!!$ !!$ MLD2P4 version 2.1 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package !!$ based on PSBLAS (Parallel Sparse BLAS version 3.4) !!$ !!$ (C) Copyright 2008, 2010, 2012, 2015 !!$ !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari CNRS-IRIT, Toulouse !!$ Pasqua D'Ambra ICAR-CNR, Naples !!$ Daniela di Serafino Second University of Naples !!$ !!$ Redistribution and use in source and binary forms, with or without !!$ modification, are permitted provided that the following conditions !!$ are met: !!$ 1. Redistributions of source code must retain the above copyright !!$ notice, this list of conditions and the following disclaimer. !!$ 2. Redistributions in binary form must reproduce the above copyright !!$ notice, this list of conditions, and the following disclaimer in the !!$ documentation and/or other materials provided with the distribution. !!$ 3. The name of the MLD2P4 group or the names of its contributors may !!$ not be used to endorse or promote products derived from this !!$ software without specific written permission. !!$ !!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS !!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED !!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR !!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS !!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR !!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF !!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS !!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN !!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) !!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE !!$ POSSIBILITY OF SUCH DAMAGE. !!$ !!$ ! ! File: mld_d_pde3d.f90 ! ! Program: mld_d_pde3d ! This sample program solves a linear system obtained by discretizing a ! PDE with Dirichlet BCs. ! ! ! The PDE is a general second order equation in 3d ! ! a1 dd(u) a2 dd(u) a3 dd(u) b1 d(u) b2 d(u) b3 d(u) ! - ------ - ------ - ------ + ----- + ------ + ------ + c u = f ! dxdx dydy dzdz dx dy dz ! ! with Dirichlet boundary conditions ! u = g ! ! on the unit cube 0<=x,y,z<=1. ! ! ! Note that if b1=b2=b3=c=0., the PDE is the Laplace equation. ! ! In this sample program the index space of the discretized ! computational domain is first numbered sequentially in a standard way, ! then the corresponding vector is distributed according to a BLOCK ! data distribution. ! module mld_d_pde3d_mod contains ! ! functions parametrizing the differential equation ! function b1(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: b1 real(psb_dpk_), intent(in) :: x,y,z b1=0.d0/sqrt(3.d0) end function b1 function b2(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: b2 real(psb_dpk_), intent(in) :: x,y,z b2=0.d0/sqrt(3.d0) end function b2 function b3(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: b3 real(psb_dpk_), intent(in) :: x,y,z b3=0.d0/sqrt(3.d0) end function b3 function c(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: c real(psb_dpk_), intent(in) :: x,y,z c=0.d0 end function c function a1(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: a1 real(psb_dpk_), intent(in) :: x,y,z a1=1.d0!/80 end function a1 function a2(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: a2 real(psb_dpk_), intent(in) :: x,y,z a2=1.d0!/80 end function a2 function a3(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: a3 real(psb_dpk_), intent(in) :: x,y,z a3=1.d0!