!!$ !!$ MLD2P4 version 1.0 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package !!$ based on PSBLAS (Parallel Sparse BLAS version 2.2) !!$ !!$ (C) Copyright 2008 !!$ !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari University of Rome Tor Vergata !!$ 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 PSBLAS 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 PSBLAS 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: ppde.f90 ! ! Program: ppde ! This sample program shows how to build and solve a sparse linear ! ! The program solves a linear system based on the partial differential ! equation ! ! ! ! The equation generated is ! ! b1 d d (u) b2 d d (u) a1 d (u)) a2 d (u))) ! - ------ - ------ + ----- + ------ + a3 u = 0 ! dx dx dy dy dx dy ! ! ! with Dirichlet boundary conditions on the unit cube ! ! 0<=x,y,z<=1 ! ! The equation is discretized with finite differences and uniform stepsize; ! the resulting discrete equation is ! ! ( u(x,y,z)(2b1+2b2+a1+a2)+u(x-1,y)(-b1-a1)+u(x,y-1)(-b2-a2)+ ! -u(x+1,y)b1-u(x,y+1)b2)*(1/h**2) ! ! Example taken from: C.T.Kelley ! Iterative Methods for Linear and Nonlinear Equations ! SIAM 1995 ! ! ! 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. ! ! Boundary conditions are set in a very simple way, by adding ! equations of the form ! ! u(x,y) = rhs(x,y) ! program ppde use psb_base_mod use mld_prec_mod use psb_krylov_mod use psb_util_mod use data_input implicit none ! input parameters character(len=20) :: kmethd, ptype character(len=5) :: afmt integer :: idim ! miscellaneous real(psb_dpk_), parameter :: one = 1.d0 real(psb_dpk_) :: t1, t2, tprec ! sparse matrix and preconditioner type(psb_dspmat_type) :: a type(mld_dprec_type) :: prec ! descriptor type(psb_desc_type) :: desc_a ! dense matrices real(psb_dpk_), allocatable :: b(:), x(:) ! blacs parameters integer :: ictxt, iam, np ! solver parameters integer :: iter, itmax,itrace, istopc, irst, nlv real(psb_dpk_) :: err, eps type precdata character(len=20) :: descr ! verbose description of the prec character(len=10) :: prec ! overall prectype integer :: novr ! number of overlap layers character(len=16) :: restr ! restriction over application of as character(len=16) :: prol ! prolongation over application of as character(len=16) :: solve ! Factorization type: ILU, SuperLU, UMFPACK. integer :: fill1 ! Fill-in for factorization 1 real(psb_dpk_) :: thr1 ! Threshold for fact. 1 ILU(T) integer :: 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) :: mltype ! additive or multiplicative 2nd level prec character(len=16) :: smthpos ! side: pre, post, both smoothing 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 :: cfill ! Fill-in for factorization 1 real(psb_dpk_) :: cthres ! Threshold for fact. 1 ILU(T) integer :: cjswp ! Jacobi sweeps real(psb_dpk_) :: omega ! smoother omega real(psb_dpk_) :: athres ! smoother aggregation threshold end type precdata type(precdata) :: prectype ! other variables integer :: info character(len=20) :: name,ch_err info=0 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='pde90' call psb_set_errverbosity(2) ! ! get parameters ! call get_parms(ictxt,kmethd,prectype,afmt,idim,istopc,itmax,itrace,irst) ! ! allocate and fill in the coefficient matrix, rhs and initial guess ! call psb_barrier(ictxt) t1 = psb_wtime() call create_matrix(idim,a,b,x,desc_a,part_block,ictxt,afmt,info) t2 = psb_wtime() - t1 if(info /= 0) then info=4010 ch_err='create_matrix' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if call psb_amx(ictxt,t2) if (iam == psb_root_) write(*,'("Overall matrix creation time : ",es10.4)')t2 if (iam == psb_root_) write(*,'(" ")') ! ! prepare the preconditioner. ! if (psb_toupper(prectype%prec) =='ML') then nlv = prectype%nlev else nlv = 1 end if call mld_precinit(prec,prectype%prec,info,nlev=nlv) call mld_precset(prec,mld_sub_ovr_,prectype%novr,info) call mld_precset(prec,mld_sub_restr_,prectype%restr,info) call mld_precset(prec,mld_sub_prol_,prectype%prol,info) call mld_precset(prec,mld_sub_solve_,prectype%solve,info) call mld_precset(prec,mld_sub_fillin_,prectype%fill1,info) call mld_precset(prec,mld_sub_iluthrs_,prectype%thr1,info) if (psb_toupper(prectype%prec) =='ML') then call mld_precset(prec,mld_aggr_kind_, prectype%aggrkind,info) call mld_precset(prec,mld_aggr_alg_, prectype%aggr_alg,info) call mld_precset(prec,mld_ml_type_, prectype%mltype, info) call mld_precset(prec,mld_smoother_pos_, prectype%smthpos, info) call mld_precset(prec,mld_aggr_thresh_, prectype%athres, info) call mld_precset(prec,mld_coarse_solve_, prectype%csolve, info) call mld_precset(prec,mld_coarse_subsolve_, prectype%csbsolve,info) call mld_precset(prec,mld_coarse_mat_, prectype%cmat, info) call mld_precset(prec,mld_coarse_fillin_, prectype%cfill, info) call mld_precset(prec,mld_coarse_iluthrs_, prectype%cthres, info) call mld_precset(prec,mld_coarse_sweeps_, prectype%cjswp, info) if (prectype%omega>=0.0) then call mld_precset(prec,mld_aggr_damp_,prectype%omega,info) end if end if call psb_barrier(ictxt) t1 = psb_wtime() call mld_precbld(a,desc_a,prec,info) if(info /= 0) then info=4010 ch_err='psb_precbld' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if tprec = psb_wtime()-t1 call psb_amx(ictxt,tprec) if (iam == psb_root_) write(*,'("Preconditioner time : ",es10.4)')tprec if (iam == psb_root_) call mld_precdescr(prec,info) if (iam == psb_root_) write(*,'(" ")') ! ! iterative method parameters ! if(iam == psb_root_) write(*,'("Calling iterative method ",a)')kmethd call psb_barrier(ictxt) t1 = psb_wtime() eps = 1.d-9 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 /= 0) then info=4010 ch_err='solver routine' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if call psb_barrier(ictxt) t2 = psb_wtime() - t1 call psb_amx(ictxt,t2) if (iam == psb_root_) then write(*,'(" ")') write(*,'("Time to solve matrix : ",es10.4)')t2 write(*,'("Time per iteration : ",es10.4)')t2/iter write(*,'("Number of iterations : ",i0)')iter write(*,'("Convergence indicator on exit : ",es10.4)')err write(*,'("Info on exit : ",i0)')info 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 /= 0) then info=4010 ch_err='free routine' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if 9999 continue if(info /= 0) then call psb_error(ictxt) end if call psb_exit(ictxt) stop contains ! ! get iteration parameters from the command line ! subroutine get_parms(ictxt,kmethd,prectype,afmt,idim,istopc,itmax,itrace,irst) integer :: ictxt type(precdata) :: prectype character(len=*) :: kmethd, afmt integer :: idim, istopc,itmax,itrace,irst integer :: np, iam, info character(len=20) :: buffer call psb_info(ictxt, iam, np) if (iam==psb_root_) then call read_data(kmethd,5) call read_data(afmt,5) call read_data(idim,5) call read_data(istopc,5) call read_data(itmax,5) call read_data(itrace,5) call read_data(irst,5) call read_data(eps,5) call read_data(prectype%descr,5) ! verbose description of the prec call read_data(prectype%prec,5) ! overall prectype call read_data(prectype%novr,5) ! number of overlap layers call read_data(prectype%restr,5) ! restriction over application of as call read_data(prectype%prol,5) ! prolongation over application of as call read_data(prectype%solve,5) ! Factorization type: ILU, SuperLU, UMFPACK. call read_data(prectype%fill1,5) ! Fill-in for factorization 1 call read_data(prectype%thr1,5) ! Threshold for fact. 1 ILU(T) if (psb_toupper(prectype%prec) == 'ML') then call read_data(prectype%nlev,5) ! Number of levels in multilevel prec. call