! ! ! MLD2P4 version 2.1 ! MultiLevel Domain Decomposition Parallel Preconditioners Package ! based on PSBLAS (Parallel Sparse BLAS version 3.5) ! ! (C) Copyright 2008, 2010, 2012, 2015, 2017 ! ! Salvatore Filippone Cranfield University, UK ! Ambra Abdullahi Hassan University of Rome Tor Vergata, IT ! Alfredo Buttari CNRS-IRIT, Toulouse, FR ! Pasqua D'Ambra IAC-CNR, Naples, IT ! Daniela di Serafino University of Campania "L. Vanvitelli", Caserta, IT ! ! 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_dexample_1lev.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. ! 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_1lev use psb_base_mod use mld_prec_mod use psb_krylov_mod use psb_util_mod use data_input use dpde_mod implicit none ! sparse matrices type(psb_dspmat_type) :: A ! descriptor of sparse matrices 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 parameters real(psb_dpk_) :: tol, err integer :: itmax, iter, itrace, istop ! parallel environment parameters integer :: ictxt, iam, np ! other variables integer :: i,info,j integer(psb_long_int_k_) :: amatsize, precsize, descsize integer :: idim, nlev, 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,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(*,'(" ")') ! set RAS with overlap 2 and ILU(0) on the local blocks call mld_precinit(P,'AS',info) call mld_precset(P,mld_sub_ovr_,2,info) ! 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 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,idim,itmax,tol) use psb_base_mod implicit none integer :: 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(idim,5) call read_data(itmax,5) call read_data(tol,5) end if call psb_bcast(ictxt,idim) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) end subroutine get_parms end program mld_dexample_1lev