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742 lines
27 KiB
Fortran
742 lines
27 KiB
Fortran
!!$
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!!$
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!!$ MLD2P4 version 2.0
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!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
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!!$ based on PSBLAS (Parallel Sparse BLAS version 3.0)
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!!$
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!!$ (C) Copyright 2008,2009,2010
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!!$
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!!$ Salvatore Filippone University of Rome Tor Vergata
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!!$ Alfredo Buttari CNRS-IRIT, Toulouse
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!!$ Pasqua D'Ambra ICAR-CNR, Naples
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!!$ Daniela di Serafino Second University of Naples
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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 MLD2P4 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 MLD2P4 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 solves a linear system obtained by discretizing a
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! PDE with Dirichlet BCs.
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!
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!
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! The PDE is a general second order equation in 3d
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!
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! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
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! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0
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! dxdx dydy dzdz dx dy dz
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!
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! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
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!
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! Example taken from:
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! 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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! 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) = exp(-x^2-y^2-z^2)
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!
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! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
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!
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program spde
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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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use data_input
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implicit none
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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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! miscellaneous
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real(psb_spk_), parameter :: one = 1.0
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real(psb_dpk_) :: t1, t2, tprec
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! sparse matrix and preconditioner
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type(psb_sspmat_type) :: a
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type(mld_sprec_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(psb_spk_), allocatable :: b(:), x(:)
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! blacs parameters
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integer :: ictxt, iam, np
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! solver parameters
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integer :: iter, itmax,itrace, istopc, irst, nlv
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integer(psb_long_int_k_) :: amatsize, precsize, descsize
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real(psb_spk_) :: err, eps
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type precdata
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character(len=20) :: descr ! verbose description of the prec
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character(len=10) :: prec ! overall prectype
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integer :: novr ! number of overlap layers
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integer :: jsweeps ! Jacobi/smoother sweeps
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character(len=16) :: restr ! restriction over application of as
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character(len=16) :: prol ! prolongation over application of as
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character(len=16) :: solve ! Solver type: ILU, SuperLU, UMFPACK.
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integer :: fill1 ! Fill-in for factorization 1
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real(psb_spk_) :: thr1 ! Threshold for fact. 1 ILU(T)
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character(len=16) :: smther ! Smoother
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integer :: nlev ! Number of levels in multilevel prec.
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character(len=16) :: aggrkind ! smoothed/raw aggregatin
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character(len=16) :: aggr_alg ! local or global aggregation
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character(len=16) :: mltype ! additive or multiplicative 2nd level prec
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character(len=16) :: smthpos ! side: pre, post, both smoothing
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character(len=16) :: cmat ! coarse mat
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character(len=16) :: csolve ! Coarse solver: bjac, umf, slu, sludist
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character(len=16) :: csbsolve ! Coarse subsolver: ILU, ILU(T), SuperLU, UMFPACK.
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integer :: cfill ! Fill-in for factorization 1
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real(psb_spk_) :: cthres ! Threshold for fact. 1 ILU(T)
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integer :: cjswp ! Jacobi sweeps
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real(psb_spk_) :: athres ! smoother aggregation threshold
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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
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character(len=20) :: name,ch_err
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info=psb_success_
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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
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! 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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if(psb_get_errstatus() /= 0) goto 9999
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name='pde90'
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call psb_set_errverbosity(2)
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!
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! Hello world
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!
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if (iam == psb_root_) then
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write(*,*) 'Welcome to MLD2P4 version: ',mld_version_string_
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write(*,*) 'This is the ',trim(name),' sample program'
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end if
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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,eps)
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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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t1 = psb_wtime()
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call create_matrix(idim,a,b,x,desc_a,ictxt,afmt,info)
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call psb_barrier(ictxt)
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t2 = psb_wtime() - t1
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='create_matrix'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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if (iam == psb_root_) write(*,'("Overall matrix creation time : ",es12.5)')t2
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if (iam == psb_root_) write(*,'(" ")')
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!
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! prepare the preconditioner.
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!
