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!!$
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!!$ Parallel Sparse BLAS v2.0
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!!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata
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!!$ Alfredo Buttari University of Rome Tor Vergata
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!!$
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!!$ Redistribution and use in source and binary forms, with or without
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!!$ modification, are permitted provided that the following conditions
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!!$ are met:
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!!$ 1. Redistributions of source code must retain the above copyright
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!!$ notice, this list of conditions and the following disclaimer.
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!!$ 2. Redistributions in binary form must reproduce the above copyright
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!!$ notice, this list of conditions, and the following disclaimer in the
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!!$ documentation and/or other materials provided with the distribution.
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!!$ 3. The name of the PSBLAS group or the names of its contributors may
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!!$ not be used to endorse or promote products derived from this
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!!$ software without specific written permission.
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!!$
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!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
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!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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!!$ POSSIBILITY OF SUCH DAMAGE.
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!!$
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!!$
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! File: ppde.f90
|
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|
!
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|
|
! Program: ppde
|
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|
|
|
! This sample program shows how to build and solve a sparse linear
|
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!
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! The program solves a linear system based on the partial differential
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! equation
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!
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!
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!
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! The equation generated is
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!
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! b1 d d (u) b2 d d (u) a1 d (u)) a2 d (u)))
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! - ------ - ------ + ----- + ------ + a3 u = 0
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! dx dx dy dy dx dy
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!
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!
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! with Dirichlet boundary conditions on the unit cube
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!
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! 0<=x,y,z<=1
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!
|
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|
|
! The equation is discretized with finite differences and uniform stepsize;
|
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|
|
! the resulting discrete equation is
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|
!
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! ( u(x,y,z)(2b1+2b2+a1+a2)+u(x-1,y)(-b1-a1)+u(x,y-1)(-b2-a2)+
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|
|
|
! -u(x+1,y)b1-u(x,y+1)b2)*(1/h**2)
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|
|
!
|
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|
|
|
! Example taken from: C.T.Kelley
|
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|
|
! Iterative Methods for Linear and Nonlinear Equations
|
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|
|
! SIAM 1995
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!
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!
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|
|
! In this sample program the index space of the discretized
|
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|
! computational domain is first numbered sequentially in a standard way,
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! then the corresponding vector is distributed according to a BLOCK
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! data distribution.
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!
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|
! Boundary conditions are set in a very simple way, by adding
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|
! equations of the form
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!
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! u(x,y) = rhs(x,y)
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!
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|
|
program ppde
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|
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use psb_base_mod
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use mld_prec_mod
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use psb_krylov_mod
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use psb_util_mod
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|
|
implicit none
|
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|
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|
|
|
|
|
|
! input parameters
|
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|
|
character(len=20) :: kmethd, ptype
|
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|
|
character(len=5) :: afmt
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|
|
integer :: idim
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|
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|
|
! miscellaneous
|
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|
|
real(kind(1.d0)), parameter :: one = 1.d0
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|
|
real(kind(1.d0)) :: t1, t2, tprec
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|
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|
|
! sparse matrix and preconditioner
|
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|
|
type(psb_dspmat_type) :: a
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|
|
type(mld_dprec_type) :: prec
|
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|
|
! descriptor
|
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|
|
type(psb_desc_type) :: desc_a
|
|
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|
|
! dense matrices
|
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|
|
real(kind(1.d0)), allocatable :: b(:), x(:)
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|
|
|
|
! blacs parameters
|
|
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|
|
integer :: ictxt, iam, np
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|
|
|
|
|
|
|
|
|
! solver parameters
|
|
|
|
|
integer :: iter, itmax,itrace, istopc, irst
|
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|
|
|
real(kind(1.d0)) :: err, eps
|
|
|
|
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|
|
|
|
type precdata
|
|
|
|
|
character(len=10) :: lv1, lvn ! First level(s) and last level prec type
|
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|
|
integer :: nlev !
|
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|
|
integer :: novr ! number of overlapping levels
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|
|
integer :: restr ! restriction over application of as
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|
|
integer :: prol ! prolongation over application of as
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|
|
integer :: ftype1 ! Factorization type: ILU, SuperLU, UMFPACK.
