CHOICE was specified for mld_aggr_omega_alg_, otherwise it is computed by the library, using the - selected estimate of the spectral radius $\rho(D^{-1}A)$ of - $\rho(D^{-1}A)$ of + $D^{-1}A$.
          @@ -494,7 +503,7 @@ Parameters defining the aggregation algorithm.


          -
          +
          - + ALT="$> 0$"> - + ALT="$\ge 0$"> - + ALT="$p$"> of the incomplete LU factorizations. - - + + ALT="$\ge 0$"> - + ALT="$p,t$">) factorization. - + - + - +
          Table 5: Parameters defining the coarse-space correction at the coarsest @@ -535,63 +544,63 @@ level.
          See note Solver for the diagonal blocks of the coarse matrix, in case the block Jacobi solver - is chosen as coarsest-level solver: ILU($p$), MILU($p$), MILU($p$), - ILU($p$), + ILU($p,t$), LU from UMFPACK, + ALT="$p,t$">), LU from UMFPACK, LU from SuperLU, plus triangular solve.
          mld_coarse_sweeps_
          COARSE_SWEEPS          		 integerAny int. num. Any int. num. $> 0$ 4 Number of Block-Jacobi sweeps when 'BJAC' is used as coarsest-level solver.
          mld_coarse_fillin_
          COARSE_FILLIN          		 integerAny int. num. Any int. num. $\ge 0$ 0Fill-in level Fill-in level $p$ of the incomplete LU factorizations.
          mld_coarse_iluthrs_
          COARSE_ILUTHRS          		real(kind_parameter)Any real. num. real(kind_parameter)Any real. num. $\ge 0$ 0Drop tolerance Drop tolerance $t$ in the ILU($t$ in the ILU($p,t$) factorization.
          Note: defaults for - mld_coarse_subsolve_ are chosen as
          Note: defaults for + mld_coarse_subsolve_ are chosen as
          single precision version: 'SLU' if installed, 'ILU' otherwise
          single precision version: 'SLU' if installed, 'ILU' otherwise
          double precision version: 'UMF' if installed, - else 'SLU' if installed, 'ILU' otherwise
          double precision version: 'UMF' if installed, + else 'SLU' if installed, 'ILU' otherwise
          @@ -603,30 +612,29 @@ level.
          - + + HREF="node25.html#PSBLASGUIDE">16]. @@ -89,13 +88,13 @@ single/double precision version of MLD2P4 under use. + HREF="node25.html#PSBLASGUIDE">16]. - + - @@ -108,29 +107,29 @@ single/double precision version of MLD2P4 under use.

          -

          +
          - next - up - previous - contents
          - Next: Next: Subroutine mld_precaply - Up: Up: User Interface - Previous: Previous: Subroutine mld_precset -   Contents
          +   Contents diff --git a/docs/html/node2.html b/docs/html/node2.html index a8c690d4..f0a641b5 100644 --- a/docs/html/node2.html +++ b/docs/html/node2.html @@ -1,4 +1,4 @@ - + - + next - up - previous
          - Next: Next: General Overview - Up: Up: userhtml - Previous: Previous: Abstract
          -
          +

          @@ -53,64 +52,64 @@ Contents -
          atype(psb_xspmat_type), intent(in).type(psb_xspmat_type), intent(in).
            The sparse matrix structure containing the local part of the - matrix to be preconditioned. Note that x must be chosen according + matrix to be preconditioned. Note that x must be chosen according to the real/complex, single/double precision version of MLD2P4 under use. See the PSBLAS User's Guide for details [15].
          desc_a type(psb_desc_type), intent(in).
            The communication descriptor of a. See the PSBLAS User's Guide for details [15].
          ptype(mld_xprec_type), intent(inout).type(mld_xprec_type), intent(inout).
           The preconditioner data structure. Note that x must be chosen according +The preconditioner data structure. Note that x must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
          info
          - + - - + - - + - @@ -143,39 +142,39 @@ and hence it is completely transparent to the user. + ALT="$M^{-1})$">. - +
          ptype(mld_xprec_type), intent(inout).type(mld_xprec_type), intent(inout).
           The preconditioner data structure, containing the local part of The preconditioner data structure, containing the local part of $M$. - Note that x must be chosen according + ALT="$M$">. + Note that x must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
          xtype(kind_parameter), dimension(:), intent(in).type(kind_parameter), dimension(:), intent(in).
           The local part of the vector The local part of the vector $x$. Note that type and - kind_parameter must be chosen according + ALT="$x$">. Note that type and + kind_parameter must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
          ytype(kind_parameter), dimension(:), intent(out).type(kind_parameter), dimension(:), intent(out).
           The local part of the vector The local part of the vector $y$. Note that type and - kind_parameter must be chosen according + ALT="$y$">. Note that type and + kind_parameter must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
          desc_aIf trans = 'N','n' then -$op(M^{-1}) = M^{-1}$; + ALT="$op(M^{-1}) = M^{-1}$">; if trans = 'T','t' then -$op(M^{-1}) = M^{-T}$ - (transpose of $op(M^{-1}) = M^{-T}$ + (transpose of $M^{-1})$; if trans = 'C','c' then -$op(M^{-1}) = M^{-C}$ - (conjugate transpose of $op(M^{-1}) = M^{-C}$ + (conjugate transpose of $M^{-1})$.
          worktype(kind_parameter), dimension(:), optional, target.type(kind_parameter), dimension(:), optional, target.
            Workspace. Its size should be at least 4 * psb_cd_get_local_ cols(desc_a) (see the PSBLAS User's Guide). - Note that type and kind_parameter must be chosen according + Note that type and kind_parameter must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
          @@ -183,30 +182,29 @@ and hence it is completely transparent to the user.

          - -

          +
          - next - up - previous - contents
          - Next: Next: Subroutine mld_precfree - Up: Up: User Interface - Previous: Previous: Subroutine mld_precbld -   Contents
          +   Contents diff --git a/docs/html/node21.html b/docs/html/node21.html index 8be4d56f..4365a27a 100644 --- a/docs/html/node21.html +++ b/docs/html/node21.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Subroutine mld_precdescr - Up: Up: User Interface - Previous: Previous: Subroutine mld_precaply -   Contents
          -
          +

          @@ -67,15 +66,15 @@ Subroutine mld_precfree This routine deallocates the preconditioner data structure.

          -Arguments +Arguments

          - + - diff --git a/docs/html/node22.html b/docs/html/node22.html index fc57620a..ab990b35 100644 --- a/docs/html/node22.html +++ b/docs/html/node22.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Error Handling - Up: Up: User Interface - Previous: Previous: Subroutine mld_precfree -   Contents
          -
          +

          @@ -68,15 +67,15 @@ This routine prints a description of the preconditioner to the standard output o to a file. It must be called after mld_precbld has been called.

          -Arguments +Arguments

          ptype(mld_xprec_type), intent(inout).type(mld_xprec_type), intent(inout).
           The preconditioner data structure. Note that x must be chosen according +The preconditioner data structure. Note that x must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
          info
          - + - diff --git a/docs/html/node23.html b/docs/html/node23.html index 99d48fb1..8a0e1872 100644 --- a/docs/html/node23.html +++ b/docs/html/node23.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: License - Up: Up: userhtml - Previous: Previous: Subroutine mld_precdescr -   Contents
          -
          +

          @@ -69,7 +68,7 @@ will then take action, and whether an error message should be printed. These options may be set by using the PSBLAS error handling routines; for further details see the PSBLAS User's Guide [15]. + HREF="node25.html#PSBLASGUIDE">16].

          diff --git a/docs/html/node24.html b/docs/html/node24.html index 1c9ae721..47737ef7 100644 --- a/docs/html/node24.html +++ b/docs/html/node24.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Bibliography - Up: Up: userhtml - Previous: Previous: Error Handling -   Contents
          -
          +

          diff --git a/docs/html/node25.html b/docs/html/node25.html index 4faa5ab3..ebee82a2 100644 --- a/docs/html/node25.html +++ b/docs/html/node25.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
          - Next: Next: About this document ... - Up: Up: userhtml - Previous: Previous: License -   Contents

          @@ -102,35 +102,44 @@ T.A. Davis, Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal Method with a Column Pre-ordering Strategy, ACM Transactions on Mathematical Software, 30, 2004, 196-199. -(See also http://www.cise.ufl.edu/ davis/)

          10 +(See also http://www.cise.ufl.edu/ davis/) +

          +

          10 +
          +P.R. Amestoy, C. Ashcraft, O. Boiteau, A. Buttari, J. L'Excellent, C. Weisbecker +Improving multifrontal methods by means of block low-rank representations, +SIAM SISC, volume 37, number 3, pages A1452-A1474. +(See also http://mumps.enseeiht.fr) +

          +

          11
          J.W. Demmel, S.C. Eisenstat, J.R. Gilbert, X.S. Li and J.W.H. Liu, A supernodal approach to sparse partial pivoting, -SIAM Journal on Matrix Analysis and Applications, 20, 3, 1999, 720-755.

