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643 lines
20 KiB
Fortran
643 lines
20 KiB
Fortran
!!$
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!!$
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!!$ MLD2P4 version 1.0
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!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
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!!$ based on PSBLAS (Parallel Sparse BLAS version 2.2)
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!!$
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!!$ (C) Copyright 2008
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!!$
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!!$ Salvatore Filippone University of Rome Tor Vergata
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!!$ Alfredo Buttari University of Rome Tor Vergata
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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: mld_sexample_ml.f90
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!
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! This sample program solves a linear system obtained by discretizing a
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! PDE with Dirichlet BCs. The solver is BiCGStab coupled with one of the
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! following multi-level preconditioner, as explained in Section 6.1 of
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! the MLD2P4 User's and Reference Guide:
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! - choice = 1, default multi-level Schwarz preconditioner (Sec. 6.1, Fig. 2)
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! - choice = 2, hybrid three-level Schwarz preconditioner (Sec. 6.1, Fig. 3)
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! - choice = 3, additive three-level Schwarz preconditioner (Sec. 6.1, Fig. 4)
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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 mld_sexample_ml
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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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! sparse matrices
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type(psb_sspmat_type) :: A
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! sparse matrices descriptor
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type(psb_desc_type):: desc_A
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! preconditioner
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type(mld_sprec_type) :: P
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! right-hand side, solution and residual vectors
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real(psb_spk_), allocatable , save :: b(:), x(:), r(:)
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! solver and preconditioner parameters
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real(psb_spk_) :: tol, err
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integer :: itmax, iter, istop
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integer :: nlev
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! parallel environment parameters
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integer :: ictxt, iam, np
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! other variables
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integer :: choice
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integer :: i,info,j,amatsize,descsize,precsize
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integer :: idim, ierr, ircode
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real(psb_dpk_) :: t1, t2, tprec
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real(psb_spk_) :: resmx, resmxp
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character(len=20) :: name
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! initialize the parallel environment
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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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name='mld_sexample_ml'
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if(psb_get_errstatus() /= 0) goto 9999
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info=0
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call psb_set_errverbosity(2)
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! get parameters
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call get_parms(ictxt,choice,idim,itmax,tol)
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! allocate and fill in the coefficient matrix, rhs and initial guess
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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,part_block,ictxt,info)
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t2 = psb_wtime() - t1
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if(info /= 0) then
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info=4010
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call psb_errpush(info,name)
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goto 9999
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end if
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call psb_amx(ictxt,t2)
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if (iam == psb_root_) write(*,'("Overall matrix creation time : ",es10.4)')t2
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if (iam == psb_root_) write(*,'(" ")')
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select case(choice)
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case(1)
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! initialize the default multi-level preconditioner, i.e. hybrid
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! Schwarz, using RAS (with overlap 1 and ILU(0) on the blocks)
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! as post-smoother and 4 block-Jacobi sweeps (with UMFPACK LU
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! on the blocks) as distributed coarse-level solver
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call mld_precinit(P,'ML',info)
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case(2)
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! set a three-level hybrid Schwarz preconditioner, which uses
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! block Jacobi (with ILU(0) on the blocks) as post-smoother,
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! a coarsest matrix replicated on the processors, and the
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! LU factorization from UMFPACK as coarse-level solver
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call mld_precinit(P,'ML',info,nlev=3)
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call mld_precset(P,mld_smoother_type_,'BJAC',info)
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call mld_precset(P,mld_coarse_mat_,'REPL',info)
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call mld_precset(P,mld_coarse_solve_,'UMF',info)
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case(3)
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! set a three-level additive Schwarz preconditioner, which uses
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! RAS (with overlap 1 and ILU(0) on the blocks) as pre- and
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! post-smoother, and 5 block-Jacobi sweeps (with UMFPACK LU
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! on the blocks) as distributed coarsest-level solver
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call mld_precinit(P,'ML',info,nlev=3)
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call mld_precset(P,mld_ml_type_,'ADD',info)
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call mld_precset(P,mld_smoother_pos_,'TWOSIDE',info)
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call mld_precset(P,mld_coarse_sweeps_,5,info)
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end select
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! build the preconditioner
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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,P,info)
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tprec = psb_wtime()-t1
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call psb_amx(ictxt, tprec)
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if (info /= 0) then
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call psb_errpush(4010,name,a_err='psb_precbld')
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goto 9999
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end if
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! set the solver parameters and the initial guess
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call psb_geall(x,desc_A,info)
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x(:) =0.0
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call psb_geasb(x,desc_A,info)
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! solve Ax=b with preconditioned BiCGSTAB
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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call psb_krylov('BICGSTAB',A,P,b,x,tol,desc_A,info,itmax,iter,err,itrace=1,istop=2)
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t2 = psb_wtime() - t1
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call psb_amx(ictxt,t2)
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call psb_geall(r,desc_A,info)
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r(:) =0.0
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call psb_geasb(r,desc_A,info)
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call psb_geaxpby(sone,b,szero,r,desc_A,info)
