! ! ! MLD2P4 version 2.2 ! MultiLevel Domain Decomposition Parallel Preconditioners Package ! based on PSBLAS (Parallel Sparse BLAS version 3.5) ! ! (C) Copyright 2008-2018 ! ! Salvatore Filippone ! Pasqua D'Ambra ! Daniela di Serafino ! ! 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_,done,dzero real(psb_dpk_) :: b1 real(psb_dpk_), intent(in) :: x,y,z b1=dzero/sqrt((3*done)) end function b1 function b2(x,y,z) use psb_base_mod, only : psb_dpk_,done,dzero real(psb_dpk_) :: b2 real(psb_dpk_), intent(in) :: x,y,z b2=dzero/sqrt((3*done)) end function b2 function b3(x,y,z) use psb_base_mod, only : psb_dpk_,done,dzero real(psb_dpk_) :: b3 real(psb_dpk_), intent(in) :: x,y,z b3=dzero/sqrt((3*done)) end function b3 function c(x,y,z) use psb_base_mod, only : psb_dpk_,done,dzero real(psb_dpk_) :: c real(psb_dpk_), intent(in) :: x,y,z c=dzero end function c function a1(x,y,z) use psb_base_mod, only : psb_dpk_,done,dzero real(psb_dpk_) :: a1 real(psb_dpk_), intent(in) :: x,y,z a1=done!/80 end function a1 function a2(x,y,z) use psb_base_mod, only : psb_dpk_,done,dzero real(psb_dpk_) :: a2 real(psb_dpk_), intent(in) :: x,y,z a2=done!/80 end function a2 function a3(x,y,z) use psb_base_mod, only : psb_dpk_,done,dzero real(psb_dpk_) :: a3 real(psb_dpk_), intent(in) :: x,y,z a3=done!/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 use mld_d_tlu_solver 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 type(mld_d_tlu_solver_type) :: tlusv ! 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_epk_) :: amatsize, precsize, descsize real(psb_dpk_) :: err, eps ! 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,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: an ML with defaults, but with TLU solver at ! intermediate levels. All other parameters are at default values. ! call prec%init('ML', info) call psb_barrier(ictxt) t1 = psb_wtime() call prec%hierarchy_build(a,desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='prec%hierarchy_bld' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if thier = psb_wtime()-t1 nlv = prec%get_nlevs() call prec%set(tlusv, info,ilev=1,ilmax=max(1,nlv-1)) call psb_barrier(ictxt) t1 = psb_wtime() call prec%smoothers_build(a,desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='prec%smoothers_build' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if tprec = psb_wtime()-t1 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 prec%descr(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 prec%free(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,afmt,idim,istopc,itmax,itrace,irst,eps) integer(psb_ipk_) :: ictxt 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) 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) 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)') 'ML-TLU' 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