          11 +SIAM Journal on Matrix Analysis and Applications, 20, 3, 1999, 720-755.

          12
          J. J. Dongarra, J. Du Croz, I. S. Duff, S. Hammarling, A set of Level 3 Basic Linear Algebra Subprograms, -ACM Transactions on Mathematical Software, 16, 1990, 1-17.

          12 +ACM Transactions on Mathematical Software, 16, 1990, 1-17.

          13
          J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson, An extended set of FORTRAN Basic Linear Algebra Subprograms, -ACM Transactions on Mathematical Software, 14, 1988, 1-17.

          13 +ACM Transactions on Mathematical Software, 14, 1988, 1-17.

          14
          J. J. Dongarra and R. C. Whaley, A User's Guide to the BLACS v. 1.1, Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of -Tennessee, March 1995 (updated May 1997).

          14 +Tennessee, March 1995 (updated May 1997).

          15
          E. Efstathiou, J. G. Gander, Why Restricted Additive Schwarz Converges Faster than Additive Schwarz, -BIT Numerical Mathematics, 43, 2003, 945-959.

          15 +BIT Numerical Mathematics, 43, 2003, 945-959.

          16
          S. Filippone, A. Buttari, PSBLAS-3.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library, 2012, available from http://www.ce.uniroma2.it/psblas/.

          -

          16 +

          17
          Salvatore Filippone and Alfredo Buttari. Object-Oriented Techniques for Sparse Matrix Computations in Fortran @@ -138,49 +147,49 @@ Salvatore Filippone and Alfredo Buttari. ACM Trans. on Math Software, 38(4), 2012.

          -

          17 +

          18
          S. Filippone, M. Colajanni, PSBLAS: A Library for Parallel Linear Algebra Computation on Sparse Matrices, -ACM Transactions on Mathematical Software, 26, 4, 2000, 527-550.

          18 +ACM Transactions on Mathematical Software, 26, 4, 2000, 527-550.

          19
          W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, B. Nitzberg, W. Saphir, M. Snir, MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions, -MIT Press, 1998.

          19 +MIT Press, 1998.

          20
          C. L. Lawson, R. J. Hanson, D. Kincaid, F. T. Krogh, Basic Linear Algebra Subprograms for FORTRAN usage, -ACM Transactions on Mathematical Software, 5, 1979, 308-323.

          20 +ACM Transactions on Mathematical Software, 5, 1979, 308-323.

          21
          X. S. Li, J. W. Demmel, SuperLU_DIST: A Scalable Distributed-memory Sparse Direct Solver for Unsymmetric Linear Systems, -ACM Transactions on Mathematical Software, 29, 2, 2003, 110-140.

          21 +ACM Transactions on Mathematical Software, 29, 2, 2003, 110-140.

          22
          Y. Saad, Iterative methods for sparse linear systems, 2nd edition, SIAM, 2003

          -

          22 +

          23
          B. Smith, P. Bjorstad, W. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, -Cambridge University Press, 1996.

          23 +Cambridge University Press, 1996.

          24
          M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI: The Complete Reference. Volume 1 - The MPI Core, second edition, -MIT Press, 1998.

          24 +MIT Press, 1998.

          25
          K. Stüben, Algebraic Multigrid (AMG): an Introduction with Applications, in A. Schüller, U. Trottenberg, C. Oosterlee, editors, Multigrid, -Academic Press, 2000.

          25 +Academic Press, 2000.

          26
          R. S. Tuminaro, C. Tong, Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines, -in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.

          26 +in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.

          27
          P. Vanek, J. Mandel and M. Brezina, Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems, diff --git a/docs/html/node26.html b/docs/html/node26.html index 1ca5a142..4e8c276f 100644 --- a/docs/html/node26.html +++ b/docs/html/node26.html @@ -25,21 +25,21 @@ original version by: Nikos Drakos, CBLU, University of Leeds next - up - previous - contents
          - Up: Up: userhtml - Previous: Previous: Bibliography -   Contents

          @@ -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 2016-02-29 +The translation was initiated by Salvatore Filippone on 2016-05-09

          diff --git a/docs/html/node3.html b/docs/html/node3.html index 42070266..fd040ff8 100644 --- a/docs/html/node3.html +++ b/docs/html/node3.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Code Distribution - Up: Up: userhtml - Previous: Previous: Contents -   Contents
          -
          +

          @@ -59,18 +58,17 @@ General Overview

          The MULTI-LEVEL DOMAIN DECOMPOSITION PARALLEL PRECONDITIONERS PACKAGE BASED ON -PSBLAS (MLD2P4) provides multi-level Schwarz preconditioners [22], +PSBLAS (MLD2P4) provides multi-level Schwarz preconditioners [23], to be used in the iterative solutions of sparse linear systems:
          -

          +
          -

          ptype(mld_xprec_type), intent(in).type(mld_xprec_type), intent(in).
           The preconditioner data structure. Note that x must be chosen according +The preconditioner data structure. Note that x must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
          info
          - +
          \begin{displaymath} Ax=b, \end{displaymath} -(1)
          +(1)

          -where $A$ is a square, real or complex, sparse matrix with a symmetric + ALT="$A$"> is a square, real or complex, sparse matrix with a symmetric sparsity pattern. These preconditioners have the following general features:
            -
          • both additive and hybrid multilevel variants are implemented, +
          • both additive and hybrid multilevel variants are implemented, i.e. variants that are additive among the levels and inside each level, and variants that are multiplicative among the levels and additive inside each level; the basic Additive Schwarz (AS) preconditioners are obtained by considering only one level;
            • -
          • a purely algebraic approach is used to +
          • a purely algebraic approach is used to generate a sequence of coarse-level corrections to a basic AS preconditioner, without explicitly using any information on the geometry of the original problem (e.g. the -discretization of a PDE). The smoothed aggregation technique is applied +discretization of a PDE). The smoothed aggregation technique is applied as algebraic coarsening strategy [1,26]. + HREF="node25.html#VANEK_MANDEL_BREZINA">27].

          -Version 2.0 of the package is written in Fortran 2003, following an -object-oriented design through the exploitation of features +Version 2.0 of the package is written in Fortran 2003, following an +object-oriented design through the exploitation of features such as abstract data type creation, functional overloading and dynamic memory management. The parallel implementation is based on a Single Program Multiple Data (SPMD) paradigm for distributed-memory architectures. Single and @@ -116,10 +114,10 @@ interface.

          MLD2P4 has been designed to implement scalable and easy-to-use -multilevel preconditioners in the context of the PSBLAS - (Parallel Sparse BLAS) computational framework [17,16]. +multilevel preconditioners in the context of the PSBLAS + (Parallel Sparse BLAS) computational framework [18,17]. PSBLAS is a library originally developed to address the parallel implementation of iterative solvers for sparse linear system, by providing basic linear algebra operators and data management facilities for distributed sparse matrices; it @@ -132,10 +130,10 @@ portability, modularity ed extensibility in the development of the preconditione package. On the other hand, the implementation of MLD2P4 has led to some revisions and extentions of the PSBLAS kernels, leading to the PSBLAS 2.0 version [15]. The inter-process comunication required + HREF="node25.html#PSBLASGUIDE">16]. The inter-process comunication required by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where MPI [23] is explicitly called. Therefore, MLD2P4 can be run on any parallel + HREF="node25.html#MPI1">24] is explicitly called. Therefore, MLD2P4 can be run on any parallel machine where PSBLAS and MPI implementations are available.

          @@ -172,30 +170,29 @@ in Section 7. The copyright terms conc of MLD2P4 are reported in Appendix A.

          - -

          +
          - next - up - previous - contents
          - Next: Next: Code Distribution - Up: Up: userhtml - Previous: Previous: Contents -   Contents
          +   Contents diff --git a/docs/html/node4.html b/docs/html/node4.html index 0749c00a..09ac7047 100644 --- a/docs/html/node4.html +++ b/docs/html/node4.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Configuring and Building MLD2P4 - Up: Up: userhtml - Previous: Previous: General Overview -   Contents
          -
          +

          @@ -76,7 +75,7 @@ account when treating derived works. The library defines a version string with the constant

          -
          + +

          @@ -80,16 +79,16 @@ real and complex data, in both single and double precision. Subsections -

          +

          @@ -61,9 +60,9 @@ The following base libraries are needed:
          BLAS
          [11,12,19] Many vendors provide optimized versions + HREF="node25.html#blas3">12,13,20] Many vendors provide optimized versions of the Basic Linear Algebra Subprograms; if no vendor version is available for a given platform, the ATLAS software (http://math-atlas.sourceforge.net/) @@ -78,15 +77,15 @@ The following base libraries are needed:
          MPI
          [18,23] A version of MPI is available on most + HREF="node25.html#MPI2">19,24] A version of MPI is available on most high-performance computing systems;
          PSBLAS
          [15,17] Parallel Sparse BLAS is + HREF="node25.html#PSBLASGUIDE">16,18] Parallel Sparse BLAS is available from
          http://www.ce.uniroma2.it/psblas; version 3.3 (or later) is required. Indeed, all the prerequisites @@ -99,31 +98,7 @@ usually this means that they should all be built with the same compiler as MLD2P4.