read_data(prectype%aggrkind,5) ! smoothed/raw aggregatin call read_data(prectype%aggr_alg,5) ! local or global aggregation call read_data(prectype%mltype,5) ! additive or multiplicative 2nd level prec call read_data(prectype%smthpos,5) ! side: pre, post, both smoothing call read_data(prectype%cmat,5) ! coarse mat call read_data(prectype%csolve,5) ! Factorization type: ILU, SuperLU, UMFPACK. call read_data(prectype%csbsolve,5) ! Factorization type: ILU, SuperLU, UMFPACK. call read_data(prectype%cfill,5) ! Fill-in for factorization 1 call read_data(prectype%cthres,5) ! Threshold for fact. 1 ILU(T) call read_data(prectype%cjswp,5) ! Jacobi sweeps call read_data(prectype%omega,5) ! smoother omega call read_data(prectype%athres,5) ! smoother aggr thresh end if 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,prectype%descr) ! verbose description of the prec call psb_bcast(ictxt,prectype%prec) ! overall prectype 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) ! Factorization type: ILU, SuperLU, UMFPACK. call psb_bcast(ictxt,prectype%fill1) ! Fill-in for factorization 1 call psb_bcast(ictxt,prectype%thr1) ! Threshold for fact. 1 ILU(T) if (psb_toupper(prectype%prec) == 'ML') then 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%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 call psb_bcast(ictxt,prectype%csolve) ! Factorization type: ILU, SuperLU, UMFPACK. call psb_bcast(ictxt,prectype%csbsolve) ! Factorization type: ILU, SuperLU, UMFPACK. 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 call psb_bcast(ictxt,prectype%omega) ! smoother omega call psb_bcast(ictxt,prectype%athres) ! smoother aggr thresh end if if (iam==psb_root_) then write(*,'("Solving matrix : ell1")') write(*,'("Grid dimensions : ",i4,"x",i4,"x",i4)')idim,idim,idim write(*,'("Number of processors : ",i0)') np write(*,'("Data distribution : BLOCK")') write(*,'("Preconditioner : ",a)') prectype%descr write(*,'("Iterative method : ",a)') kmethd write(*,'(" ")') endif return end subroutine get_parms ! ! print an error message ! subroutine pr_usage(iout) integer :: iout write(iout,*)'incorrect parameter(s) found' write(iout,*)' usage: pde90 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 ! ! subroutine to allocate and fill in the coefficient matrix and ! the rhs. ! subroutine create_matrix(idim,a,b,xv,desc_a,parts,ictxt,afmt,info) ! ! discretize the partial diferential equation ! ! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u) ! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u ! dxdx dydy dzdz dx dy dz ! ! = 0 ! ! boundary condition: dirichlet ! 0< x,y,z<1 ! ! u(x,y,z)(2b1+2b2+2b3+a1+a2+a3)+u(x-1,y,z)(-b1-a1)+u(x,y-1,z)(-b2-a2)+ ! + u(x,y,z-1)(-b3-a3)-u(x+1,y,z)b1-u(x,y+1,z)b2-u(x,y,z+1)b3 use psb_base_mod implicit none integer :: idim integer, parameter :: nbmax=10 real(psb_dpk_), allocatable :: b(:),xv(:) type(psb_desc_type) :: desc_a integer :: ictxt, info character :: afmt*5 interface ! .....user passed subroutine..... subroutine parts(global_indx,n,np,pv,nv) implicit none integer, intent(in) :: global_indx, n, np integer, intent(out) :: nv integer, intent(out) :: pv(*) end subroutine parts end interface ! local variables type(psb_dspmat_type) :: a real(psb_dpk_) :: zt(nbmax),glob_x,glob_y,glob_z integer :: m,n,nnz,glob_row integer :: x,y,z,ia,indx_owner integer :: np, iam integer :: element integer :: nv, inv integer, allocatable :: irow(:),icol(:) real(psb_dpk_), allocatable :: val(:) integer, allocatable :: prv(:) ! deltah dimension of each grid cell ! deltat discretization time real(psb_dpk_) :: deltah real(psb_dpk_),parameter :: rhs=0.d0,one=1.d0,zero=0.d0 real(psb_dpk_) :: t1, t2, t3, tins, tasb real(psb_dpk_) :: a1, a2, a3, a4, b1, b2, b3 external :: a1, a2, a3, a4, b1, b2, b3 