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529 lines
22 KiB
Fortran
529 lines
22 KiB
Fortran
!!!$
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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 3.4)
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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
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!!$ Ambra Abdullahi Hassan 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 University of Campania "L. Vanvitelli", Caserta
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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: mld_d_pde2d.f90
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!
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! Program: mld_d_pde2d
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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 2d
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!
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! a1 dd(u) a2 dd(u) b1 d(u) b2 d(u)
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! - ------ - ------ ----- + ------ + c u = f
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! dxdx dydy dx dy
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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 square 0<=x,y<=1.
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!
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!
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! Note that if b1=b2=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 mld_d_pde2d_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)
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use psb_base_mod, only : psb_dpk_,done,dzero
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real(psb_dpk_) :: b1
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real(psb_dpk_), intent(in) :: x,y
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b1=dzero/sqrt((2*done))
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end function b1
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function b2(x,y)
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use psb_base_mod, only : psb_dpk_,done,dzero
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real(psb_dpk_) :: b2
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real(psb_dpk_), intent(in) :: x,y
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b2=dzero/sqrt((2*done))
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end function b2
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function c(x,y)
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use psb_base_mod, only : psb_dpk_,done,dzero
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real(psb_dpk_) :: c
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real(psb_dpk_), intent(in) :: x,y
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c=dzero
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end function c
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function a1(x,y)
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use psb_base_mod, only : psb_dpk_,done,dzero
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real(psb_dpk_) :: a1
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real(psb_dpk_), intent(in) :: x,y
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a1=done!/80
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end function a1
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function a2(x,y)
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use psb_base_mod, only : psb_dpk_,done,dzero
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real(psb_dpk_) :: a2
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real(psb_dpk_), intent(in) :: x,y
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a2=done!/80
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end function a2
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function g(x,y)
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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
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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)
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end if
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end function g
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end module mld_d_pde2d_mod
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program mld_d_pde2d
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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 mld_d_pde2d_mod
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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(psb_ipk_) :: idim
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! miscellaneous
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real(psb_dpk_) :: t1, t2, tprec, thier, tslv
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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 vectors
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type(psb_d_vect_type) :: x,b
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! parallel environment
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integer(psb_ipk_) :: ictxt, iam, np
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! solver parameters
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integer(psb_ipk_) :: 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(psb_ipk_) :: novr ! number of overlap layers
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integer(psb_ipk_) :: 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(psb_ipk_) :: fill1 ! Fill-in for factorization 1
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integer(psb_ipk_) :: svsweeps ! Solver sweeps for GS
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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(psb_ipk_) :: maxlevs ! Maximum 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) :: aggr_ord ! Ordering for aggregation
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character(len=16) :: aggr_filter ! Use filtering?
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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(psb_ipk_) :: 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(psb_ipk_) :: 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(psb_ipk_) :: cjswp ! Jacobi sweeps
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real(psb_dpk_) :: athres ! smoother aggregation threshold
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real(psb_dpk_) :: mnaggratio ! Minimum aggregation ratio
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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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logical :: dump_prec
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character(len=40) :: dump_prefix
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integer(psb_ipk_) :: info, i
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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='mld_d_pde2d'
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call psb_set_errverbosity(itwo)
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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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& dump_prec,dump_prefix)
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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_pde2d(ictxt,idim,a,b,x,desc_a,afmt,&
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& a1,a2,b1,b2,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='psb_gen_pde2d'
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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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call mld_precinit(prec,prectype%prec, info)
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if (prectype%csize>0)&
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& call mld_precset(prec,'coarse_aggr_size', prectype%csize, info)
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if (prectype%maxlevs>0)&
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& call mld_precset(prec,'max_prec_levs', prectype%maxlevs, info)
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if (prectype%mnaggratio>0)&
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& call mld_precset(prec,'min_aggr_ratio', prectype%mnaggratio, info)
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if (prectype%athres >= dzero) &
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& call mld_precset(prec,'aggr_thresh', prectype%athres, info)
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call mld_precset(prec,'aggr_kind', prectype%aggrkind,info)
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call mld_precset(prec,'aggr_alg', prectype%aggr_alg,info)
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call mld_precset(prec,'aggr_ord', prectype%aggr_ord,info)
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call mld_precset(prec,'aggr_filter', prectype%aggr_filter, info)
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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call mld_hierarchy_bld(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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thier = psb_wtime()-t1
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call mld_precset(prec,'smoother_type', prectype%smther, info)
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call mld_precset(prec,'smoother_sweeps', prectype%jsweeps, info)
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call mld_precset(prec,'sub_ovr', prectype%novr, info)
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call mld_precset(prec,'sub_restr', prectype%restr, info)
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call mld_precset(prec,'sub_prol', prectype%prol, info)
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call mld_precset(prec,'sub_solve', prectype%solve, info)
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call mld_precset(prec,'sub_fillin', prectype%fill1, info)
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call mld_precset(prec,'solver_sweeps', prectype%svsweeps, info)
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call mld_precset(prec,'sub_iluthrs', prectype%thr1, info)
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call mld_precset(prec,'ml_type', prectype%mltype, info)
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call mld_precset(prec,'smoother_pos', prectype%smthpos, info)
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call mld_precset(prec,'coarse_solve', prectype%csolve, info)
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call mld_precset(prec,'coarse_subsolve', prectype%csbsolve,info)
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call mld_precset(prec,'coarse_mat', prectype%cmat, info)
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call mld_precset(prec,'coarse_fillin', prectype%cfill, info)
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call mld_precset(prec,'coarse_iluthrs', prectype%cthres, info)
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call mld_precset(prec,'coarse_sweeps', prectype%cjswp, info)
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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call mld_smoothers_bld(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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else
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nlv = 1
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call mld_precinit(prec,prectype%prec, info)
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call mld_precset(prec,'smoother_sweeps', prectype%jsweeps, info)
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call mld_precset(prec,'sub_ovr', prectype%novr, info)
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call mld_precset(prec,'sub_restr', prectype%restr, info)
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call mld_precset(prec,'sub_prol', prectype%prol, info)
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call mld_precset(prec,'sub_solve', prectype%solve, info)
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call mld_precset(prec,'sub_fillin', prectype%fill1, info)
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call mld_precset(prec,'solver_sweeps', prectype%svsweeps, info)
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call mld_precset(prec,'sub_iluthrs', prectype%thr1, info)
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call psb_barrier(ictxt)
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thier = dzero
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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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end if
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!!$ call prec%dump(info,prefix='test-ml',ac=.true.,solver=.true.,smoother=.true.)