/80 end function a3 function g(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero real(psb_dpk_) :: g real(psb_dpk_), intent(in) :: x,y,z g = dzero if (x == done) then g = done else if (x == dzero) then g = exp(y**2-z**2) end if end function g end module mld_d_pde3d_mod program mld_d_pde3d use psb_base_mod use mld_prec_mod use psb_krylov_mod use psb_util_mod use data_input use mld_d_pde3d_mod implicit none ! input parameters character(len=20) :: kmethd, ptype character(len=5) :: afmt integer(psb_ipk_) :: idim ! miscellaneous real(psb_dpk_) :: t1, t2, tprec, thier, tslv ! sparse matrix and preconditioner type(psb_dspmat_type) :: a type(mld_dprec_type) :: prec ! descriptor type(psb_desc_type) :: desc_a ! dense vectors type(psb_d_vect_type) :: x,b ! parallel environment integer(psb_ipk_) :: ictxt, iam, np ! solver parameters integer(psb_ipk_) :: iter, itmax,itrace, istopc, irst, nlv integer(psb_long_int_k_) :: amatsize, precsize, descsize real(psb_dpk_) :: err, eps type precdata character(len=20) :: descr ! verbose description of the prec character(len=10) :: prec ! overall prectype integer(psb_ipk_) :: novr ! number of overlap layers integer(psb_ipk_) :: jsweeps ! Jacobi/smoother sweeps character(len=16) :: restr ! restriction over application of as character(len=16) :: prol ! prolongation over application of as character(len=16) :: solve ! Solver type: ILU, SuperLU, UMFPACK. integer(psb_ipk_) :: fill1 ! Fill-in for factorization 1 integer(psb_ipk_) :: svsweeps ! Solver sweeps for GS real(psb_dpk_) :: thr1 ! Threshold for fact. 1 ILU(T) character(len=16) :: smther ! Smoother integer(psb_ipk_) :: nlevs ! Number of levels in multilevel prec. integer(psb_ipk_) :: maxlevs ! Maximum 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. character(len=16) :: cmat ! coarse mat character(len=16) :: csolve ! Coarse solver: bjac, umf, slu, sludist character(len=16) :: csbsolve ! Coarse subsolver: ILU, ILU(T), SuperLU, UMFPACK. integer(psb_ipk_) :: cfill ! Fill-in for factorization 1 real(psb_dpk_) :: cthres ! Threshold for fact. 1 ILU(T) integer(psb_ipk_) :: cjswp ! Jacobi sweeps real(psb_dpk_) :: athres ! smoother aggregation threshold real(psb_dpk_) :: mnaggratio ! Minimum aggregation ratio end type precdata type(precdata) :: prectype type(psb_d_coo_sparse_mat) :: acoo ! other variables integer(psb_ipk_) :: info, i character(len=20) :: name,ch_err info=psb_success_ call psb_init(ictxt) call psb_info(ictxt,iam,np) if (iam < 0) then ! This should not happen, but just in case call psb_exit(ictxt) stop endif if(psb_get_errstatus() /= 0) goto 9999 name='mld_d_pde3d' call psb_set_errverbosity(itwo) ! ! Hello world ! if (iam == psb_root_) then write(*,*) 'Welcome to MLD2P4 version: ',mld_version_string_ write(*,*) 'This is the ',trim(name),' sample program' end if ! ! get parameters ! call get_parms(ictxt,kmethd,prectype,afmt,idim,istopc,itmax,itrace,irst,eps) ! ! allocate and fill in the coefficient matrix, rhs and initial guess ! call psb_barrier(ictxt) t1 = psb_wtime() call psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,& & a1,a2,a3,b1,b2,b3,c,g,info) call psb_barrier(ictxt) t2 = psb_wtime() - t1 if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='create_matrix' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if if (iam == psb_root_) & & write(psb_out_unit,'("Overall matrix creation time : ",es12.5)')t2 if (iam == psb_root_) & & write(psb_out_unit,'(" ")') ! ! prepare the preconditioner. ! if (psb_toupper(prectype%prec) == 'ML') then call mld_precinit(prec,prectype%prec, info) if (prectype%nlevs > 0) then ! Force number of levels, so disregard the other related arguments. call mld_precset(prec,'n_prec_levs', prectype%nlevs, info) else if (prectype%csize>0)& & call