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!
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!
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! MLD2P4 version 2.1
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! MultiLevel Domain Decomposition Parallel Preconditioners Package
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! based on PSBLAS (Parallel Sparse BLAS version 3.5)
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!
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! (C) Copyright 2008, 2010, 2012, 2015, 2017
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!
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! Salvatore Filippone Cranfield University, UK
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! Ambra Abdullahi Hassan University of Rome Tor Vergata, IT
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! Alfredo Buttari CNRS-IRIT, Toulouse, FR
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! Pasqua D'Ambra IAC-CNR, Naples, IT
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! Daniela di Serafino University of Campania "L. Vanvitelli", Caserta, IT
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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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!
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! File: ppde3d.f90
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!
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! Program: ppde3d
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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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! a1 dd(u) a2 dd(u) a3 dd(u) b1 d(u) b2 d(u) b3 d(u)
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! - ------ - ------ - ------ + ----- + ------ + ------ + c u = f
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! dxdx dydy dzdz dx dy dz
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!
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! with Dirichlet boundary conditions
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! u = g
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!
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! on the unit cube 0<=x,y,z<=1.
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!
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!
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! Note that if b1=b2=b3=c=0., the PDE is the Laplace equation.
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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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module ppde3d_mod
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contains
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!
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! functions parametrizing the differential equation
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!
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function b1(x,y,z)
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use psb_base_mod, only : psb_dpk_
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real(psb_dpk_) :: b1
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real(psb_dpk_), intent(in) :: x,y,z
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b1=1.d0/sqrt(3.d0)
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end function b1
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function b2(x,y,z)
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use psb_base_mod, only : psb_dpk_
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real(psb_dpk_) :: b2
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real(psb_dpk_), intent(in) :: x,y,z
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b2=1.d0/sqrt(3.d0)
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end function b2
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function b3(x,y,z)
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use psb_base_mod, only : psb_dpk_
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real(psb_dpk_) :: b3
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real(psb_dpk_), intent(in) :: x,y,z
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b3=1.d0/sqrt(3.d0)
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end function b3
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function c(x,y,z)
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use psb_base_mod, only : psb_dpk_
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real(psb_dpk_) :: c
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real(psb_dpk_), intent(in) :: x,y,z
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c=0.d0
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end function c
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function a1(x,y,z)
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use psb_base_mod, only : psb_dpk_
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real(psb_dpk_) :: a1
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real(psb_dpk_), intent(in) :: x,y,z
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a1=1.d0/80
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end function a1
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function a2(x,y,z)
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use psb_base_mod, only : psb_dpk_
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real(psb_dpk_) :: a2
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real(psb_dpk_), intent(in) :: x,y,z
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a2=1.d0/80
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end function a2
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function a3(x,y,z)
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use psb_base_mod, only : psb_dpk_
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real(psb_dpk_) :: a3
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real(psb_dpk_), intent(in) :: x,y,z
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a3=1.d0/80
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end function a3
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function g(x,y,z)
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use psb_base_mod, only : psb_dpk_, done, dzero
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real(psb_dpk_) :: g
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real(psb_dpk_), intent(in) :: x,y,z
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g = dzero
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if (x == done) then
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g = done
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else if (x == dzero) then
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g = exp(y**2-z**2)
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end if
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end function g
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end module ppde3d_mod
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program ppde3d
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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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use ppde3d_mod
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use mld_d_tlu_solver
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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_dpk_), parameter :: one = 1.d0
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real(psb_dpk_) :: t1, t2, tprec
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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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type(mld_d_tlu_solver_type) :: tlusv
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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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type(psb_d_vect_type) :: x,b
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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_dpk_) :: 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_dpk_) :: 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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integer :: csize ! aggregation size at which to stop.