          - -

          - - -next - -up - -previous - -contents -
          - Next: Optional third party libraries - Up: Configuring and Building MLD2P4 - Previous: Configuring and Building MLD2P4 -   Contents
          - +
          diff --git a/docs/html/node7.html b/docs/html/node7.html index cc199872..d5920ad6 100644 --- a/docs/html/node7.html +++ b/docs/html/node7.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Configuration options - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Prerequisites -   Contents
          -
          +

          @@ -74,7 +73,7 @@ for multilevel preconditioners may change to reflect their presence.

          SuperLU
          [10] + HREF="node25.html#SUPERLU">11] A sparse direct factorization package available from
          http://crd.lbl.gov/~xiaoye/SuperLU/; provides serial factorization and triangular system solution for single and double precision, @@ -83,15 +82,16 @@ for multilevel preconditioners may change to reflect their presence.
          SuperLU_Dist
          [20] + HREF="node25.html#SUPERLUDIST">21] A sparse direct factorization package available from the same site as SuperLU; provides parallel factorization and triangular system solution for double precision real and complex data. We have tested version 3.3 and 4.2.
          MUMPS
          -
          [] - MUMPS (“Multifrontal Massively Parallel Solver”) is a sparse, direct factorization +
          [10] + MUMPS (“MUltifrontal Massively Parallel Solver”) is a sparse, direct factorization package available from
          http://mumps.enseeiht.fr/. It implements a direct method based on a multifrontal approach which performs @@ -100,30 +100,29 @@ for multilevel preconditioners may change to reflect their presence.

          -
          -
          +
          - next - up - previous - contents
          - Next: Next: Configuration options - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Prerequisites -   Contents
          +   Contents diff --git a/docs/html/node8.html b/docs/html/node8.html index 110ae992..26ed2d49 100644 --- a/docs/html/node8.html +++ b/docs/html/node8.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Bug reporting - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Optional third party libraries -   Contents
          -
          +

          @@ -208,6 +207,10 @@ generated the file Make.inc which will then be used by all Makefiles in the directory tree; this file will be copied in the install directory under the name Make.inc.MLD2P4. +

          +In order to use the MUMPS solver based on multifrontal factorization, the user has to add MUMPS flags, include directories and libraries in the Make.inc file. +The necessary MUMPS libraries are -ldmumps, -lsmumps -lzmumps -lzmumps -mumps_common -lpord. The flag -DHAVE_MUMPS_ is mandatory too. Since MUMPS uses openmp and ScaLAPACK, LINKOPT=-fonemp must be added as well, along with the ScaLAPACK flags, include directories and library (which can be set using the configure script). +

          To build the library the user will now enter 

          @@ -216,8 +219,30 @@ make
 followed (optionally) by 
 
           make install
-
          
-
          
+
          + +           +next + +up + +previous + +contents +
          + Next: Bug reporting + Up: Configuring and Building MLD2P4 + Previous: Optional third party libraries +   Contents + diff --git a/docs/html/node9.html b/docs/html/node9.html index cca2b947..f348fff2 100644 --- a/docs/html/node9.html +++ b/docs/html/node9.html @@ -1,4 +1,4 @@ - + - + next - up - previous - contents
          - Next: Next: Example and test programs - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Configuration options -   Contents
          -
          +

          diff --git a/docs/html/userhtml.html b/docs/html/userhtml.html index 9c76bb1d..91af5ad7 100644 --- a/docs/html/userhtml.html +++ b/docs/html/userhtml.html @@ -1,4 +1,4 @@ - + - + next up previous - contents
          - Next: Next: Abstract -   Contents
          -
          +
          -MLD2P4 +MLD2P4

          -User's and Reference Guide           -
          A guide for the Multi-Level Domain Decomposition +User's and Reference Guide           +
          A guide for the Multi-Level Domain Decomposition Parallel Preconditioners Package -based on PSBLAS           +based on PSBLAS