mld_precset(prec,'coarse_aggr_size', prectype%csize, info) if (prectype%maxlevs>0)& & call mld_precset(prec,'max_prec_levs', prectype%maxlevs, info) if (prectype%mnaggratio>0)& & call mld_precset(prec,'min_aggr_ratio', prectype%mnaggratio, info) end if if (prectype%athres >= dzero) & & call mld_precset(prec,'aggr_thresh', prectype%athres, 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 psb_barrier(ictxt) t1 = psb_wtime() call mld_hierarchy_bld(a,desc_a,prec,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='psb_precbld' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if thier = psb_wtime()-t1 call mld_precset(prec,'smoother_type', prectype%smther, info) call mld_precset(prec,'smoother_sweeps', prectype%jsweeps, info) call mld_precset(prec,'sub_ovr', prectype%novr, info) call mld_precset(prec,'sub_restr', prectype%restr, info) call mld_precset(prec,'sub_prol', prectype%prol, info) call mld_precset(prec,'sub_solve', prectype%solve, info) call mld_precset(prec,'sub_fillin', prectype%fill1, info) call mld_precset(prec,'solver_sweeps', prectype%svsweeps, info) call mld_precset(prec,'sub_iluthrs', prectype%thr1, info) call mld_precset(prec,'ml_type', prectype%mltype, info) call mld_precset(prec,'smoother_pos', prectype%smthpos, info) call mld_precset(prec,'coarse_solve', prectype%csolve, info) call mld_precset(prec,'coarse_subsolve', prectype%csbsolve,info) call mld_precset(prec,'coarse_mat', prectype%cmat, info) call mld_precset(prec,'coarse_fillin', prectype%cfill, info) call mld_precset(prec,'coarse_iluthrs', prectype%cthres, info) call mld_precset(prec,'coarse_sweeps', prectype%cjswp, info) call psb_barrier(ictxt) t1 = psb_wtime() call mld_ml_prec_bld(a,desc_a,prec,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='psb_precbld' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if tprec = psb_wtime()-t1 else nlv = 1 call mld_precinit(prec,prectype%prec, info) call mld_precset(prec,'smoother_sweeps', prectype%jsweeps, info) call mld_precset(prec,'sub_ovr', prectype%novr, info) call mld_precset(prec,'sub_restr', prectype%restr, info) call mld_precset(prec,'sub_prol', prectype%prol, info) call mld_precset(prec,'sub_solve', prectype%solve, info) call mld_precset(prec,'sub_fillin', prectype%fill1, info) call mld_precset(prec,'solver_sweeps', prectype%svsweeps, info) call mld_precset(prec,'sub_iluthrs', prectype%thr1, info) call psb_barrier(ictxt) thier = dzero t1 = psb_wtime() call mld_precbld(a,desc_a,prec,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='psb_precbld' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if tprec = psb_wtime()-t1 end if !!$ call prec%dump(info,prefix='test-ml',ac=.true.,solver=.true.,smoother=.true.) call psb_amx(ictxt,thier) call psb_amx(ictxt,tprec) if (iam == psb_root_) & & write(psb_out_unit,'("Preconditioner time : ",es12.5)') tprec+thier if (iam == psb_root_) call mld_precdescr(prec,info) if (iam == psb_root_) & & write(psb_out_unit,'(" ")') ! ! iterative method parameters ! if(iam == psb_root_) & & write(psb_out_unit,'("Calling iterative method ",a)')kmethd call psb_barrier(ictxt) t1 = psb_wtime() call psb_krylov(kmethd,a,prec,b,x,eps,desc_a,info,& & itmax=itmax,iter=iter,err=err,itrace=itrace,istop=istopc,irst=irst) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='solver routine' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if call psb_barrier(ictxt) tslv = psb_wtime() - t1 call psb_amx(ictxt,tslv) amatsize = a%sizeof() descsize = desc_a%sizeof() precsize = prec%sizeof() call psb_sum(ictxt,amatsize) call psb_sum(ictxt,descsize) call psb_sum(ictxt,precsize) if (iam == psb_root_) then