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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_dpk_) :: cthres ! Threshold for fact. 1 ILU(T)
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integer :: cjswp ! Jacobi sweeps
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real(psb_dpk_) :: athres ! smoother aggregation threshold
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end type precdata
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type(precdata) :: prectype
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type(psb_d_coo_sparse_mat) :: acoo
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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 psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,&
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& a1,a2,a3,b1,b2,b3,c,g,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_) &
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& write(psb_out_unit,'("Overall matrix creation time : ",es12.5)')t2
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if (iam == psb_root_) &
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& write(psb_out_unit,'(" ")')
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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 prec%init(prectype%prec, info, nlev=nlv)
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call prec%set(mld_smoother_type_, prectype%smther, info)
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call prec%set(mld_smoother_sweeps_, prectype%jsweeps, info)
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call prec%set(mld_sub_ovr_, prectype%novr, info)
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call prec%set(mld_sub_restr_, prectype%restr, info)
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call prec%set(mld_sub_prol_, prectype%prol, info)
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call prec%set(tlusv,info)
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call prec%set(mld_sub_fillin_, prectype%fill1, info)
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call prec%set(mld_sub_iluthrs_, prectype%thr1, info)
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call prec%set(mld_aggr_kind_, prectype%aggrkind,info)
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call prec%set(mld_aggr_alg_, prectype%aggr_alg,info)
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call prec%set(mld_ml_type_, prectype%mltype, info)
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call prec%set(mld_smoother_pos_, prectype%smthpos, info)
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if (prectype%athres >= dzero) &
|
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|
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& call prec%set(mld_aggr_thresh_, prectype%athres, info)
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call prec%set(mld_coarse_solve_, prectype%csolve, info)
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call prec%set(mld_coarse_subsolve_, prectype%csbsolve,info)
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call prec%set(mld_coarse_mat_, prectype%cmat, info)
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|
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call prec%set(mld_coarse_fillin_, prectype%cfill, info)
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|
|
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call prec%set(mld_coarse_iluthrs_, prectype%cthres, info)
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|
|
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call prec%set(mld_coarse_sweeps_, prectype%cjswp, info)
|
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|
|
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call prec%set(mld_coarse_aggr_size_, prectype%csize, info)
|
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|
|
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else
|
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|
|
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nlv = 1
|
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|
|
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call prec%init(prectype%prec, info, nlev=nlv)
|
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|
|
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call prec%set(mld_smoother_sweeps_, prectype%jsweeps, info)
|
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|
|
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call prec%set(mld_sub_ovr_, prectype%novr, info)
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|
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call prec%set(mld_sub_restr_, prectype%restr, info)
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call prec%set(mld_sub_prol_, prectype%prol, info)
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|
|
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call prec%set(tlusv,info)
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|
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call prec%set(mld_sub_fillin_, prectype%fill1, info)
|
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|
|
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call prec%set(mld_sub_iluthrs_, prectype%thr1, info)
|
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end if
|
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|
|
|
call psb_barrier(ictxt)
|
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|
|
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t1 = psb_wtime()
|
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|
|
|
call prec%build(a,desc_a,info)
|
|
|
|
|
if(info /= psb_success_) then
|
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|
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info=psb_err_from_subroutine_
|
|
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|
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ch_err='psb_precbld'
|
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|
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call psb_errpush(info,name,a_err=ch_err)
|
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|
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goto 9999
|
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|
|
end if
|
|
|
|
|
|
|
|
|
|
tprec = psb_wtime()-t1
|
|
|
|
|
!!$ call prec%dump(info,prefix='test-ml',ac=.true.,solver=.true.,smoother=.true.)
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|
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|
|
call psb_amx(ictxt,tprec)
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|
|
if (iam == psb_root_) &
|
|
|
|
|
& write(psb_out_unit,'("Preconditioner time : ",es12.5)')tprec
|
|
|
|
|
if (iam == psb_root_) call prec%descr(info)
|
|
|
|
|
if (iam == psb_root_) &
|
|
|
|
|
& write(psb_out_unit,'(" ")')
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! iterative method parameters
|
|
|
|
|
!
|
|
|
|
|
if(iam == psb_root_) &
|
|
|
|
|
& write(psb_out_unit,'("Calling iterative method ",a)')kmethd
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
t1 = psb_wtime()
|
|
|
|
|
call psb_krylov(kmethd,a,prec,b,x,eps,desc_a,info,&
|
|
|
|
|
& itmax=itmax,iter=iter,err=err,itrace=itrace,istop=istopc,irst=irst)
|
|
|
|
|
|
|
|
|
|
if(info /= psb_success_) then
|
|
|
|
|
info=psb_err_from_subroutine_
|
|
|
|
|
ch_err='solver routine'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
t2 = psb_wtime() - t1
|
|
|
|
|
call psb_amx(ictxt,t2)
|
|
|
|
|
|
|
|
|
|
amatsize = a%sizeof()
|
|
|
|
|
descsize = desc_a%sizeof()
|
|
|
|
|
precsize = prec%sizeof()
|
|
|
|
|
call psb_sum(ictxt,amatsize)
|
|
|
|
|
call psb_sum(ictxt,descsize)
|
|
|
|
|
call psb_sum(ictxt,precsize)
|
|
|
|
|
if (iam == psb_root_) then
|
|
|
|
|
write(psb_out_unit,'(" ")')
|
|
|
|
|
write(psb_out_unit,'("Time to solve matrix : ",es12.5)') t2
|
|
|
|
|
write(psb_out_unit,'("Time per iteration : ",es12.5)') t2/iter
|
|
|
|
|
write(psb_out_unit,'("Number of iterations : ",i0)') iter
|
|
|
|
|
write(psb_out_unit,'("Convergence indicator on exit : ",es12.5)') err
|
|
|
|
|
write(psb_out_unit,'("Info on exit : ",i0)') info
|
|
|
|
|
write(psb_out_unit,'("Total memory occupation for A: ",i12)') amatsize
|
|
|
|
|
write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)') descsize
|
|
|
|
|
write(psb_out_unit,'("Total memory occupation for PREC: ",i12)') precsize
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! cleanup storage and exit
|
|
|
|
|
!