          @@ -62,9 +61,9 @@ University of Rome ``Tor Vergata'', Italy


          -Software version: 2.0 +Software version: 2.1
          -Oct. 12, 2015 +Mar. 31, 2016
          @@ -77,70 +76,70 @@ Oct. 12, 2015 -
            -
          • Abstract + diff --git a/docs/mld2p4-2.1-guide.pdf b/docs/mld2p4-2.1-guide.pdf index df345bcb..6b363369 100644 --- a/docs/mld2p4-2.1-guide.pdf +++ b/docs/mld2p4-2.1-guide.pdf @@ -24,7 +24,7 @@ BT /F17 11.9552 Tf 218.644 -79.389 Td [(P)31(asqua)-375(D'Am)31(bra)]TJ/F37 11.9552 Tf -31.595 -13.947 Td [(ICAR-CNR,)-326(Naples,)-327(Italy)]TJ/F17 11.9552 Tf 20.434 -29.39 Td [(Daniela)-375(di)-375(Sera\014no)]TJ/F37 11.9552 Tf -62.784 -13.948 Td [(Second)-326(Univ)27(ersit)27(y)-326(of)-327(Na)1(ples,)-327(Italy)]TJ/F17 11.9552 Tf 60.715 -29.39 Td [(Salv)62(atore)-375(Filipp)-31(one)]TJ/F37 11.9552 Tf -93.327 -13.947 Td [(Univ)27(ersit)27(y)-326(of)-326(Rome)-327(\134T)82(or)-326(V)81(ergata",)-326(Italy)]TJ 0 g 0 G 0 g 0 G - 100.3 -78.924 Td [(Soft)27(w)28(are)-327(v)27(ersion)1(:)-436(2.0)]TJ 37.459 -13.948 Td [(Oct.)-435(12,)-326(2015)]TJ + 100.3 -78.924 Td [(Soft)27(w)28(are)-327(v)27(ersion)1(:)-436(2.1)]TJ 35.187 -13.948 Td [(Mar.)-435(31,)-326(2016)]TJ 0 g 0 G 0 g 0 G ET @@ -45,21 +45,21 @@ endstream endobj 118 0 obj << -/Length 3728 +/Length 3770 >> stream 0 g 0 G BT /F15 10.9091 Tf 503.021 740.002 Td [(i)]TJ 0 g 0 G -/F17 14.3462 Tf -409.421 -35.866 Td [(Abstract)]TJ/F41 10.9091 Tf 0 -24.352 Td [(MLD2P4)-514(\050Mul)66(ti-Level)-514(Domain)-515(Decomposition)-514(P)87(arallel)-514(Preconditioners)]TJ 0 -13.549 Td [(P)88(a)22(cka)22(ge)-370(based)-370(on)-370(PSBLAS)]TJ/F15 10.9091 Tf 149.304 0 Td [(\051)-326(is)-326(a)-326(pac)28(k)55(age)-326(of)-326(parallel)-326(al)1(ge)-1(b)1(raic)-326(m)27(ulti-lev)28(el)-326(precondi-)]TJ -149.304 -13.549 Td [(tioners.)-442(It)-328(implemen)28(ts)-327(v)55(arious)-327(v)28(ers)-1(i)1(ons)-328(of)-327(one-lev)28(e)-1(l)-327(additiv)28(e)-327(and)-328(of)-327(m)28(ulti-lev)28(el)-328(additiv)28(e)]TJ 0 -13.549 Td [(and)-339(h)28(ybrid)-339(Sc)28(h)28(w)27(ar)1(z)-339(algorithms.)-462(In)-339(the)-339(m)28(ulti-lev)28(el)-339(case,)-341(a)-338(purely)-339(algebraic)-339(approac)28(h)-339(is)]TJ 0 -13.55 Td 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[(in)-424(this)-423(framew)27(or)1(k.)-716(MLD2P4)-424(enab)1(le)-1(s)-423(the)-424(user)-424(to)-423(easily)-424(sp)-28(ecify)-423(di\013eren)27(t)-423(asp)-28(ects)-424(of)-424(a)]TJ 0 -13.549 Td [(generic)-485(algebraic)-485(m)28(ultilev)27(el)-485(Sc)28(h)28(w)28(arz)-485(preconditioner,)-523(th)28(us)-485(allo)27(wing)-485(to)-485(searc)28(h)-485(for)-485(the)]TJ 0 -13.549 Td [(\134b)-28(est")-333(preconditioner)-333(for)-334(the)-333(problem)-333(at)-334(h)1(and.)]TJ 16.937 -13.549 Td [(The)-307(pac)28(k)55(age)-307(emplo)28(ys)-307(ob)-55(ject-orien)27(ted)-307(design)-306(te)-1(c)28(hniques)-307(in)-307(F)84(ortran)-307(2003,)-312(with)-307(in)28(ter-)]TJ -16.937 -13.55 Td [(faces)-392(to)-392(add)1(itional)-392(third)-392(part)28(y)-392(lib)1(raries)-392(suc)28(h)-392(as)-392(UMFP)83(A)28(CK,)-392(S)1(up)-28(erLU,)-392(Sup)-28(erLU)]TJ ET q -1 0 0 1 481.345 490.295 cm +1 0 0 1 482.869 490.295 cm []0 d 0 J 0.398 w 0 0 m 3.273 0 l S Q BT -/F15 10.9091 Tf 484.618 490.095 Td [(Dist,)]TJ -391.018 -13.549 Td [(that)-383(can)-384(b)-27(e)-384(exploited)-383(in)-383(building)-383(m)28(ulti-lev)27(el)-383(preconditioners.)-594(The)-383(parallel)-384(implemen-)]TJ 0 -13.549 Td [(tation)-345(is)-345(based)-345(on)-344(a)-345(Single)-345(Program)-345(Multiple)-345(Data)-345(\050)1(SPMD\051)-345(paradigm)-345(for)-345(distributed-)]TJ 0 -13.549 Td [(memory)-406(arc)28(hitectures;)-441(the)-406(in)28(ter-pro)-28(cess)-406(data)-405(comm)28(unication)-406(is)-405(based)-406(on)-405(MPI)-406(and)-405(is)]TJ 0 -13.549 Td [(managed)-333(mainly)-334(throu)1(gh)-334(PSBLAS.)]TJ 16.937 -13.55 Td [(This)-353(guide)-354(pro)28(vides)-353(a)-354(brief)-353(description)-354(of)-353(the)-354(fu)1(nctionalities)-354(and)-353(the)-354(user)-353(in)28(terface)]TJ -16.937 -13.549 Td [(of)-333(MLD2P4.)]TJ +/F15 10.9091 Tf 486.142 490.095 Td [(Dist)]TJ -392.542 -13.549 Td [(and)-376(MUMPS,)-376(that)-376(c)-1(an)-376(b)-27(e)-377(exploited)-376(in)-376(building)-376(m)28(ulti-lev)27(el)-376(preconditioners.)-573(The)-376(par-)]TJ 0 -13.549 Td [(allel)-408(impl)1(e)-1(men)28(tation)-407(is)-408(based)-407(on)-408(a)-407(Single)-408(Program)-407(Multiple)-408(Data)-407(\050SPMD\051)-408(paradigm)]TJ 0 -13.549 Td [(for)-429(distribu)1(te)-1(d)1(-)-1(memory)-428(arc)27(h)1(itec)-1(tu)1(re)-1(s;)-476(the)-429(in)28(ter-pro)-28(cess)-428(data)-429(comm)28(unication)-429(is)-429(based)]TJ 0 -13.549 Td [(on)-333(MPI)-334(and)-333(is)-333(managed)-334(main)1(ly)-334(through)-333(PSBLAS.)]TJ 16.937 -13.55 Td [(This)-353(guide)-354(pro)28(vides)-353(a)-354(brief)-353(description)-354(of)-353(the)-354(fu)1(nctionalities)-354(and)-353(the)-354(user)-353(in)28(terface)]TJ -16.937 -13.549 Td [(of)-333(MLD2P4.)]TJ 0 g 0 G 0 g 0 G ET @@ -140,7 +140,7 @@ BT 0 g 0 G [-669(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1780(8)]TJ + [-1780(9)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG /F43 10.9091 Tf -16.364 -24.458 Td [(4)-925(Multi-lev)32(el)-384(Domain)-383(Decomp)-32(osition)-383(Bac)32(kground)]TJ @@ -306,7 +306,7 @@ BT 0 g 0 G /F17 14.3462 Tf -406.997 -35.866 Td [(1)-1125(General)-375(Ov)31(erview)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)]TJ/F41 10.9091 Tf 23.408 0 Td [(Mul)67(ti-Level)-473(Domain)-472(Decomposition)-472(P)87(arallel)-472(Preconditioners)-473(P)88(a)22(ck-)]TJ -23.408 -13.549 Td [(a)22(ge)-278(based)-277(on)-278(PSBLAS)-278(\050MLD2P)1(4)]TJ/F15 10.9091 Tf 174.54 0 Td [(\051)-238(pro)28(vides)]TJ/F18 10.9091 Tf 48.921 0 Td [(multi-level)-270(Schwarz)-270(pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 168.99 0 Td [([)]TJ 1 0 0 rg 1 0 0 RG - [(22)]TJ + [(23)]TJ 0 g 0 G [(],)]TJ -392.451 -13.549 Td [(to)-333(b)-28(e)-333(used)-334(in)-333(the)-333(iterativ)27(e)-333(solutions)-333(of)-333(s)-1(p)1(arse)-334(linear)-333(systems:)]TJ/F22 10.9091 Tf 186.98 -23.153 Td [(Ax)]TJ/F15 10.9091 Tf 17.446 0 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(b;)]TJ 0 g 0 G @@ -326,23 +326,23 @@ BT 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-284(26)]TJ + [-284(27)]TJ 0 g 0 G [(].)]TJ -114.289 -21.385 Td [(V)83(ersion)-379(2.0)-380(of)-379(the)-380(pac)28(k)56(age)-380(is)-379(written)-380(in)]TJ/F18 10.9091 Tf 194.214 0 Td [(F)77(ortr)51(an)-400(2003)]TJ/F15 10.9091 Tf 62.505 0 Td [(,)-391(follo)28(wing)-380(an)]TJ/F18 10.9091 Tf 69.517 0 Td [(obje)51(ct-oriente)51(d)]TJ -343.173 -13.55 Td [(design)]TJ/F15 10.9091 Tf 34.51 0 Td [(through)-378(the)-377(exploitation)-378(of)-378(features)-378(suc)28(h)-378(as)-377(abstract)-378(data)-378(t)28(yp)-28(e)-378(creation,)-389(fun)1(c)-1(-)]TJ -34.51 -13.549 Td [(tional)-347(o)27(v)28(erloading)-347(and)-347(dynamic)-348(memory)-347(managemen)27(t.)