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if (psb_toupper(prectype%prec) == 'ML') then
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nlv = prectype%nlev
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call mld_precinit(prec,prectype%prec, info, nlev=nlv)
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call mld_precset(prec,mld_smoother_type_, prectype%smther, info)
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call mld_precset(prec,mld_smoother_sweeps_, prectype%jsweeps, info)
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call mld_precset(prec,mld_sub_ovr_, prectype%novr, info)
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call mld_precset(prec,mld_sub_restr_, prectype%restr, info)
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call mld_precset(prec,mld_sub_prol_, prectype%prol, info)
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call mld_precset(prec,mld_sub_solve_, prectype%solve, info)
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call mld_precset(prec,mld_sub_fillin_, prectype%fill1, info)
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call mld_precset(prec,mld_sub_iluthrs_, prectype%thr1, info)
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call mld_precset(prec,mld_aggr_kind_, prectype%aggrkind,info)
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call mld_precset(prec,mld_aggr_alg_, prectype%aggr_alg,info)
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call mld_precset(prec,mld_ml_type_, prectype%mltype, info)
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call mld_precset(prec,mld_smoother_pos_, prectype%smthpos, info)
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if (prectype%athres >= szero) &
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& call mld_precset(prec,mld_aggr_thresh_, prectype%athres, info)
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call mld_precset(prec,mld_coarse_solve_, prectype%csolve, info)
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call mld_precset(prec,mld_coarse_subsolve_, prectype%csbsolve,info)
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call mld_precset(prec,mld_coarse_mat_, prectype%cmat, info)
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call mld_precset(prec,mld_coarse_fillin_, prectype%cfill, info)
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call mld_precset(prec,mld_coarse_iluthrs_, prectype%cthres, info)
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call mld_precset(prec,mld_coarse_sweeps_, prectype%cjswp, info)
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else
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nlv = 1
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call mld_precinit(prec,prectype%prec, info, nlev=nlv)
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call mld_precset(prec,mld_smoother_sweeps_, prectype%jsweeps, info)
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call mld_precset(prec,mld_sub_ovr_, prectype%novr, info)
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call mld_precset(prec,mld_sub_restr_, prectype%restr, info)
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call mld_precset(prec,mld_sub_prol_, prectype%prol, info)
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call mld_precset(prec,mld_sub_solve_, prectype%solve, info)
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call mld_precset(prec,mld_sub_fillin_, prectype%fill1, info)
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call mld_precset(prec,mld_sub_iluthrs_, prectype%thr1, info)
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end if
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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call mld_precbld(a,desc_a,prec,info)
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='psb_precbld'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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tprec = psb_wtime()-t1
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call psb_amx(ictxt,tprec)
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if (iam == psb_root_) write(*,'("Preconditioner time : ",es12.5)')tprec
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if (iam == psb_root_) call mld_precdescr(prec,info)
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if (iam == psb_root_) write(*,'(" ")')
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!
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! iterative method parameters
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!
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if(iam == psb_root_) write(*,'("Calling iterative method ",a)')kmethd
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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call psb_krylov(kmethd,a,prec,b,x,eps,desc_a,info,&
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& itmax=itmax,iter=iter,err=err,itrace=itrace,istop=istopc,irst=irst)
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='solver routine'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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call psb_barrier(ictxt)
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t2 = psb_wtime() - t1
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call psb_amx(ictxt,t2)
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amatsize = psb_sizeof(a)
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descsize = psb_sizeof(desc_a)
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precsize = mld_sizeof(prec)
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call psb_sum(ictxt,amatsize)
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call psb_sum(ictxt,descsize)
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call psb_sum(ictxt,precsize)
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if (iam == psb_root_) then
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write(*,'(" ")')
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write(*,'("Time to solve matrix : ",es12.5)')t2
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write(*,'("Time per iteration : ",es12.5)')t2/iter
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write(*,'("Number of iterations : ",i0)')iter
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write(*,'("Convergence indicator on exit : ",es12.5)')err
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write(*,'("Info on exit : ",i0)')info
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write(*,'("Total memory occupation for A: ",i12)')amatsize
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write(*,'("Total memory occupation for DESC_A: ",i12)')descsize
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write(*,'("Total memory occupation for PREC: ",i12)')precsize
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end if
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!
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! cleanup storage and exit
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!
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call psb_gefree(b,desc_a,info)
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call psb_gefree(x,desc_a,info)
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call psb_spfree(a,desc_a,info)
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call mld_precfree(prec,info)
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call psb_cdfree(desc_a,info)
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='free routine'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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|
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9999 continue
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if(info /= psb_success_) then
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call psb_error(ictxt)
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end if
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call psb_exit(ictxt)
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stop
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contains
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!
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! get iteration parameters from standard input
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!