|
|
|
|
|
call psb_gefree(b,desc_a,info)
|
|
|
|
|
call psb_gefree(x,desc_a,info)
|
|
|
|
|
call psb_spfree(a,desc_a,info)
|
|
|
|
|
call prec%free(info)
|
|
|
|
|
call psb_cdfree(desc_a,info)
|
|
|
|
|
if(info /= psb_success_) then
|
|
|
|
|
info=psb_err_from_subroutine_
|
|
|
|
|
ch_err='free routine'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
call psb_exit(ictxt)
|
|
|
|
|
stop
|
|
|
|
|
|
|
|
|
|
9999 continue
|
|
|
|
|
call psb_error(ictxt)
|
|
|
|
|
|
|
|
|
|
contains
|
|
|
|
|
!
|
|
|
|
|
! get iteration parameters from standard input
|
|
|
|
|
!
|
|
|
|
|
subroutine get_parms(ictxt,kmethd,prectype,afmt,idim,istopc,itmax,itrace,irst,eps)
|
|
|
|
|
integer :: ictxt
|
|
|
|
|
type(precdata) :: prectype
|
|
|
|
|
character(len=*) :: kmethd, afmt
|
|
|
|
|
integer :: idim, istopc,itmax,itrace,irst
|
|
|
|
|
integer :: np, iam, info
|
|
|
|
|
real(psb_dpk_) :: eps
|
|
|
|
|
character(len=20) :: buffer
|
|
|
|
|
|
|
|
|
|
call psb_info(ictxt, iam, np)
|
|
|
|
|
|
|
|
|
|
if (iam == psb_root_) then
|
|
|
|
|
call read_data(kmethd,5)
|
|
|
|
|
call read_data(afmt,5)
|
|
|
|
|
call read_data(idim,5)
|
|
|
|
|
call read_data(istopc,5)
|
|
|
|
|
call read_data(itmax,5)
|
|
|
|
|
call read_data(itrace,5)
|
|
|
|
|
call read_data(irst,5)
|
|
|
|
|
call read_data(eps,5)
|
|
|
|
|
call read_data(prectype%descr,5) ! verbose description of the prec
|
|
|
|
|
call read_data(prectype%prec,5) ! overall prectype
|
|
|
|
|
call read_data(prectype%novr,5) ! number of overlap layers
|
|
|
|
|
call read_data(prectype%restr,5) ! restriction over application of as
|
|
|
|
|
call read_data(prectype%prol,5) ! prolongation over application of as
|
|
|
|
|
call read_data(prectype%solve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
|
|
|
|
|
call read_data(prectype%fill1,5) ! Fill-in for factorization 1
|
|
|
|
|
call read_data(prectype%thr1,5) ! Threshold for fact. 1 ILU(T)
|
|
|
|
|
call read_data(prectype%jsweeps,5) ! Jacobi sweeps for PJAC
|
|
|
|
|
if (psb_toupper(prectype%prec) == 'ML') then
|
|
|
|
|
call read_data(prectype%smther,5) ! Smoother type.
|
|
|
|
|
call read_data(prectype%nlev,5) ! Number of levels in multilevel prec.
|
|
|
|
|
call read_data(prectype%aggrkind,5) ! smoothed/raw aggregatin
|
|
|
|
|
call read_data(prectype%aggr_alg,5) ! local or global aggregation
|
|
|
|
|
call read_data(prectype%mltype,5) ! additive or multiplicative 2nd level prec
|
|
|
|
|
call read_data(prectype%smthpos,5) ! side: pre, post, both smoothing
|
|
|
|
|
call read_data(prectype%cmat,5) ! coarse mat
|
|
|
|
|
call read_data(prectype%csolve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
|
|
|
|
|
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
|
|
|
|
|
call read_data(prectype%athres,5) ! smoother aggr thresh
|
|
|
|
|
call read_data(prectype%csize,5) ! coarse size
|
|
|
|
|
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,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
|
|
|
|
|
call psb_bcast(ictxt,prectype%csize) ! coarse size
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
if (iam == psb_root_) then
|
|
|
|
|
write(psb_out_unit,'("Solving matrix : ell1")')
|
|
|
|
|
write(psb_out_unit,'("Grid dimensions : ",i4,"x",i4,"x",i4)')idim,idim,idim
|
|
|
|
|
write(psb_out_unit,'("Number of processors : ",i0)') np
|
|
|
|
|
write(psb_out_unit,'("Data distribution : BLOCK")')
|
|
|
|
|
write(psb_out_unit,'("Preconditioner : ",a)') prectype%descr
|
|
|
|
|
write(psb_out_unit,'("Iterative method : ",a)') kmethd
|
|
|
|
|
write(psb_out_unit,'(" ")')
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
end subroutine get_parms
|
|
|
|
|
!
|
|
|
|
|
! print an error message
|
|
|
|
|
!
|
|
|
|
|
subroutine pr_usage(iout)
|
|
|
|
|
integer :: 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
|
|
|
|
|
end program ppde3d
|
|
|
|
|
|