-486(The)-348(parallel)-347(implemen)28(tation)-348(is)]TJ 0 -13.549 Td [(based)-389(on)-389(a)-389(Single)-389(Program)-389(Multiple)-389(Data)-390(\050SPM)1(D\051)-390(p)1(aradigm)-390(for)-389(distribu)1(ted-m)-1(emory)]TJ 0 -13.549 Td [(arc)28(hitectures.)-654(Single)-403(and)-403(d)1(ouble)-403(precision)-403(implemen)27(tations)-403(of)-403(MLD2P)1(4)-403(are)-403(a)27(v)56(ailable)]TJ 0 -13.549 Td [(for)-333(b)-28(oth)-333(the)-334(real)-333(and)-333(the)-334(complex)-333(case,)-333(that)-334(can)-333(b)-28(e)-333(used)-333(through)-334(a)-333(single)-333(in)28(terface.)]TJ 16.937 -13.549 Td [(MLD2P4)-229(has)-230(b)-27(e)-1(en)-229(designed)-229(to)-230(implemen)28(t)-230(scalable)-229(and)-229(easy-to-use)-230(m)28(ultilev)28(el)-230(precon-)]TJ -16.937 -13.55 Td [(ditioners)-348(in)-348(the)-349(con)28(text)-348(of)-348(the)]TJ/F18 10.9091 Tf 147.432 0 Td [(PSBLAS)-372(\050Par)52(al)-52(l)1(el)-372(Sp)51(arse)-371(BLAS\051)-372(c)51(omputational)-371(fr)51(ame-)]TJ -147.432 -13.549 Td [(work)]TJ/F15 10.9091 Tf 28.375 0 Td [([)]TJ 1 0 0 rg 1 0 0 RG - [(17)]TJ + [(18)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-436(16)]TJ + [-436(17)]TJ 0 g 0 G [(].)-753(PSBLAS)-436(is)-437(a)-436(library)-436(originally)-436(dev)28(elop)-28(ed)-436(to)-436(address)-436(the)-437(parallel)-436(im-)]TJ -28.375 -13.549 Td [(plemen)28(tation)-489(of)-489(iterativ)28(e)-489(solv)28(ers)-489(for)-489(sparse)-489(linear)-489(system,)-527(b)27(y)-488(pro)27(vi)1(ding)-489(basic)-489(linear)]TJ 0 -13.549 Td [(algebra)-453(op)-28(erators)-452(and)-453(data)-453(managemen)28(t)-453(facilities)-453(for)-453(distributed)-453(sparse)-453(matrices;)-512(it)]TJ 0 -13.549 Td [(also)-278(includes)-279(parallel)-278(Krylo)28(v)-278(solv)27(ers,)-289(built)-278(on)-278(the)-279(top)-278(of)-278(the)-278(basic)-279(PSBLAS)-278(k)28(ernels.)-426(The)]TJ 0 -13.55 Td [(preconditioners)-268(a)28(v)56(ailable)-268(in)-267(MLD2P4)-268(can)-267(b)-28(e)-268(used)-267(with)-268(these)-268(Krylo)28(v)-267(solv)27(ers.)-422(The)-268(c)28(hoice)]TJ 0 -13.549 Td [(of)-362(PSBLAS)-361(has)-362(b)-28(een)-361(mainly)-362(motiv)56(ated)-362(b)28(y)-362(the)-362(need)-361(of)-362(ha)28(ving)-362(a)-361(p)-28(ortable)-362(and)-361(e\016cien)27(t)]TJ 0 -13.549 Td [(soft)28(w)28(are)-313(infrastructure)-312(implemen)28(ting)-312(\134de)-313(facto")-312(standard)-312(parallel)-312(sparse)-313(linear)-312(algebra)]TJ 0 -13.549 Td [(k)28(ernels,)-304(to)-297(pursue)-297(goals)-296(suc)27(h)-296(as)-297(p)-28(erformance,)-304(p)-28(or)1(tabilit)27(y)84(,)-304(mo)-28(dularit)28(y)-297(ed)-296(e)-1(xt)1(e)-1(nsib)1(ilit)27(y)-296(in)]TJ 0 -13.549 Td [(the)-272(dev)27(elopmen)28(t)-272(of)-273(the)-272(preconditioner)-272(pac)27(k)56(age.)-424(On)-273(the)-272(other)-272(hand,)-285(the)-272(implemen)27(tation)]TJ 0 -13.55 Td [(of)-288(MLD2P4)-289(has)-288(led)-289(to)-288(some)-289(r)1(e)-1(vi)1(s)-1(ion)1(s)-289(and)-288(exten)27(ti)1(ons)-289(of)-288(the)-289(PSBLAS)-288(k)28(ernels,)-298(leading)-288(to)]TJ 0 -13.549 Td [(the)-352(PSBLAS)-352(2.0)-352(v)28(ersion)-353([)]TJ 1 0 0 rg 1 0 0 RG - [1(15)]TJ + [1(16)]TJ 0 g 0 G [(].)-501(The)-352(in)27(ter-pr)1(o)-28(cess)-353(com)28(unication)-352(required)-352(b)28(y)-352(MLD2P4)-352(is)]TJ 0 -13.549 Td [(encapsulated)-353(in)27(to)-353(the)-354(PSBLAS)-353(routines,)-358(exce)-1(p)1(t)-354(few)-353(c)-1(ases)-353(where)-354(MPI)-353([)]TJ 1 0 0 rg 1 0 0 RG - [(23)]TJ + [(24)]TJ 0 g 0 G [(])-354(is)-353(explicitly)]TJ 0 -13.549 Td [(called.)-647(Therefore,)-417(MLD2P4)-401(can)-401(b)-27(e)-401(run)-401(on)-401(an)28(y)-401(par)1(alle)-1(l)-400(mac)27(h)1(ine)-401(where)-401(PSBLAS)-401(and)]TJ 0 -13.549 Td [(MPI)-333(implemen)27(tati)1(ons)-334(are)-333(a)28(v)55(ailable.)]TJ 16.937 -13.55 Td [(MLD2P4)-342(has)-341(a)-342(la)28(y)28(ered)-342(and)-342(mo)-27(dular)-342(soft)28(w)28(are)-342(arc)28(hitecture)-342(where)-342(th)1(ree)-342(main)-342(la)28(y)28(ers)]TJ -16.937 -13.549 Td [(can)-458(b)-28(e)-458(iden)28(ti\014ed.)-819(The)-458(lo)28(w)28(er)-458(la)27(y)28(er)-458(consists)-458(of)-458(the)-458(PSBLAS)-458(k)28(ernels,)-490(the)-458(middle)-458(one)]TJ 0 -13.549 Td [(implemen)28(ts)-458(the)-457(construction)-457(and)-458(application)-457(phases)-458(of)-457(the)-457(preconditioners,)-489(and)-457(the)]TJ 0 g 0 G @@ -894,15 +894,15 @@ BT 0 g 0 G /F15 10.9091 Tf 38.378 0 Td [([)]TJ 1 0 0 rg 1 0 0 RG - [(11)]TJ + [(12)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-315(12)]TJ + [-315(13)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-316(19)]TJ + [-316(20)]TJ 0 g 0 G [(])-315(Man)28(y)-316(v)28(endors)-315(pro)28(vide)-316(opt)1(im)-1(i)1(z)-1(ed)-315(v)28(ersions)-316(of)-315(the)-315(Basic)-316(Linear)-315(Alge-)]TJ -11.105 -13.549 Td [(bra)-229(Subprograms;)-264(if)-229(no)-229(v)28(e)-1(n)1(dor)-230(v)28(ersion)-229(is)-229(a)27(v)56(ailable)-229(for)-229(a)-230(giv)28(en)-229(platform,)-250(the)-229(A)83(TLAS)]TJ 0 -13.549 Td [(soft)28(w)28(are)-404(\050)]TJ/F44 10.9091 Tf 47.821 0 Td [(http://math-atlas.sourceforge.net/)]TJ/F15 10.9091 Tf 194.726 0 Td [(\051)-403(ma)28(y)-403(b)-28(e)-403(emplo)27(y)28(ed.)-653(The)-404(ref-)]TJ -242.547 -13.55 Td [(erence)-415(BLAS)-414(from)-415(Netlib)-414(\050)]TJ/F44 10.9091 Tf 132.392 0 Td [(http://www.netlib.org/blas)]TJ/F15 10.9091 Tf 148.908 0 Td [(\051)-415(ar)1(e)-415(mean)28(t)-415(to)-414(de\014ne)]TJ -281.3 -13.549 Td [(the)-332(stand)1(ard)-332(b)-28(eha)28(viour)-331(of)-332(the)-331(BLAS)-332(in)28(terface,)-332(so)-332(they)-331(are)-332(not)-331(optimized)-332(for)-331(an)27(y)]TJ 0 -13.549 Td [(particular)-396(plaftorm,)-412(and)-396(should)-397(onl)1(y)-397(b)-28(e)-396(used)-396(as)-397(a)-396(last)-396(resort.)-634(Note)-396(that)-396(BLAS)]TJ 0 -13.549 Td [(computations)-223(form)-222(a)-223(relativ)28(e)-1(l)1(y)-223(small)-223(part)-223(of)-223(the)-222(MLD2P4/PSBLAS)-223(computations;)]TJ 0 -13.549 Td [(they)-308(are)-308(ho)28(w)28(ev)28(er)-308(critical)-308(when)-308(using)-307(preconditioners)-308(based)-308(on)-308(the)-307(UMFP)83(A)28(CK)-308(or)]TJ 0 -13.55 Td [(Sup)-28(erLU)-333(third)-333(part)28(y)-334(libr)1(aries)-1(.)]TJ 0 g 0 G @@ -910,11 +910,11 @@ BT 0 g 0 G /F15 10.9091 Tf 30.697 0 Td [([)]TJ 1 0 0 rg 1 0 0 RG - [(18)]TJ + [(19)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-340(23)]TJ + [-340(24)]TJ 0 g 0 G [(])-340(A)-341(v)28(ersion)-340(of)-340(MPI)-340(is)-341(a)28(v)56(ailable)-341(on)-340(most)-340(high-p)-28(erformance)-340(computing)-340(sys-)]TJ -3.424 -13.549 Td [(tems;)]TJ 0 g 0 G @@ -922,11 +922,11 @@ BT 0 g 0 G /F15 10.9091 Tf 53.924 0 Td [([)]TJ 1 0 0 rg 1 0 0 RG - [(15)]TJ + [(16)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-333(17)]TJ + [-333(18)]TJ 0 g 0 G [(])-334(P)28(arallel)-333(Sparse)-333(BLAS)-334(is)-333(a)28(v)55(ailable)-333(from)]TJ/F44 10.9091 Tf -26.651 -13.549 Td [(http://www.ce.uniroma2.it/psblas)]TJ/F15 10.9091 Tf 183.27 0 Td [(;)-339(v)27(ersion)-337(3.3)-337(\050or)-338(later\051)-337(is)-338(required.)