|
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|
|
integer :: fill1 ! Fill-in for factorization 1
|
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|
|
real(kind(1.d0)) :: thr1 ! Threshold for fact. 1 ILU(T)
|
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|
|
|
integer :: mltype ! additive or multiplicative 2nd level prec
|
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|
|
integer :: aggr ! local or global aggregation
|
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|
|
integer :: smthkind ! smoothing type
|
|
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|
|
integer :: cmat ! coarse mat
|
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|
|
integer :: smthpos ! pre, post, both smoothing
|
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|
|
integer :: glbsmth ! global smoothing
|
|
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|
|
integer :: ftype2 ! Factorization type: ILU, SuperLU, UMFPACK.
|
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|
|
|
integer :: fill2 ! Fill-in for factorization 1
|
|
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|
|
real(kind(1.d0)) :: thr2 ! Threshold for fact. 1 ILU(T)
|
|
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|
|
integer :: jswp ! Jacobi sweeps
|
|
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|
|
real(kind(1.d0)) :: omega ! smoother omega
|
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|
|
character(len=20) :: descr ! verbose description of the prec
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|
|
end type precdata
|
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|
|
type(precdata) :: prectype
|
|
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|
|
! other variables
|
|
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|
|
integer :: info
|
|
|
|
|
character(len=20) :: name,ch_err
|
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|
|
|
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|
|
|
if(psb_get_errstatus() /= 0) goto 9999
|
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|
|
info=0
|
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|
|
name='pde90'
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|
|
|
call psb_set_errverbosity(2)
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|
|
call psb_set_erraction(0)
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|
|
call psb_init(ictxt)
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|
|
call psb_info(ictxt,iam,np)
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|
|
if (iam < 0) then
|
|
|
|
|
! This should not happen, but just in case
|
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|
|
call psb_exit(ictxt)
|
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|
|
|
stop
|
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|
|
|
endif
|
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|
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|
|
!
|
|
|
|
|
! get parameters
|
|
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|
|
!
|
|
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|
|
call get_parms(ictxt,kmethd,prectype,afmt,idim,istopc,itmax,itrace,irst)
|
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|
|
|
|
|
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|
|
!
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|
|
|
|