write(psb_out_unit,'(" ")') write(psb_out_unit,'("Numer of levels of aggr. hierarchy: ",i12)') prec%get_nlevs() write(psb_out_unit,'("Time to build aggr. hierarchy : ",es12.5)') thier write(psb_out_unit,'("Time to build smoothers : ",es12.5)') tprec write(psb_out_unit,'("Total preconditioner time : ",es12.5)') tprec+thier write(psb_out_unit,'("Time to solve system : ",es12.5)') tslv write(psb_out_unit,'("Time per iteration : ",es12.5)') tslv/iter write(psb_out_unit,'("Number of iterations : ",i0)') iter write(psb_out_unit,'("Convergence indicator on exit : ",es12.5)') err write(psb_out_unit,'("Info on exit : ",i0)') info write(psb_out_unit,'("Total memory occupation for A: ",i12)') amatsize write(psb_out_unit,'("Storage format for A: ",a)') trim(a%get_fmt()) write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)') descsize write(psb_out_unit,'("Storage format for DESC_A: ",a)') trim(desc_a%get_fmt()) write(psb_out_unit,'("Total memory occupation for PREC: ",i12)') precsize end if ! ! cleanup storage and exit ! call psb_gefree(b,desc_a,info) call psb_gefree(x,desc_a,info) call psb_spfree(a,desc_a,info) call mld_precfree(prec,info) call psb_cdfree(desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='free routine' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if call psb_exit(ictxt) stop 9999 continue call psb_error(ictxt) contains ! ! get iteration parameters from standard input ! subroutine get_parms(ictxt,kmethd,prectype,afmt,idim,istopc,itmax,itrace,irst,eps) integer(psb_ipk_) :: ictxt type(precdata) :: prectype character(len=*) :: kmethd, afmt integer(psb_ipk_) :: idim, istopc,itmax,itrace,irst integer(psb_ipk_) :: np, iam, info real(psb_dpk_) :: eps character(len=20) :: buffer call psb_info(ictxt, iam, np) if (iam == psb_root_) then call read_data(kmethd,psb_inp_unit) call read_data(afmt,psb_inp_unit) call read_data(idim,psb_inp_unit) call read_data(istopc,psb_inp_unit) call read_data(itmax,psb_inp_unit) call read_data(itrace,psb_inp_unit) call read_data(irst,psb_inp_unit) call read_data(eps,psb_inp_unit) call read_data(prectype%descr,psb_inp_unit) ! verbose description of the prec call read_data(prectype%prec,psb_inp_unit) ! overall prectype call read_data(prectype%nlevs,psb_inp_unit) ! Prescribed number of levels call read_data(prectype%csize,psb_inp_unit) ! coarse size call read_data(prectype%mnaggratio,psb_inp_unit) ! Minimum aggregation ratio call read_data(prectype%athres,psb_inp_unit) ! smoother aggr thresh call read_data(prectype%maxlevs,psb_inp_unit) ! Maximum number of levels call read_data(prectype%aggrkind,psb_inp_unit) ! smoothed/nonsmoothed/minenergy aggregatin call read_data(prectype%aggr_alg,psb_inp_unit) ! decoupled or sym. decoupled aggregation call read_data(prectype%aggr_ord,psb_inp_unit) ! aggregation ordering: natural, node degree 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%jsweeps,psb_inp_unit) ! Smoother sweeps call read_data(prectype%smther,psb_inp_unit) ! Smoother type. call read_data(prectype%novr,psb_inp_unit) ! number of overlap layers call read_data(prectype%restr,psb_inp_unit) ! restriction over application of as call read_data(prectype%prol,psb_inp_unit) ! prolongation over application of as call read_data(prectype%solve,psb_inp_unit) ! Subdomain solver: DSCALE ILU MILU ILUT FWGS BWGS MUMPS UMF SLU call read_data(prectype%svsweeps,psb_inp_unit) ! Solver sweeps (GS) call read_data(prectype%fill1,psb_inp_unit) ! Fill-in for factorization 1 call read_data(prectype%thr1,psb_inp_unit) ! Threshold for fact. 1 ILU(T) call read_data(prectype%cmat,psb_inp_unit) ! coarse mat call