-456(Indeed,)]TJ -183.27 -13.549 Td [(all)-333(the)-334(prerequ)1(is)-1(i)1(te)-1(s)-333(listed)-333(so)-334(far)-333(are)-333(also)-334(prerequ)1(is)-1(i)1(te)-1(s)-333(of)-333(PSBLAS.)]TJ -27.273 -22.959 Td [(Please)-430(note)-431(that)-430(the)-430(four)-430(previous)-430(libraries)-431(m)28(ust)-430(ha)28(v)28(e)-431(F)84(ortran)-431(in)28(terfaces)-430(compatible)]TJ 0 -13.549 Td [(with)-300(MLD2P4;)-311(usual)1(ly)-300(this)-300(means)-300(that)-300(th)1(e)-1(y)-299(should)-300(all)-300(b)-27(e)-300(built)-300(with)-300(the)-299(same)-300(compiler)]TJ 0 -13.55 Td [(as)-333(MLD2P4.)]TJ/F17 11.9552 Tf 0 -29.846 Td [(3.2)-1125(Optional)-375(third)-375(part)31(y)-375(libraries)]TJ/F15 10.9091 Tf 0 -20.81 Td [(W)83(e)-426(pro)28(vide)-427(in)28(terfaces)-427(to)-426(the)-427(follo)28(wing)-426(third-part)28(y)-427(soft)28(w)28(are)-427(libraries;)-473(note)-426(that)-427(these)]TJ 0 -13.549 Td [(are)-370(optional,)-379(bu)1(t)-370(if)-370(y)28(ou)-370(enable)-370(them)-370(some)-370(defau)1(lts)-370(for)-370(m)28(ultilev)28(el)-370(preconditioners)-370(ma)28(y)]TJ 0 -13.549 Td [(c)28(hange)-334(to)-333(re\015ect)-333(their)-334(p)1(res)-1(ence.)]TJ 0 g 0 G @@ -943,9 +943,9 @@ ET endstream endobj -223 0 obj +224 0 obj << -/Length 5149 +/Length 5443 >> stream 0 g 0 G @@ -957,59 +957,67 @@ BT 0 g 0 G -379.724 -35.866 Td [(ization)-275(and)-274(triangular)-275(system)-275(solution)-274(for)-275(double)-275(p)1(rec)-1(ision)-274(real)-275(and)-275(complex)-274(data.)]TJ 0 -13.549 Td [(W)83(e)-333(ha)28(v)28(e)-334(tested)-333(v)28(ersions)-334(5.4.)]TJ 0 g 0 G -/F43 10.9091 Tf -27.273 -22.542 Td [(Sup)-32(erLU)]TJ +/F43 10.9091 Tf -27.273 -23.068 Td [(Sup)-32(erLU)]TJ 0 g 0 G /F15 10.9091 Tf 54.826 0 Td [([)]TJ 1 0 0 rg 1 0 0 RG - [(10)]TJ + [(11)]TJ 0 g 0 G - [(])-333(A)-334(sparse)-333(direct)-333(factorization)-334(p)1(ac)27(k)56(age)-334(a)28(v)56(ailable)-333(from)]TJ/F44 10.9091 Tf -27.553 -13.549 Td [(http://crd.lbl.gov/~xiaoye/SuperLU/)]TJ/F15 10.9091 Tf 200.452 0 Td [(;)-498(pro)27(vides)-443(serial)-443(factorization)-444(and)-443(tri-)]TJ -200.452 -13.55 Td [(angular)-389(system)-390(solution)-389(for)-389(single)-390(and)-389(double)-389(precision,)-403(real)-390(and)-389(complex)-389(data.)]TJ 0 -13.549 Td [(W)83(e)-333(ha)28(v)28(e)-334(tested)-333(v)28(ersion)-334(4.3)-333(and)-333(5.0.)]TJ + [(])-333(A)-334(sparse)-333(direct)-333(factorization)-334(p)1(ac)27(k)56(age)-334(a)28(v)56(ailable)-333(from)]TJ/F44 10.9091 Tf -27.553 -13.549 Td [(http://crd.lbl.gov/~xiaoye/SuperLU/)]TJ/F15 10.9091 Tf 200.452 0 Td [(;)-498(pro)27(vides)-443(serial)-443(factorization)-444(and)-443(tri-)]TJ -200.452 -13.549 Td 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[(fileread)]TJ/F15 10.9091 Tf 49.454 0 Td [(and)]TJ/F44 10.9091 Tf 21.212 0 Td [(pdegen)]TJ/F15 10.9091 Tf 38 0 Td [(sub)-28(directories.)-444(Their)-333(purp)-28(ose)-334(is)-333(as)-333(follo)28(ws:)]TJ +0 g 0 G +/F44 10.9091 Tf -169.272 -22.516 Td [(examples)]TJ +0 g 0 G +/F15 10.9091 Tf 51.272 0 Td [(con)28(tains)-245(a)-245(set)-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(te)-1(n)1(ded)-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 -/F44 10.9091 Tf -406.997 -35.866 Td [(tests)]TJ +/F44 10.9091 Tf -27.273 -22.516 Td [(tests)]TJ 0 g 0 G -/F15 10.9091 Tf 34.091 0 Td [(con)28(tains)-380(a)-380(set)-380(of)-380(more)-380(soph)1(istic)-1(at)1(e)-1(d)-379(examples)-380(that)-380(will)-380(allo)28(w)-380(the)-380(user,)-391(via)-380(the)]TJ -6.818 -13.549 Td [(input)-286(\014les)-287(in)-286(the)]TJ/F44 10.9091 Tf 80.438 0 Td [(runs)]TJ/F15 10.9091 Tf 26.034 0 Td [(sub)-28(directories,)-296(to)-286(exp)-28(erimen)28(t)-286(with)-287(the)-286(full)-286(range)-287(of)-286(precon-)]TJ -106.472 -13.549 Td [(ditioners)-333(implemen)27(t)1(e)-1(d)-333(in)-333(the)-333(library)83(.)]TJ -27.273 -22.516 Td [(The)]TJ/F44 10.9091 Tf 24.239 0 Td [(fileread)]TJ/F15 10.9091 Tf 51.269 0 Td [(directories)-500(con)28(tain)-500(sample)-499(programs)-500(that)-500(read)-499(sparse)-500(matrices)-500(from)]TJ -75.508 -13.549 Td [(\014les,)-295(according)-285(to)-285(the)-285(Matrix)-285(Mark)28(et)-285(or)-285(the)-285(Harw)27(ell-Bo)-27(e)-1(i)1(ng)-286(storage)-285(format;)-301(the)]TJ/F44 10.9091 Tf 378.088 0 Td [(pdegen)]TJ/F15 10.9091 Tf -378.088 -13.549 Td [(instead)-272(generate)-272(matrices)-272(in)-272(full)-272(parallel)-272(mo)-28(de)-272(f)1(rom)-272(the)-272(discretiz)-1(at)1(ion)-272(of)-272(a)-272(sample)-272(PDE.)]TJ +/F15 10.9091 Tf 34.091 0 Td [(con)28(tains)-380(a)-380(set)-380(of)-380(more)-380(soph)1(isticate)-1(d)-379(examples)-380(that)-380(will)-380(allo)28(w)-380(the)-380(user,)-391(via)-380(the)]TJ -6.818 -13.549 Td [(input)-286(\014les)-287(in)-286(the)]TJ/F44 10.9091 Tf 80.438 0 Td [(runs)]TJ/F15 10.9091 Tf 26.034 0 Td [(sub)-28(directories,)-296(to)-286(exp)-28(erimen)28(t)-286(with)-287(the)-286(full)-286(range)-287(of)-286(precon-)]TJ -106.472 -13.549 Td [(ditioners)-333(implemen)28(te)-1(d)-333(in)-333(the)-333(library)83(.)]TJ -27.273 -22.516 Td [(The)]TJ/F44 10.9091 Tf 24.239 0 Td [(fileread)]TJ/F15 10.9091 Tf 51.269 0 Td [(directories)-500(con)28(tain)-500(sample)-499(programs)-500(that)-500(read)-499(sparse)-500(matrices)-500(from)]TJ -75.508 -13.549 Td [(\014les,)-295(according)-285(to)-285(the)-285(Matrix)-285(Mark)28(et)-285(or)-285(the)-285(Harw)27(ell-Bo)-27(eing)-286(storage)-285(format;)-301(the)]TJ/F44 10.9091 Tf 378.088 0 Td [(pdegen)]TJ/F15 10.9091 Tf -378.088 -13.549 Td [(instead)-272(generate)-272(matrices)-272(in)-272(full)-272(parallel)-272(mo)-28(de)-272(f)1(rom)-272(the)-272(discretization)-272(of)-272(a)-272(sample)-272(PDE.)]TJ 0 g 0 G 0 g 0 G ET endstream endobj -254 0 obj +256 0 obj << /Length 8148 >> @@ -1096,15 +1105,15 @@ BT 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-334(22)]TJ + [-334(23)]TJ 0 g 0 G [(].)]TJ/F18 10.9091 Tf 16.936 -14.011 Td [(A)51(dditive)-468(Schwarz)]TJ/F15 10.9091 Tf 89.059 0 Td [(preconditioners)-453(are)-453(DD)-454(precondi)1(tioners)-454(using)-453(o)28(v)28(erlapping)-454(sub)1(-)]TJ -105.995 -13.55 Td [(matrices,)-403(i.e.)-389(with)-389(some)-389(common)-389(ro)27(ws,)-403(to)-389(couple)-389(the)-389(lo)-28(cal)-389(information)-389(related)-389(to)-389(the)]TJ 0 -13.549 Td [(submatrices)-362(\050see,)-369(e.g.,)-369([)]TJ 1 0 0 rg 1 0 0 RG - [(22)]TJ + [(23)]TJ 0 g 0 G [(]\051.)