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subroutine get_parms(ictxt,kmethd,prectype,afmt,idim,istopc,itmax,itrace,irst,eps)
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integer :: ictxt
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type(precdata) :: prectype
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character(len=*) :: kmethd, afmt
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integer :: idim, istopc,itmax,itrace,irst
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integer :: np, iam, info
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real(psb_spk_) :: eps
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character(len=20) :: buffer
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|
|
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call psb_info(ictxt, iam, np)
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|
|
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if (iam == psb_root_) then
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call read_data(kmethd,5)
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call read_data(afmt,5)
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call read_data(idim,5)
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call read_data(istopc,5)
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call read_data(itmax,5)
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call read_data(itrace,5)
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call read_data(irst,5)
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call read_data(eps,5)
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call read_data(prectype%descr,5) ! verbose description of the prec
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call read_data(prectype%prec,5) ! overall prectype
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call read_data(prectype%novr,5) ! number of overlap layers
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call read_data(prectype%restr,5) ! restriction over application of as
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call read_data(prectype%prol,5) ! prolongation over application of as
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call read_data(prectype%solve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
|
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call read_data(prectype%fill1,5) ! Fill-in for factorization 1
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call read_data(prectype%thr1,5) ! Threshold for fact. 1 ILU(T)
|
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call read_data(prectype%jsweeps,5) ! Jacobi sweeps for PJAC
|
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if (psb_toupper(prectype%prec) == 'ML') then
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call read_data(prectype%smther,5) ! Smoother type.
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call read_data(prectype%nlev,5) ! Number of levels in multilevel prec.
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call read_data(prectype%aggrkind,5) ! smoothed/raw aggregatin
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call read_data(prectype%aggr_alg,5) ! local or global aggregation
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call read_data(prectype%mltype,5) ! additive or multiplicative 2nd level prec
|
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call read_data(prectype%smthpos,5) ! side: pre, post, both smoothing
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call read_data(prectype%cmat,5) ! coarse mat
|
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call read_data(prectype%csolve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
|
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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
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call read_data(prectype%athres,5) ! smoother aggr thresh
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|
end if
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end if
|
|
|
|
! broadcast parameters to all processors
|
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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)
|
|
|
|
|
|
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)
|
|
call psb_bcast(ictxt,prectype%jsweeps) ! Jacobi sweeps
|
|
if (psb_toupper(prectype%prec) == 'ML') then
|
|
call psb_bcast(ictxt,prectype%smther) ! Smoother type.
|
|
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%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,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
|
|
!
|
|
! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
|
|
!
|
|
! Boundary conditions are set in a very simple way, by adding
|
|
! equations of the form
|
|
!
|
|
! u(x,y) = exp(-x^2-y^2-z^2)
|
|
!
|
|
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
|
|
!
|
|
use psb_base_mod
|
|
implicit none
|
|
integer :: idim
|
|
integer, parameter :: nb=20
|
|
real(psb_spk_), allocatable :: b(:),xv(:)
|
|
type(psb_desc_type) :: desc_a
|
|
integer :: ictxt, info
|
|
character :: afmt*5
|
|
type(psb_sspmat_type) :: a
|
|
real(psb_spk_) :: zt(nb),x,y,z
|
|
integer :: m,n,nnz,glob_row,nlr,i,ii,ib,k
|
|
integer :: ix,iy,iz,ia,indx_owner
|
|
integer :: np, iam, nr, nt
|
|
integer :: element
|
|
integer, allocatable :: irow(:),icol(:),myidx(:)
|
|
real(psb_spk_), allocatable :: val(:)
|
|
! deltah dimension of each grid cell
|
|
! deltat discretization time
|
|
real(psb_spk_) :: deltah, deltah2
|
|
real(psb_spk_),parameter :: rhs=0.0,one=1.0,zero=0.0
|
|
real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen
|
|
real(psb_spk_) :: a1, a2, a3, a4, b1, b2, b3
|
|
external :: a1, a2, a3, a4, b1, b2, b3
|
|
integer :: err_act
|
|
|
|
character(len=20) :: name, ch_err
|
|
|
|
info = psb_success_
|
|
name = 'create_matrix'
|
|
call psb_erractionsave(err_act)
|
|
|
|
call psb_info(ictxt, iam, np)
|
|
|
|
deltah = 1.d0/(idim-1)
|
|
deltah2 = deltah*deltah
|
|
|
|
! 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(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n
|
|
|
|
!
|
|
! Using a simple BLOCK distribution.
|
|
!