integer :: err_act ! common area character(len=20) :: name, ch_err info = 0 name = 'create_matrix' call psb_erractionsave(err_act) call psb_info(ictxt, iam, np) deltah = 1.d0/(idim-1) ! initialize array descriptor and sparse matrix storage. provide an ! estimate of the number of non zeroes m = idim*idim*idim n = m nnz = ((n*9)/(np)) if(iam == psb_root_) write(0,'("Generating Matrix (size=",i0x,")...")')n call psb_cdall(ictxt,desc_a,info,mg=n,parts=parts) call psb_spall(a,desc_a,info,nnz=nnz) ! define rhs from boundary conditions; also build initial guess call psb_geall(b,desc_a,info) call psb_geall(xv,desc_a,info) if(info /= 0) then info=4010 ch_err='allocation rout.' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if ! we build an auxiliary matrix consisting of one row at a ! time; just a small matrix. might be extended to generate ! a bunch of rows per call. ! allocate(val(20*nbmax),irow(20*nbmax),& &icol(20*nbmax),prv(np),stat=info) if (info /= 0 ) then info=4000 call psb_errpush(info,name) goto 9999 endif tins = 0.d0 call psb_barrier(ictxt) t1 = psb_wtime() ! loop over rows belonging to current process in a block ! distribution. ! icol(1)=1 do glob_row = 1, n call parts(glob_row,n,np,prv,nv) do inv = 1, nv indx_owner = prv(inv) if (indx_owner == iam) then ! local matrix pointer element=1 ! compute gridpoint coordinates if (mod(glob_row,(idim*idim)) == 0) then x = glob_row/(idim*idim) else x = glob_row/(idim*idim)+1 endif if (mod((glob_row-(x-1)*idim*idim),idim) == 0) then y = (glob_row-(x-1)*idim*idim)/idim else y = (glob_row-(x-1)*idim*idim)/idim+1 endif z = glob_row-(x-1)*idim*idim-(y-1)*idim ! glob_x, glob_y, glob_x coordinates glob_x=x*deltah glob_y=y*deltah glob_z=z*deltah ! check on boundary points zt(1) = 0.d0 ! internal point: build discretization ! ! term depending on (x-1,y,z) ! if (x==1) then val(element)=-b1(glob_x,glob_y,glob_z)& & -a1(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) zt(1) = exp(-glob_y**2-glob_z**2)*(-val(element)) else val(element)=-b1(glob_x,glob_y,glob_z)& & -a1(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) icol(element)=(x-2)*idim*idim+(y-1)*idim+(z) element=element+1 endif ! term depending on (x,y-1,z) if (y==1) then val(element)=-b2(glob_x,glob_y,glob_z)& & -a2(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element)) else val(element)=-b2(glob_x,glob_y,glob_z)& & -a2(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) icol(element)=(x-1)*idim*idim+(y-2)*idim+(z) element=element+1 endif ! term depending on (x,y,z-1) if (z==1) then val(element)=-b3(glob_x,glob_y,glob_z)& & -a3(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element)) else val(element)=-b3(glob_x,glob_y,glob_z)& & -a3(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) icol(element)=(x-1)*idim*idim+(y-1)*idim+(z-1) element=element+1 endif ! term depending on (x,y,z) val(element)=2*b1(glob_x,glob_y,glob_z)& & +2*b2(glob_x,glob_y,glob_z)& & +2*b3(glob_x,glob_y,glob_z)& & +a1(glob_x,glob_y,glob_z)& & +a2(glob_x,glob_y,glob_z)& & +a3(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) icol(element)=(x-1)*idim*idim+(y-1)*idim+(z) element=element+1 ! term depending on (x,y,z+1) if (z==idim) then val(element)=-b1(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element)) else val(element)=-b1(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) icol(element)=(x-1)*idim*idim+(y-1)*idim+(z+1) element=element+1 endif ! term depending on (x,y+1,z) if (y==idim) then val(element)=-b2(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element)) else val(element)=-b2(glob_x,glob_y,glob_z) val(element) = val(element)/(deltah*& & deltah) icol(element)=(x-1)*idim*idim+(y)*idim+(z) element=element+1 endif ! term depending on (x+1,y,z) if (x