! allocate and fill in the coefficient matrix, rhs and initial guess
|
|
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|
|
!
|
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|
|
call psb_barrier(ictxt)
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|
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|
|
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 (prectype%nlev > 1) then
|
|
|
|
|
call mld_precinit(prec,prectype%lvn,info,nlev=prectype%nlev)
|
|
|
|
|
if (prectype%omega>=0.0) then
|
|
|
|
|
call mld_precset(prec,mld_aggr_damp_,prectype%omega,info,ilev=prectype%nlev)
|
|
|
|
|
end if
|
|
|
|
|
call mld_precset(prec,mld_ml_type_, prectype%mltype, info,ilev=prectype%nlev)
|
|
|
|
|
call mld_precset(prec,mld_aggr_alg_, prectype%aggr, info,ilev=prectype%nlev)
|
|
|
|
|
call mld_precset(prec,mld_coarse_mat_, prectype%cmat, info,ilev=prectype%nlev)
|
|
|
|
|
call mld_precset(prec,mld_smooth_pos_, prectype%smthpos, info,ilev=prectype%nlev)
|
|
|
|
|
call mld_precset(prec,mld_sub_solve_, prectype%ftype2, info,ilev=prectype%nlev)
|
|
|
|
|
call mld_precset(prec,mld_sub_fill_in_, prectype%fill2, info,ilev=prectype%nlev)
|
|
|
|
|
call mld_precset(prec,mld_fact_thrs_, prectype%thr2, info,ilev=prectype%nlev)
|
|
|
|
|
call mld_precset(prec,mld_smooth_sweeps_, prectype%jswp, info,ilev=prectype%nlev)
|
|
|
|
|
call mld_precset(prec,mld_aggr_kind_, prectype%smthkind, info,ilev=prectype%nlev)
|
|
|
|
|
else
|
|
|
|
|
call mld_precinit(prec,prectype%lv1,info)
|
|
|
|
|
endif
|
|
|
|
|
call mld_precset(prec,mld_n_ovr_, prectype%novr, info,ilev=1)
|
|
|
|
|
call mld_precset(prec,mld_sub_restr_, prectype%restr, info,ilev=1)
|
|
|
|
|
call mld_precset(prec,mld_sub_prol_, prectype%prol, info,ilev=1)
|
|
|
|
|
call mld_precset(prec,mld_sub_solve_, prectype%ftype1, info,ilev=1)
|
|
|
|
|
call mld_precset(prec,mld_sub_fill_in_, prectype%fill1, info,ilev=1)
|
|
|
|
|
call mld_precset(prec,mld_fact_thrs_, prectype%thr1, info,ilev=1)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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_prec_descr(6,prec)
|
|
|
|
|
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
|
|
|
|
|
read(*,*) kmethd
|
|
|
|
|
read(*,*) afmt
|
|
|
|
|
read(*,*) idim
|
|
|
|
|
read(*,*) istopc
|
|
|
|
|
read(*,*) itmax
|
|
|
|
|
read(*,*) itrace
|
|
|
|
|
read(*,*) irst
|
|
|
|
|
read(*,*) prectype%descr
|
|
|
|
|
read(*,*) prectype%nlev
|
|
|
|
|
read(*,*) prectype%lv1
|
|
|
|
|
read(*,*) buffer
|
|
|
|
|
call get_stringval(buffer,prectype%ftype1,info)
|
|
|
|
|
read(*,*) prectype%fill1
|
|
|
|
|
read(*,*) prectype%thr1
|
|
|
|
|
read(*,*) prectype%novr
|
|
|
|
|
read(*,*) buffer
|
|
|
|
|
call get_stringval(buffer,prectype%restr,info)
|
|
|
|
|
read(*,*) buffer
|
|
|
|
|
call get_stringval(buffer,prectype%prol,info)
|
|
|
|
|
if (prectype%nlev>1) then
|
|
|
|
|
read(*,*) prectype%lvn
|
|
|
|
|
read(*,*) buffer
|
|
|
|
|
call get_stringval(buffer,prectype%mltype,info)
|
|
|
|
|
read(*,*) buffer
|
|
|
|
|
call get_stringval(buffer,prectype%aggr,info)
|
|
|
|
|
read(*,*) buffer
|
|
|
|
|
call get_stringval(buffer,prectype%smthkind,info)
|
|
|
|
|
read(*,*) buffer
|
|
|
|
|
call get_stringval(buffer,prectype%cmat,info)
|
|
|
|
|
read(*,*) buffer
|
|
|
|
|
call get_stringval(buffer,prectype%smthpos,info)
|
|
|
|
|
read(*,*) buffer
|
|
|
|
|
call get_stringval(buffer,prectype%ftype2,info)
|
|
|
|
|
read(*,*) prectype%fill2
|
|
|
|
|