-530(The)-362(main)-362(motiv)56(ation)-362(for)-362(c)28(ho)-28(osing)-362(Additiv)28(e)-362(Sc)28(h)28(w)27(arz)-362(pre-)]TJ 0 -13.549 Td [(conditioners)-361(is)-361(their)-361(in)28(trinsic)-361(parallelism.)-528(A)-361(dra)28(wbac)28(k)-361(of)-362(th)1(e)-1(se)-361(preconditioners)-361(is)-361(that)]TJ 0 -13.549 Td [(the)-388(n)28(um)27(b)-27(er)-388(of)-389(iteration)1(s)-389(of)-388(the)-388(preconditioned)-388(solv)28(ers)-388(generally)-389(gr)1(o)27(ws)-388(with)-388(the)-388(n)28(um-)]TJ 0 -13.549 Td [(b)-28(er)-370(of)-370(submatrices.)-555(This)-370(ma)28(y)-370(b)-28(e)-370(a)-370(serious)-370(limitation)-370(on)-370(parallel)-370(computers,)-380(since)-370(the)]TJ 0 -13.55 Td [(n)28(um)28(b)-28(er)-403(of)-403(s)-1(u)1(bmatrice)-1(s)-403(usually)-403(matc)28(hes)-403(the)-404(n)28(um)28(b)-28(er)-403(of)-403(a)28(v)55(ailable)-403(pro)-28(cessors.)-654(Optimal)]TJ 0 -13.549 Td [(con)28(v)28(ergence)-262(rates,)-276(i.e.)-262(iteration)-262(n)28(um)28(b)-28(ers)-262(indep)-27(enden)27(t)-261(of)-262(the)-262(n)28(um)28(b)-28(er)-262(of)-261(submatrices,)-277(can)]TJ 0 -13.549 Td [(b)-28(e)-369(obtained)-369(b)27(y)-369(correcting)-369(the)-370(preconditioner)-369(through)-369(a)-370(suitable)-369(appro)28(ximation)-370(of)-369(the)]TJ 0 -13.549 Td [(original)-323(linear)-323(system)-323(in)-323(a)-323(coarse)-323(space,)-325(whic)28(h)-323(globally)-323(couples)-323(the)-323(inf)1(ormation)-323(related)]TJ 0 -13.549 Td [(to)-333(the)-334(single)-333(submatrices.)]TJ/F18 10.9091 Tf 16.936 -14.012 Td [(Two-level)-308(Schwarz)]TJ/F15 10.9091 Tf 91.53 0 Td [(preconditioners)-279(are)-280(obtained)-279(b)27(y)-279(com)28(bining)-280(basic)-279(\050one-le)-1(v)28(el\051)-279(Sc)27(h)1(-)]TJ -108.466 -13.549 Td [(w)28(arz)-362(preconditioners)-363(with)-362(a)-362(coarse-lev)28(el)-363(correction.)-531(In)-362(this)-362(con)28(text,)-370(the)-362(one-lev)28(el)-363(pre-)]TJ 0 -13.549 Td [(conditioner)-344(is)-345(often)-344(called)-344(`s)-1(mo)-27(other'.)-478(Di\013eren)28(t)-345(t)28(w)28(o-lev)28(el)-345(preconditioners)-344(are)-344(obtained)]TJ 0 -13.549 Td [(b)28(y)-371(v)56(arying)-371(the)-371(c)28(hoice)-371(of)-370(the)-371(smo)-28(other)-371(and)-370(of)-371(the)-371(coarse-lev)28(el)-371(correction,)-380(and)-371(th)1(e)-371(w)27(a)28(y)]TJ 0 -13.549 Td [(they)-374(are)-373(com)27(bined)-373([)]TJ 1 0 0 rg 1 0 0 RG - [(22)]TJ + [(23)]TJ 0 g 0 G [(].)-566(The)-373(same)-374(reasoning)-374(can)-373(b)-28(e)-374(applied)-373(s)-1(t)1(arting)-374(from)-374(the)-373(coarse-)]TJ 0 -13.55 Td [(lev)28(el)-281(system,)-291(i.e.)-281(a)-280(coarse-s)-1(p)1(ac)-1(e)-280(correction)-281(can)-280(b)-28(e)-281(built)-280(from)-281(this)-280(sys)-1(t)1(e)-1(m,)-291(th)28(us)-280(obtaining)]TJ/F18 10.9091 Tf 0 -13.549 Td [(multi-level)]TJ/F15 10.9091 Tf 53.83 0 Td [(preconditioners.)]TJ -36.894 -14.011 Td [(It)-443(is)-444(w)28(orth)-443(noting)-444(that)-443(optimal)-444(p)1(rec)-1(on)1(ditioners)-444(do)-443(not)-444(necessarily)-443(corresp)-28(ond)-443(to)]TJ -16.936 -13.549 Td [(minim)28(um)-480(exec)-1(u)1(tion)-481(times.)-885(Indeed,)-517(to)-480(obtain)-480(e\013ectiv)28(e)-481(m)28(ulti-lev)28(el)-480(preconditioners)-480(a)]TJ 0 -13.549 Td [(tradeo\013)-381(b)-28(et)28(w)28(ee)-1(n)-381(optimalit)28(y)-381(of)-381(con)28(v)27(ergence)-381(and)-381(the)-381(cost)-382(of)-381(building)-381(and)-381(applying)-381(the)]TJ 0 -13.55 Td [(coarse-space)-384(corrections)-384(m)28(ust)-384(b)-28(e)-383(ac)27(hiev)28(ed.)-596(Th)1(e)-384(c)27(hoice)-383(of)-384(the)-384(n)28(um)28(b)-28(er)-384(of)-383(lev)27(els,)-396(i.e.)-384(of)]TJ 0 -13.549 Td [(the)-379(coarse-space)-379(corr)1(e)-1(ctions,)-390(al)1(s)-1(o)-378(a\013ects)-379(the)-379(e\013ectiv)28(eness)-379(of)-378(the)-379(preconditioners.)-580(One)]TJ 0 -13.549 Td [(more)-392(goal)-391(is)-392(to)-392(get)-391(con)28(v)27(ergence)-391(rates)-392(as)-392(less)-392(sensitiv)28(e)-392(as)-391(p)-28(ossible)-392(to)-391(v)55(ariations)-391(in)-392(the)]TJ 0 -13.549 Td [(matrix)-333(co)-28(e\016cien)28(ts.)]TJ 16.936 -14.012 Td [(Tw)28(o)-303(main)-303(approac)28(hes)-303(can)-303(b)-28(e)-303(used)-303(to)-303(build)-303(coarse-space)-303(corrections.)-434(The)-303(geometric)]TJ -16.936 -13.549 Td [(approac)28(h)-412(applies)-413(coarsening)-412(strategies)-413(b)1(as)-1(ed)-412(on)-412(the)-412(kno)27(wledge)-412(of)-412(some)-413(ph)28(ysical)-412(grid)]TJ 0 -13.549 Td [(asso)-28(ciated)-279(to)-280(the)-279(matrix)-280(and)-279(requires)-280(the)-279(user)-280(to)-280(d)1(e)-1(\014)1(ne)-280(grid)-279(transfer)-280(op)-28(erators)-279(from)-280(the)]TJ 0 -13.549 Td [(\014ne)-393(to)-394(the)-394(coarse)-393(lev)28(e)-1(l)1(s)-394(and)-394(vice)-393(v)28(ersa.)-626(Th)1(is)-394(ma)28(y)-394(result)-393(di\016cult)-394(for)-393(complex)-394(geome-)]TJ 0 -13.549 Td [(tries;)-464(furthermore,)-442(suitable)-420(one-lev)28(e)-1(l)-420(preconditioners)-420(ma)28(y)-421(b)-28(e)-420(required)-420(to)-421(get)-420(e\016cien)28(t)]TJ 0 -13.549 Td [(in)28(terpla)28(y)-381(b)-28(et)28(w)27(een)-381(\014ne)-381(and)-381(coarse)-381(lev)27(els,)-393(e.g.)-381(when)-381(matrices)-381(with)-381(highly)-381(v)55(arying)-381(co)-28(ef-)]TJ 0 -13.55 Td [(\014cien)28(ts)-417(are)-417(consid)1(e)-1(r)1(e)-1(d)1(.)-695(The)-416(alge)-1(b)1(raic)-417(approac)28(h)-417(builds)-416(coarse-s)-1(p)1(ac)-1(e)-416(corrections)-417(using)]TJ 0 -13.549 Td [(only)-442(matrix)-442(information.)-770(It)-442(p)-28(erforms)-442(a)-442(fully)-442(automatic)-442(coarsening)-442(and)-442(enforces)-443(th)1(e)]TJ 0 g 0 G @@ -1113,7 +1122,7 @@ ET endstream endobj -273 0 obj +275 0 obj << /Length 14867 >> @@ -1127,7 +1136,7 @@ BT 0 g 0 G -401.542 -35.866 Td [(in)28(terpla)28(y)-352(b)-28(et)28(w)28(een)-352(the)-352(\014ne)-351(and)-352(coarse)-352(lev)28(els)-352(b)28(y)-351(s)-1(u)1(itably)-352(c)28(ho)-28(osing)-352(the)-351(coarse)-352(space)-352(and)]TJ 0 -13.549 Td [(the)-333(coarse-to-\014ne)-334(in)28(terp)-28(olation)-333([)]TJ 1 0 0 rg 1 0 0 RG - [(24)]TJ + [(25)]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 @@ -1135,11 +1144,11 @@ BT 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-402(26)]TJ + [-402(27)]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 + [(26)]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 @@ -1159,7 +1168,7 @@ BT 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-333(22)]TJ + [-333(23)]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 @@ -1179,7 +1188,7 @@ BT 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 + [(22)]TJ 0 g 0 G [(,)-334(Chapter)-333(10].)]TJ 0 g 0 G @@ -1188,7 +1197,7 @@ ET endstream endobj -294 0 obj +296 0 obj << /Length 13838 >> @@ -1203,7 +1212,7 @@ BT 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-387(14)]TJ + [-387(15)]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 @@ -1211,7 +1220,7 @@ BT 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-359(22)]TJ + [-359(23)]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 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+2448,29 @@ BT 0 0 1 rg 0 0 1 RG [(5)]TJ 0 g 0 G - [(\051.)