!!$ !!$ !!$ MLD2P4 version 2.0 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package !!$ based on PSBLAS (Parallel Sparse BLAS version 3.3) !!$ !!$ (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. 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File: mld_dexample_ml.f90 ! ! This sample program solves a linear system obtained by discretizing a ! PDE with Dirichlet BCs. The solver is BiCGStab coupled with one of the ! following multi-level preconditioner, as explained in Section 6.1 of ! the MLD2P4 User's and Reference Guide: ! - choice = 1, default multi-level Schwarz preconditioner (Sec. 6.1, Fig. 2) ! - choice = 2, hybrid three-level Schwarz preconditioner (Sec. 6.1, Fig. 3) ! - choice = 3, additive three-level Schwarz preconditioner (Sec. 6.1, Fig. 4) ! ! 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 dpde_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=1.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=1.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=1.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 dpde_mod program mld_dexample_ml use psb_base_mod use mld_prec_mod use psb_krylov_mod use psb_util_mod use data_input use dpde_mod implicit none ! input parameters ! sparse matrices type(psb_dspmat_type) :: A ! sparse matrices descriptor type(psb_desc_type):: desc_A ! preconditioner type(mld_dprec_type) :: P ! right-hand side, solution and residual vectors type(psb_d_vect_type) :: x, b, r ! solver and preconditioner parameters real(psb_dpk_) :: tol, err integer :: itmax, iter, istop integer :: nlev ! parallel environment parameters integer :: ictxt, iam, np ! other variables integer :: choice integer :: i,info,j integer(psb_long_int_k_) :: amatsize, precsize, descsize integer :: idim, ierr, ircode real(psb_dpk_) :: t1, t2, tprec, resmx, resmxp character(len=5) :: afmt='CSR' character(len=20) :: name ! initialize the parallel environment 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 name='mld_dexample_ml' if(psb_get_errstatus() /= 0) goto 9999 info=psb_success_ call psb_set_errverbosity(2) ! ! 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,choice,idim,itmax,tol) ! 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_ call psb_errpush(info,name) goto 9999 end if if (iam == psb_root_) write(*,'("Overall matrix creation time : ",es12.5)')t2 if (iam == psb_root_) write(*,'(" ")') select case(choice) case(1) ! initialize the default multi-level preconditioner, i.e. hybrid ! Schwarz, using RAS (with overlap 1 and ILU(0) on the blocks) ! as post-smoother and 4 block-Jacobi sweeps (with UMFPACK LU ! on the blocks) as distributed coarse-level solver call mld_precinit(P,'ML',info) case(2) ! 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 ! LU factorization from UMFPACK 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_,'UMF',info) case(3) ! 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 5 block-Jacobi sweeps (with UMFPACK LU ! on the blocks) as distributed coarsest-level solver call mld_precinit(P,'ML',info,nlev=3) call mld_precset(P,mld_ml_type_,'ADD',info) call mld_precset(P,mld_smoother_pos_,'TWOSIDE',info) call mld_precset(P,mld_coarse_sweeps_,5,info) end select ! build the preconditioner call psb_barrier(ictxt) t1 = psb_wtime() call mld_precbld(A,desc_A,P,info) tprec = psb_wtime()-t1 call psb_amx(ictxt, tprec) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='psb_precbld') goto 9999 end if ! set the solver parameters and the initial guess call psb_geall(x,desc_A,info) call x%set(dzero) call psb_geasb(x,desc_A,info) ! solve Ax=b with preconditioned BiCGSTAB call psb_barrier(ictxt) t1 = psb_wtime() call psb_krylov('BICGSTAB',A,P,b,x,tol,desc_A,info,itmax,iter,err,itrace=1,istop=2) t2 = psb_wtime() - t1 call psb_amx(ictxt,t2) call psb_geall(r,desc_A,info) call r%set(dzero) call psb_geasb(r,desc_A,info) call psb_geaxpby(done,b,dzero,r,desc_A,info) call psb_spmm(-done,A,x,done,r,desc_A,info) resmx = psb_genrm2(r,desc_A,info) resmxp = psb_geamax(r,desc_A,info) amatsize = a%sizeof() descsize = desc_a%sizeof() precsize = p%sizeof() call psb_sum(ictxt,amatsize) call psb_sum(ictxt,descsize) call psb_sum(ictxt,precsize) call mld_precdescr(P,info) if (iam == psb_root_) then write(*,'(" ")') write(*,'("Matrix from PDE example")') write(*,'("Computed solution on ",i8," processors")')np write(*,'("Iterations to convergence : ",i6)')iter write(*,'("Error estimate on exit : ",es12.5)')err write(*,'("Time to build prec. : ",es12.5)')tprec write(*,'("Time to solve system : ",es12.5)')t2 write(*,'("Time per iteration : ",es12.5)')t2/(iter) write(*,'("Total time : ",es12.5)')t2+tprec write(*,'("Residual 2-norm : ",es12.5)')resmx write(*,'("Residual inf-norm : ",es12.5)')resmxp write(*,'("Total memory occupation for A : ",i12)')amatsize write(*,'("Total memory occupation for DESC_A : ",i12)')descsize write(*,'("Total memory occupation for PREC : ",i12)')precsize end if call psb_gefree(b, desc_A,info) call psb_gefree(x, desc_A,info) call psb_spfree(A, desc_A,info) call mld_precfree(P,info) call psb_cdfree(desc_A,info) call psb_exit(ictxt) stop 9999 continue call psb_error(ictxt) contains ! ! get parameters from standard input ! subroutine get_parms(ictxt,choice,idim,itmax,tol) use psb_base_mod implicit none integer :: choice, idim, ictxt, itmax real(psb_dpk_) :: tol integer :: iam, np call psb_info(ictxt,iam,np) if (iam == psb_root_) then ! read input parameters call read_data(choice,5) call read_data(idim,5) call read_data(itmax,5) call read_data(tol,5) end if call psb_bcast(ictxt,choice) call psb_bcast(ictxt,idim) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) end subroutine get_parms end program mld_dexample_ml