|
|
nt = (m+np-1)/np
|
|
nr = max(0,min(nt,m-(iam*nt)))
|
|
|
|
nt = nr
|
|
call psb_sum(ictxt,nt)
|
|
if (nt /= m) write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m
|
|
call psb_barrier(ictxt)
|
|
t0 = psb_wtime()
|
|
call psb_cdall(ictxt,desc_a,info,nl=nr)
|
|
if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz)
|
|
! define rhs from boundary conditions; also build initial guess
|
|
if (info == psb_success_) call psb_geall(b,desc_a,info)
|
|
if (info == psb_success_) call psb_geall(xv,desc_a,info)
|
|
nlr = psb_cd_get_local_rows(desc_a)
|
|
call psb_barrier(ictxt)
|
|
talc = psb_wtime()-t0
|
|
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_
|
|
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*nb),irow(20*nb),&
|
|
&icol(20*nb),myidx(nlr),stat=info)
|
|
if (info /= psb_success_ ) then
|
|
info=psb_err_alloc_dealloc_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
endif
|
|
|
|
do i=1,nlr
|
|
myidx(i) = i
|
|
end do
|
|
|
|
|
|
call psb_loc_to_glob(myidx,desc_a,info)
|
|
|
|
! loop over rows belonging to current process in a block
|
|
! distribution.
|
|
|
|
call psb_barrier(ictxt)
|
|
t1 = psb_wtime()
|
|
do ii=1, nlr,nb
|
|
ib = min(nb,nlr-ii+1)
|
|
element = 1
|
|
do k=1,ib
|
|
i=ii+k-1
|
|
! local matrix pointer
|
|
glob_row=myidx(i)
|
|
! compute gridpoint coordinates
|
|
if (mod(glob_row,(idim*idim)) == 0) then
|
|
ix = glob_row/(idim*idim)
|
|
else
|
|
ix = glob_row/(idim*idim)+1
|
|
endif
|
|
if (mod((glob_row-(ix-1)*idim*idim),idim) == 0) then
|
|
iy = (glob_row-(ix-1)*idim*idim)/idim
|
|
else
|
|
iy = (glob_row-(ix-1)*idim*idim)/idim+1
|
|
endif
|
|
iz = glob_row-(ix-1)*idim*idim-(iy-1)*idim
|
|
! x, y, x coordinates
|
|
x = ix*deltah
|
|
y = iy*deltah
|
|
z = iz*deltah
|
|
|
|
! check on boundary points
|
|
zt(k) = 0.d0
|
|
! internal point: build discretization
|
|
!
|
|
! term depending on (x-1,y,z)
|
|
!
|
|
if (ix == 1) then
|
|
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
|
|
zt(k) = exp(-x**2-y**2-z**2)*(-val(element))
|
|
else
|
|
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
|
|
icol(element) = (ix-2)*idim*idim+(iy-1)*idim+(iz)
|
|
irow(element) = glob_row
|
|
element = element+1
|
|
endif
|
|
! term depending on (x,y-1,z)
|
|
if (iy == 1) then
|
|
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
|
|
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
|
|
else
|
|
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
|
|
icol(element) = (ix-1)*idim*idim+(iy-2)*idim+(iz)
|
|
irow(element) = glob_row
|
|
element = element+1
|
|
endif
|
|
! term depending on (x,y,z-1)
|
|
if (iz == 1) then
|
|
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
|
|
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
|
|
else
|
|
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
|
|
icol(element) = (ix-1)*idim*idim+(iy-1)*idim+(iz-1)
|
|
irow(element) = glob_row
|
|
element = element+1
|
|
endif
|
|
! term depending on (x,y,z)
|
|
val(element)=(2*b1(x,y,z) + 2*b2(x,y,z) + 2*b3(x,y,z))/deltah2&
|
|
& + (a1(x,y,z) + a2(x,y,z) + a3(x,y,z)+ a4(x,y,z))/deltah
|
|
icol(element) = (ix-1)*idim*idim+(iy-1)*idim+(iz)
|
|
irow(element) = glob_row
|
|
element = element+1
|
|
! term depending on (x,y,z+1)
|
|
if (iz == idim) then
|
|
val(element)=-b1(x,y,z)/deltah2
|
|
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
|
|
else
|
|
val(element)=-b1(x,y,z)/deltah2
|
|
icol(element) = (ix-1)*idim*idim+(iy-1)*idim+(iz+1)
|
|
irow(element) = glob_row
|
|
element = element+1
|
|
endif
|
|
! term depending on (x,y+1,z)
|
|
if (iy == idim) then
|
|
val(element)=-b2(x,y,z)/deltah2
|
|
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
|
|
else
|
|
val(element)=-b2(x,y,z)/deltah2
|
|
icol(element) = (ix-1)*idim*idim+(iy)*idim+(iz)
|
|
irow(element) = glob_row
|
|
element = element+1
|
|
endif
|
|
! term depending on (x+1,y,z)
|
|
if (iy == idim) then
|
|
val(element)=-b2(x,y,z)/deltah2
|
|
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
|
|
else
|
|
val(element)=-b3(x,y,z)/deltah2
|
|
icol(element) = (ix)*idim*idim+(iy-1)*idim+(iz)
|
|
irow(element) = glob_row
|
|
element = element+1
|
|
endif
|
|
|
|
end do
|
|
call psb_spins(element-1,irow,icol,val,a,desc_a,info)
|
|
if(info /= psb_success_) exit
|
|
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),b,desc_a,info)
|
|
if(info /= psb_success_) exit
|
|
zt(:)=0.d0
|
|
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xv,desc_a,info)
|
|
if(info /= psb_success_) exit
|
|
end do
|
|
|
|
tgen = psb_wtime()-t1
|
|
if(info /= psb_success_) then
|
|
info=psb_err_from_subroutine_
|
|
ch_err='insert rout.'