-424(In)-271(b)-27(oth)-271(cases,)-283(the)-271(construction)-271(and)-270(the)-271(appli-)]TJ 0 -13.549 Td [(cation)-269(of)-268(the)-269(preconditioner)-269(are)-268(carried)-269(out)-269(as)-268(for)-269(the)-269(default)-268(m)27(ulti-lev)28(el)-269(precondi)1(tioner.)]TJ 0 -13.549 Td [(The)-368(co)-28(de)-368(fragmen)28(ts)-368(sho)28(wn)-368(in)-368(in)-368(Figures)]TJ + [(\051.)-424(In)-271(b)-27(oth)-271(cases,)-283(the)-271(construction)-271(and)-270(the)-271(appli-)]TJ 0 -13.549 Td [(cation)-269(of)-268(the)-269(preconditioner)-269(are)-268(carried)-269(out)-269(as)-268(for)-269(the)-269(default)-268(m)27(ulti-lev)28(el)-269(precondi)1(tioner.)]TJ 0 -13.549 Td [(The)-310(co)-28(de)-310(fragmen)28(ts)-311(sho)28(wn)-310(in)-310(in)-310(Figures)]TJ +0 0 1 rg 0 0 1 RG + [-310(3)]TJ +0 g 0 G 0 0 1 rg 0 0 1 RG - [-368(3)]TJ + [-310(4)]TJ 0 g 0 G [(-)]TJ 0 0 1 rg 0 0 1 RG - [(4)]TJ + [(5)]TJ 0 g 0 G - 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0 1 652.473 126.108 cm +1 0 0 1 652.473 85.261 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 +/F15 10.9091 Tf 658.451 102.875 Td [(1.0)]TJ ET q -1 0 0 1 732.46 126.108 cm +1 0 0 1 732.46 85.261 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 +/F15 10.9091 Tf 738.437 102.875 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 +1 0 0 1 914.493 85.261 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 +1 0 0 1 299.826 85.062 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 +1 0 0 1 299.826 17.117 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 +/F44 10.9091 Tf 305.803 75.378 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 +1 0 0 1 453.513 17.117 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 +/F44 10.9091 Tf 459.491 75.378 Td [(character\050len=*\051)]TJ ET q -1 0 0 1 572.487 57.963 cm +1 0 0 1 572.487 17.117 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 +/F44 10.9091 Tf 578.464 75.378 Td [('EIG)]TJ ET q -1 0 0 1 602.06 116.424 cm +1 0 0 1 602.06 75.577 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 +/F44 10.9091 Tf 605.497 75.378 Td [(EST')]TJ -27.033 -13.549 Td [('USER)]TJ ET q -1 0 0 1 607.787 102.875 cm +1 0 0 1 607.787 62.028 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 +/F44 10.9091 Tf 611.224 61.829 Td [(CHOICE')]TJ ET q -1 0 0 1 652.473 57.963 cm +1 0 0 1 652.473 17.117 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 +/F44 10.9091 Tf 658.451 75.378 Td [('EIG)]TJ ET q -1 0 0 1 682.047 116.424 cm +1 0 0 1 682.047 75.577 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 +/F44 10.9091 Tf 685.483 75.378 Td [(EST')]TJ ET q -1 0 0 1 732.46 57.963 cm +1 0 0 1 732.46 17.117 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 +/F15 10.9091 Tf 738.437 75.378 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 -13.549 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 3.958 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.958 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)-369(or)-362(ex-)]TJ -135.108 -13.55 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 +1 0 0 1 914.493 17.117 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 +1 0 0 1 299.826 16.917 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 +1 0 0 1 299.826 -23.93 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 +/F44 10.9091 Tf 305.803 7.234 Td [(mld_aggr_eig_)]TJ 0 -13.55 Td [(AGGR_EIG)]TJ ET q -1 0 0 1 453.513 16.917 cm +1 0 0 1 453.513 -23.93 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 +/F44 10.9091 Tf 459.491 7.234 Td [(character\050len=*\051)]TJ ET q -1 0 0 1 572.487 16.917 cm +1 0 0 1 572.487 -23.93 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 +/F44 10.9091 Tf 578.464 7.234 Td [('A)]TJ ET q -1 0 0 1 590.606 48.28 cm +1 0 0 1 590.606 7.433 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 +/F44 10.9091 Tf 594.042 7.234 Td [(NORMI')]TJ ET q -1 0 0 1 652.473 16.917 cm +1 0 0 1 652.473 -23.93 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 +/F44 10.9091 Tf 658.451 7.234 Td [('A)]TJ ET q -1 0 0 1 670.592 48.28 cm +1 0 0 1 670.592 7.433 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 +/F44 10.9091 Tf 674.029 7.234 Td [(NORMI')]TJ ET q -1 0 0 1 732.46 16.917 cm +1 0 0 1 732.46 -23.93 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 +/F15 10.9091 Tf 738.437 7.234 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 +1 0 0 1 914.493 -23.93 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 +1 0 0 1 299.826 -24.129 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 +1 0 0 1 299.826 -132.722 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 +/F44 10.9091 Tf 305.803 -33.812 Td [(mld_aggr_omega_val_)]TJ 0 -13.55 Td [(AGGR_OMEGA_VAL)]TJ ET q -1 0 0 1 453.513 -91.875 cm +1 0 0 1 453.513 -132.722 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 +/F44 10.9091 Tf 459.491 -33.812 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 +1 0 0 1 508.868 -33.613 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 +/F18 10.9091 Tf 512.214 -33.812 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 +1 0 0 1 572.487 -132.722 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 +/F15 10.9091 Tf 578.464 -33.812 Td [(An)28(y)-486(nonnega-)]TJ 0 -13.55 Td [(tiv)28(e)-334(real)-333(n)28(um.)]TJ ET q -1 0 0 1 652.473 -91.875 cm +1 0 0 1 652.473 -132.722 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 +/F15 10.9091 Tf 658.451 -33.812 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 3.958 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.958 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 +1 0 0 1 732.46 -132.722 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 +/F15 10.9091 Tf 738.437 -33.812 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 -13.55 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 -13.549 Td [(it)-354(is)-354(computed)-354(b)28(y)-354(the)-354(library)83(,)-359(using)]TJ 0 -13.55 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 +1 0 0 1 914.493 -132.722 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 +1 0 0 1 299.826 -132.921 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 +/F15 10.9091 Tf 459.779 -163.61 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 @@ -4503,7 +4578,7 @@ Q endstream endobj -451 0 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