read(*,*) prectype%thr2
|
|
|
|
|
read(*,*) prectype%jswp
|
|
|
|
|
read(*,*) prectype%omega
|
|
|
|
|
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)
|
|
|
|
|
call psb_bcast(ictxt,prectype%nlev)
|
|
|
|
|
call psb_bcast(ictxt,prectype%lv1)
|
|
|
|
|
call psb_bcast(ictxt,prectype%ftype1)
|
|
|
|
|
call psb_bcast(ictxt,prectype%fill1)
|
|
|
|
|
call psb_bcast(ictxt,prectype%thr1)
|
|
|
|
|
call psb_bcast(ictxt,prectype%novr)
|
|
|
|
|
call psb_bcast(ictxt,prectype%restr)
|
|
|
|
|
call psb_bcast(ictxt,prectype%prol)
|
|
|
|
|
if (prectype%nlev>1) then
|
|
|
|
|
call psb_bcast(ictxt,prectype%lvn )
|
|
|
|
|
call psb_bcast(ictxt,prectype%mltype )
|
|
|
|
|
call psb_bcast(ictxt,prectype%aggr )
|
|
|
|
|
call psb_bcast(ictxt,prectype%smthkind )
|
|
|
|
|
call psb_bcast(ictxt,prectype%cmat )
|
|
|
|
|
call psb_bcast(ictxt,prectype%smthpos )
|
|
|
|
|
call psb_bcast(ictxt,prectype%ftype2 )
|
|
|
|
|
call psb_bcast(ictxt,prectype%fill2 )
|
|
|
|
|
call psb_bcast(ictxt,prectype%thr2 )
|
|
|
|
|
call psb_bcast(ictxt,prectype%jswp )
|
|
|
|
|
call psb_bcast(ictxt,prectype%omega )
|
|
|
|
|
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
|
|
|
|
|
|
|
|
|
|
subroutine get_stringval(string,val,info)
|
|
|
|
|
character(len=*), intent(in) :: string
|
|
|
|
|
integer, intent(out) :: val, info
|
|
|
|
|
|
|
|
|
|
info = 0
|
|
|
|
|
select case(toupper(trim(string)))
|
|
|
|
|
case('NONE')
|
|
|
|
|
val = 0
|
|
|
|
|
case('HALO')
|
|
|
|
|
val = psb_halo_
|
|
|
|
|
case('SUM')
|
|
|
|
|
val = psb_sum_
|
|
|
|
|
case('AVG')
|
|
|
|
|
val = psb_avg_
|
|
|
|
|
case('ILU')
|
|
|
|
|
val = mld_ilu_n_
|
|
|
|
|
case('MILU')
|
|
|
|
|
val = mld_milu_n_
|
|
|
|
|
case('ILUT')
|
|
|
|
|
val = mld_ilu_t_
|
|
|
|
|
case('SLU')
|
|
|
|
|
val = mld_slu_
|
|
|
|
|
case('UMFP')
|
|
|
|
|
val = mld_umf_
|
|
|
|
|
case('ADD')
|
|
|
|
|
val = mld_add_ml_
|
|
|
|
|
case('MULT')
|
|
|
|
|
val = mld_mult_ml_
|
|
|
|
|
case('DEC')
|
|
|
|
|
val = mld_dec_aggr_
|
|
|
|
|
case('REPL')
|
|
|
|
|
val = mld_repl_mat_
|
|
|
|
|
case('DIST')
|
|
|
|
|
val = mld_distr_mat_
|
|
|
|
|
case('SYMDEC')
|
|
|
|
|
val = mld_sym_dec_aggr_
|
|
|
|
|
case('GLB')
|
|
|
|
|
val = mld_glb_aggr_
|
|
|
|
|
case('SMOOTH')
|
|
|
|
|
val = mld_smooth_prol_
|
|
|
|
|
case('PRE')
|
|
|
|
|
val = mld_pre_smooth_
|
|
|
|
|
case('POST')
|
|
|
|
|
val = mld_post_smooth_
|
|
|
|
|
case('TWOSIDE','BOTH')
|
|
|
|
|
val = mld_twoside_smooth_
|
|
|
|
|
case default
|
|
|
|
|
val = -1
|
|
|
|
|
info = -1
|
|
|
|
|
end select
|
|
|
|
|
if (info /= 0) then
|
|
|
|
|
write(0,*) 'Error in get_Stringval: unknown: "',trim(string),'"'
|
|
|
|
|
end if
|
|
|
|
|
end subroutine get_stringval
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! 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(kind(1.d0)), 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(kind(1.d0)) :: 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(kind(1.d0)), allocatable :: val(:)
|
|
|
|
|
integer, allocatable :: prv(:)
|
|
|
|
|
! deltah dimension of each grid cell
|
|
|
|
|
! deltat discretization time
|
|
|
|
|
real(kind(1.d0)) :: deltah
|
|
|
|
|
real(kind(1.d0)),parameter :: rhs=0.d0,one=1.d0,zero=0.d0
|
|
|
|
|
real(kind(1.d0)) :: t1, t2, t3, tins, tasb
|
|
|
|
|
real(kind(1.d0)) :: 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<idim) then
|
|
|
|
|
val(element)=-b3(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