read_data(prectype%csolve,psb_inp_unit) ! Coarse solver: JACOBI BJAC UMF SLU SLUDIST MUMPS call read_data(prectype%csbsolve,psb_inp_unit) ! subsolver: DSCALE GS BWGS ILU UMF SLU SLUDIST MUMPS call read_data(prectype%cfill,psb_inp_unit) ! Fill-in for factorization 1 call read_data(prectype%cthres,psb_inp_unit) ! Threshold for fact. 1 ILU(T) call read_data(prectype%cjswp,psb_inp_unit) ! Jacobi sweeps end if ! broadcast parameters to all processors call psb_bcast(ictxt,kmethd) call psb_bcast(ictxt,afmt) call psb_bcast(ictxt,idim) call psb_bcast(ictxt,istopc) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,itrace) call psb_bcast(ictxt,irst) call psb_bcast(ictxt,eps) call psb_bcast(ictxt,prectype%descr) ! verbose description of the prec call psb_bcast(ictxt,prectype%prec) ! overall prectype call psb_bcast(ictxt,prectype%nlevs) ! Prescribed number of levels call psb_bcast(ictxt,prectype%csize) ! coarse size call psb_bcast(ictxt,prectype%mnaggratio) ! Minimum aggregation ratio call psb_bcast(ictxt,prectype%athres) ! smoother aggr thresh call psb_bcast(ictxt,prectype%maxlevs) ! Maximum number of levels call psb_bcast(ictxt,prectype%aggrkind) ! smoothed/nonsmoothed/minenergy aggregatin call psb_bcast(ictxt,prectype%aggr_alg) ! decoupled or sym. decoupled aggregation call psb_bcast(ictxt,prectype%aggr_ord) ! aggregation ordering: natural, node degree 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%jsweeps) ! Smoother sweeps call psb_bcast(ictxt,prectype%smther) ! Smoother type. call psb_bcast(ictxt,prectype%novr) ! number of overlap layers call psb_bcast(ictxt,prectype%restr) ! restriction over application of as call psb_bcast(ictxt,prectype%prol) ! prolongation over application of as call psb_bcast(ictxt,prectype%solve) ! Subdomain solver: DSCALE ILU MILU ILUT FWGS BWGS MUMPS UMF SLU call psb_bcast(ictxt,prectype%svsweeps) ! Solver sweeps (GS) call psb_bcast(ictxt,prectype%fill1) ! Fill-in for factorization 1 call psb_bcast(ictxt,prectype%thr1) ! Threshold for fact. 1 ILU(T) call psb_bcast(ictxt,prectype%cmat) ! coarse mat call psb_bcast(ictxt,prectype%csolve) ! Coarse solver: JACOBI BJAC UMF SLU SLUDIST MUMPS call psb_bcast(ictxt,prectype%csbsolve) ! subsolver: DSCALE GS BWGS ILU UMF SLU SLUDIST MUMPS call psb_bcast(ictxt,prectype%cfill) ! Fill-in for factorization 1 call psb_bcast(ictxt,prectype%cthres) ! Threshold for fact. 1 ILU(T) call psb_bcast(ictxt,prectype%cjswp) ! Jacobi sweeps if (iam == psb_root_) then write(psb_out_unit,'("Solving matrix : ell1")') write(psb_out_unit,'("Grid dimensions : ",i4,"x",i4,"x",i4)')idim,idim,idim write(psb_out_unit,'("Number of processors : ",i0)') np write(psb_out_unit,'("Data distribution : BLOCK")') write(psb_out_unit,'("Preconditioner : ",a)') prectype%descr write(psb_out_unit,'("Iterative method : ",a)') kmethd write(psb_out_unit,'(" ")') endif return end subroutine get_parms ! ! print an error message ! subroutine pr_usage(iout) integer(psb_ipk_) :: iout write(iout,*)'incorrect parameter(s) found' write(iout,*)' usage: mld_d_pde3d methd prec dim & &[istop itmax itrace]' write(iout,*)' where:' write(iout,*)' methd: cgstab cgs rgmres bicgstabl' write(iout,*)' prec : bjac diag none' write(iout,*)' dim number of points along each axis' write(iout,*)' the size of the resulting linear ' write(iout,*)' system is dim**3' write(iout,*)' istop stopping criterion 1, 2 ' write(iout,*)' itmax maximum number of iterations [500] ' write(iout,*)' itrace <=0 (no tracing, default) or ' write(iout,*)' >= 1 do tracing every itrace' write(iout,*)' iterations ' end subroutine pr_usage end program mld_d_pde3d