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call psb_amx(ictxt,thier)
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call psb_amx(ictxt,tprec)
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if (iam == psb_root_) &
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& write(psb_out_unit,'("Preconditioner time : ",es12.5)') tprec+thier
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if (iam == psb_root_) call mld_precdescr(prec,info)
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if (iam == psb_root_) &
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& write(psb_out_unit,'(" ")')
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!
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! iterative method parameters
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!
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if(iam == psb_root_) &
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& write(psb_out_unit,'("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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tslv = psb_wtime() - t1
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call psb_amx(ictxt,tslv)
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amatsize = a%sizeof()
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descsize = desc_a%sizeof()
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precsize = prec%sizeof()
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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(psb_out_unit,'(" ")')
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write(psb_out_unit,'("Numer of levels of aggr. hierarchy: ",i12)') prec%get_nlevs()
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write(psb_out_unit,'("Time to build aggr. hierarchy : ",es12.5)') thier
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write(psb_out_unit,'("Time to build smoothers : ",es12.5)') tprec
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write(psb_out_unit,'("Total preconditioner time : ",es12.5)') tprec+thier
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write(psb_out_unit,'("Time to solve system : ",es12.5)') tslv
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write(psb_out_unit,'("Time per iteration : ",es12.5)') tslv/iter
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write(psb_out_unit,'("Number of iterations : ",i0)') iter
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write(psb_out_unit,'("Convergence indicator on exit : ",es12.5)') err
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write(psb_out_unit,'("Info on exit : ",i0)') info
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write(psb_out_unit,'("Total memory occupation for A: ",i12)') amatsize
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write(psb_out_unit,'("Storage format for A: ",a)') trim(a%get_fmt())
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write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)') descsize
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write(psb_out_unit,'("Storage format for DESC_A: ",a)') trim(desc_a%get_fmt())
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write(psb_out_unit,'("Total memory occupation for PREC: ",i12)') precsize
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end if
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if (dump_prec) call prec%dump(info,prefix=trim(dump_prefix),&
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& ac=.true.,solver=.true.,smoother=.true.,rp=.true.,global_num=.true.)
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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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call psb_exit(ictxt)
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stop
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9999 continue
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call psb_error(ictxt)
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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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& dump_prec,dump_prefix)
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integer(psb_ipk_) :: ictxt
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type(precdata) :: prectype
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character(len=*) :: kmethd, afmt
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integer(psb_ipk_) :: idim, istopc,itmax,itrace,irst
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integer(psb_ipk_) :: np, iam, info
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real(psb_dpk_) :: eps
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logical :: dump_prec
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character(len=*) :: dump_prefix
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character(len=20) :: buffer
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call psb_info(ictxt, iam, np)
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if (iam == psb_root_) then
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call read_data(kmethd,psb_inp_unit)
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call read_data(afmt,psb_inp_unit)
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call read_data(idim,psb_inp_unit)
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call read_data(istopc,psb_inp_unit)
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call read_data(itmax,psb_inp_unit)
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call read_data(itrace,psb_inp_unit)
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call read_data(irst,psb_inp_unit)
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call read_data(eps,psb_inp_unit)
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call read_data(dump_prec,psb_inp_unit)
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call read_data(dump_prefix,psb_inp_unit)
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call read_data(prectype%descr,psb_inp_unit) ! verbose description of the prec
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call read_data(prectype%prec,psb_inp_unit) ! overall prectype
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call read_data(prectype%csize,psb_inp_unit) ! coarse size
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call read_data(prectype%mnaggratio,psb_inp_unit) ! Minimum aggregation ratio
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call read_data(prectype%athres,psb_inp_unit) ! smoother aggr thresh
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call read_data(prectype%maxlevs,psb_inp_unit) ! Maximum number of levels
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call read_data(prectype%aggrkind,psb_inp_unit) ! smoothed/nonsmoothed/minenergy aggregatin
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call read_data(prectype%aggr_alg,psb_inp_unit) ! decoupled or sym. decoupled aggregation
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call read_data(prectype%aggr_ord,psb_inp_unit) ! aggregation ordering: natural, node degree
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call read_data(prectype%aggr_filter,psb_inp_unit) ! aggregation filtering: filter, no_filter
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call read_data(prectype%mltype,psb_inp_unit) ! additive or multiplicative 2nd level prec
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call read_data(prectype%smthpos,psb_inp_unit) ! side: pre, post, both smoothing
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call read_data(prectype%jsweeps,psb_inp_unit) ! Smoother sweeps
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call read_data(prectype%smther,psb_inp_unit) ! Smoother type.