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
goto 9999
|
|
end if
|
|
|
|
deallocate(val,irow,icol)
|
|
|
|
call psb_barrier(ictxt)
|
|
t1 = psb_wtime()
|
|
call psb_cdasb(desc_a,info)
|
|
if (info == psb_success_) &
|
|
& call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_,afmt=afmt)
|
|
call psb_barrier(ictxt)
|
|
if(info /= psb_success_) then
|
|
info=psb_err_from_subroutine_
|
|
ch_err='asb rout.'
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
goto 9999
|
|
end if
|
|
call psb_geasb(b,desc_a,info)
|
|
call psb_geasb(xv,desc_a,info)
|
|
if(info /= psb_success_) then
|
|
info=psb_err_from_subroutine_
|
|
ch_err='asb rout.'
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
goto 9999
|
|
end if
|
|
tasb = psb_wtime()-t1
|
|
call psb_barrier(ictxt)
|
|
ttot = psb_wtime() - t0
|
|
|
|
call psb_amx(ictxt,talc)
|
|
call psb_amx(ictxt,tgen)
|
|
call psb_amx(ictxt,tasb)
|
|
call psb_amx(ictxt,ttot)
|
|
if(iam == psb_root_) then
|
|
ch_err = a%get_fmt()
|
|
write(*,'("The matrix has been generated and assembled in ",a3," format.")')&
|
|
& ch_err(1:3)
|
|
write(*,'("-allocation time : ",es12.5)') talc
|
|
write(*,'("-coeff. gen. time : ",es12.5)') tgen
|
|
write(*,'("-assembly time : ",es12.5)') tasb
|
|
write(*,'("-total time : ",es12.5)') ttot
|
|
|
|
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 spde
|
|
!
|
|
! functions parametrizing the differential equation
|
|
!
|
|
function a1(x,y,z)
|
|
use psb_base_mod, only : psb_spk_
|
|
real(psb_spk_) :: a1
|
|
real(psb_spk_) :: x,y,z
|
|
a1=1.e0
|
|
end function a1
|
|
function a2(x,y,z)
|
|
use psb_base_mod, only : psb_spk_
|
|
real(psb_spk_) :: a2
|
|
real(psb_spk_) :: x,y,z
|
|
a2=2.e1*y
|
|
end function a2
|
|
function a3(x,y,z)
|
|
use psb_base_mod, only : psb_spk_
|
|
real(psb_spk_) :: a3
|
|
real(psb_spk_) :: x,y,z
|
|
a3=1.e0
|
|
end function a3
|
|
function a4(x,y,z)
|
|
use psb_base_mod, only : psb_spk_
|
|
real(psb_spk_) :: a4
|
|
real(psb_spk_) :: x,y,z
|
|
a4=1.e0
|
|
end function a4
|
|
function b1(x,y,z)
|
|
use psb_base_mod, only : psb_spk_
|
|
real(psb_spk_) :: b1
|
|
real(psb_spk_) :: x,y,z
|
|
b1=1.e0
|
|
end function b1
|
|
function b2(x,y,z)
|
|
use psb_base_mod, only : psb_spk_
|
|
real(psb_spk_) :: b2
|
|
real(psb_spk_) :: x,y,z
|
|
b2=1.e0
|
|
end function b2
|
|
function b3(x,y,z)
|
|
use psb_base_mod, only : psb_spk_
|
|
real(psb_spk_) :: b3
|
|
real(psb_spk_) :: x,y,z
|
|
b3=1.e0
|
|
end function b3
|
|
|
|
|