icol(element)=(x)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
element=element+1
|
|
|
|
|
endif
|
|
|
|
|
irow(1:element-1)=glob_row
|
|
|
|
|
ia=glob_row
|
|
|
|
|
|
|
|
|
|
t3 = psb_wtime()
|
|
|
|
|
call psb_spins(element-1,irow,icol,val,a,desc_a,info)
|
|
|
|
|
if(info /= 0) exit
|
|
|
|
|
tins = tins + (psb_wtime()-t3)
|
|
|
|
|
call psb_geins(1,(/ia/),zt(1:1),b,desc_a,info)
|
|
|
|
|
if(info /= 0) exit
|
|
|
|
|
zt(1)=0.d0
|
|
|
|
|
call psb_geins(1,(/ia/),zt(1:1),xv,desc_a,info)
|
|
|
|
|
if(info /= 0) exit
|
|
|
|
|
end if
|
|
|
|
|
end do
|
|
|
|
|
end do
|
|
|
|
|
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
t2 = psb_wtime()-t1
|
|
|
|
|
|
|
|
|
|
if(info /= 0) then
|
|
|
|
|
info=4010
|
|
|
|
|
ch_err='insert rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
deallocate(val,irow,icol)
|
|
|
|
|
|
|
|
|
|
t1 = psb_wtime()
|
|
|
|
|
call psb_cdasb(desc_a,info)
|
|
|
|
|
call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_,afmt=afmt)
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
tasb = psb_wtime()-t1
|
|
|
|
|
if(info /= 0) then
|
|
|
|
|
info=4010
|
|
|
|
|
ch_err='asb rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
call psb_amx(ictxt,t2)
|
|
|
|
|
call psb_amx(ictxt,tins)
|
|
|
|
|
call psb_amx(ictxt,tasb)
|
|
|
|
|
|
|
|
|
|
if(iam == psb_root_) then
|
|
|
|
|
write(*,'("The matrix has been generated and assembeld in ",a3," format.")')&
|
|
|
|
|
& a%fida(1:3)
|
|
|
|
|
write(*,'("-pspins time : ",es10.4)')tins
|
|
|
|
|
write(*,'("-insert time : ",es10.4)')t2
|
|
|
|
|
write(*,'("-assembly time : ",es10.4)')tasb
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
call psb_geasb(b,desc_a,info)
|
|
|
|
|
call psb_geasb(xv,desc_a,info)
|
|
|
|
|
if(info /= 0) then
|
|
|
|
|
info=4010
|
|
|
|
|
ch_err='asb rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
9999 continue
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
if (err_act == psb_act_abort_) then
|
|
|
|
|
call psb_error(ictxt)
|
|
|
|
|
return
|
|
|
|
|
end if
|
|
|
|
|
return
|
|
|
|
|
end subroutine create_matrix
|
|
|
|
|
end program ppde
|
|
|
|
|
!
|
|
|
|
|
! functions parametrizing the differential equation
|
|
|
|
|
!
|
|
|
|
|
function a1(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: a1
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
a1=1.d0
|
|
|
|
|
end function a1
|
|
|
|
|
function a2(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: a2
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
a2=2.d1*y
|
|
|
|
|
end function a2
|
|
|
|
|
function a3(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: a3
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
a3=1.d0
|
|
|
|
|
end function a3
|
|
|
|
|
function a4(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: a4
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
a4=1.d0
|
|
|
|
|
end function a4
|
|
|
|
|
function b1(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: b1
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
b1=1.d0
|
|
|
|
|
end function b1
|
|
|
|
|
function b2(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: b2
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
b2=1.d0
|
|
|
|
|
end function b2
|
|
|
|
|
function b3(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: b3
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
b3=1.d0
|
|
|
|
|
end function b3
|
|
|
|
|
|
|
|
|
|
|