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call read_data(prectype%novr,psb_inp_unit) ! number of overlap layers
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call read_data(prectype%restr,psb_inp_unit) ! restriction over application of as
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call read_data(prectype%prol,psb_inp_unit) ! prolongation over application of as
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call read_data(prectype%solve,psb_inp_unit) ! Subdomain solver: DSCALE ILU MILU ILUT FWGS BWGS MUMPS UMF SLU
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call read_data(prectype%svsweeps,psb_inp_unit) ! Solver sweeps (GS)
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call read_data(prectype%fill1,psb_inp_unit) ! Fill-in for factorization 1
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call read_data(prectype%thr1,psb_inp_unit) ! Threshold for fact. 1 ILU(T)
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call read_data(prectype%cmat,psb_inp_unit) ! coarse mat
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call read_data(prectype%csolve,psb_inp_unit) ! Coarse solver: JACOBI BJAC UMF SLU SLUDIST MUMPS
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call read_data(prectype%csbsolve,psb_inp_unit) ! subsolver: DSCALE GS BWGS ILU UMF SLU SLUDIST MUMPS
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call read_data(prectype%cfill,psb_inp_unit) ! Fill-in for factorization 1
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call read_data(prectype%cthres,psb_inp_unit) ! Threshold for fact. 1 ILU(T)
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call read_data(prectype%cjswp,psb_inp_unit) ! Jacobi sweeps
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end if
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|
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! broadcast parameters to all processors
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call psb_bcast(ictxt,kmethd)
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call psb_bcast(ictxt,afmt)
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call psb_bcast(ictxt,idim)
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|
call psb_bcast(ictxt,istopc)
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|
call psb_bcast(ictxt,itmax)
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|
call psb_bcast(ictxt,itrace)
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|
call psb_bcast(ictxt,irst)
|
|
call psb_bcast(ictxt,eps)
|
|
call psb_bcast(ictxt,dump_prec)
|
|
call psb_bcast(ictxt,dump_prefix)
|
|
call psb_bcast(ictxt,prectype%descr) ! verbose description of the prec
|
|
call psb_bcast(ictxt,prectype%prec) ! overall prectype
|
|
call psb_bcast(ictxt,prectype%csize) ! coarse size
|
|
call psb_bcast(ictxt,prectype%mnaggratio) ! Minimum aggregation ratio
|
|
call psb_bcast(ictxt,prectype%athres) ! smoother aggr thresh
|
|
call psb_bcast(ictxt,prectype%maxlevs) ! Maximum number of levels
|
|
call psb_bcast(ictxt,prectype%aggrkind) ! smoothed/nonsmoothed/minenergy aggregatin
|
|
call psb_bcast(ictxt,prectype%aggr_alg) ! decoupled or sym. decoupled aggregation
|
|
call psb_bcast(ictxt,prectype%aggr_ord) ! aggregation ordering: natural, node degree
|
|
call psb_bcast(ictxt,prectype%aggr_filter) ! aggregation filtering: filter, no_filter
|
|
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%jsweeps) ! Smoother sweeps
|
|
call psb_bcast(ictxt,prectype%smther) ! Smoother type.
|
|
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) ! Subdomain solver: DSCALE ILU MILU ILUT FWGS BWGS MUMPS UMF SLU
|
|
call psb_bcast(ictxt,prectype%svsweeps) ! Solver sweeps (GS)
|
|
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%cmat) ! coarse mat
|
|
call psb_bcast(ictxt,prectype%csolve) ! Coarse solver: JACOBI BJAC UMF SLU SLUDIST MUMPS
|
|
call psb_bcast(ictxt,prectype%csbsolve) ! subsolver: DSCALE GS BWGS ILU UMF SLU SLUDIST MUMPS
|
|
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
|
|
|
|
|
|
if (iam == psb_root_) then
|
|
write(psb_out_unit,'("Solving matrix : ell1")')
|
|
write(psb_out_unit,'("Grid dimensions : ",i4,"x",i4)')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(psb_ipk_) :: iout
|
|
write(iout,*)'incorrect parameter(s) found'
|
|
write(iout,*)' usage: mld_d_pde2d 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 mld_d_pde2d
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