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call psb_spmm(-sone,A,x,sone,r,desc_A,info)
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call psb_genrm2s(resmx,r,desc_A,info)
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call psb_geamaxs(resmxp,r,desc_A,info)
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amatsize = psb_sizeof(A)
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descsize = psb_sizeof(desc_A)
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precsize = mld_sizeof(P)
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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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call mld_precdescr(P,info)
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if (iam==psb_root_) then
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write(*,'(" ")')
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write(*,'("Matrix from PDE example")')
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write(*,'("Computed solution on ",i8," processors")')np
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write(*,'("Iterations to convergence : ",i6)')iter
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write(*,'("Error estimate on exit : ",es10.4)')err
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write(*,'("Time to build prec. : ",es10.4)')tprec
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write(*,'("Time to solve system : ",es10.4)')t2
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write(*,'("Time per iteration : ",es10.4)')t2/(iter)
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write(*,'("Total time : ",es10.4)')t2+tprec
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write(*,'("Residual 2-norm : ",es10.4)')resmx
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write(*,'("Residual inf-norm : ",es10.4)')resmxp
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write(*,'("Total memory occupation for A : ",i10)')amatsize
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write(*,'("Total memory occupation for DESC_A : ",i10)')descsize
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write(*,'("Total memory occupation for PREC : ",i10)')precsize
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end if
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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(P,info)
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call psb_cdfree(desc_A,info)
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9999 continue
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if(info /= 0) 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 parameters from standard input
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!
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subroutine get_parms(ictxt,choice,idim,itmax,tol)
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use psb_base_mod
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implicit none
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integer :: choice, idim, ictxt, itmax
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real(psb_spk_) :: tol
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integer :: iam, np
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call psb_info(ictxt,iam,np)
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if (iam==psb_root_) then
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! read input parameters
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call read_data(choice,5)
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call read_data(idim,5)
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call read_data(itmax,5)
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call read_data(tol,5)
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end if
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call psb_bcast(ictxt,choice)
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call psb_bcast(ictxt,idim)
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call psb_bcast(ictxt,itmax)
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call psb_bcast(ictxt,tol)
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end subroutine get_parms
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!
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! subroutine to allocate and fill in the coefficient matrix and
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! the rhs
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!
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subroutine create_matrix(idim,a,b,xv,desc_a,parts,ictxt,info)
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!
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! Discretize the partial diferential equation
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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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! 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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use psb_base_mod
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implicit none
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integer :: idim
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integer, parameter :: nbmax=10
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real(psb_spk_), allocatable :: b(:),xv(:)
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type(psb_desc_type) :: desc_a
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integer :: ictxt, info
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interface
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! .....user passed subroutine.....
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subroutine parts(global_indx,n,np,pv,nv)
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implicit none
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integer, intent(in) :: global_indx, n, np
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integer, intent(out) :: nv
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integer, intent(out) :: pv(*)
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end subroutine parts
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end interface
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! local variables
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type(psb_sspmat_type) :: a
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real(psb_spk_) :: zt(nbmax),glob_x,glob_y,glob_z
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integer :: m,n,nnz,glob_row,ipoints
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integer :: x,y,z,ia,indx_owner
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integer :: np, iam
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integer :: element
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integer :: nv, inv
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integer, allocatable :: irow(:),icol(:)
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real(psb_spk_), allocatable :: val(:)
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integer, allocatable :: prv(:)
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! deltah dimension of each grid cell
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! deltat discretization time
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real(psb_spk_) :: deltah
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real(psb_spk_),parameter :: rhs=0.e0,one=1.e0,zero=0.e0
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real(psb_dpk_) :: t1, t2, t3, tins, tasb
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real(psb_spk_) :: a1, a2, a3, a4, b1, b2, b3
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external :: a1, a2, a3, a4, b1, b2, b3
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integer :: err_act
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character(len=20) :: name
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info = 0
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name = 'create_matrix'
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call psb_erractionsave(err_act)
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call psb_info(ictxt, iam, np)
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deltah = 1.d0/(idim-1)
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! initialize array descriptor and sparse matrix storage; provide an
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! estimate of the number of non zeroes
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ipoints=idim-2
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m = ipoints*ipoints*ipoints
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n = m
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nnz = ((n*9)/(np))
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if(iam == psb_root_) write(0,'("Generating Matrix (size=",i0x,")...")')n
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call psb_cdall(ictxt,desc_a,info,mg=n,parts=parts)
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call psb_spall(a,desc_a,info,nnz=nnz)
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! define rhs from boundary conditions; also build initial guess
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call psb_geall(b,desc_a,info)
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call psb_geall(xv,desc_a,info)
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if(info /= 0) then
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info=4010
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call psb_errpush(info,name)
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goto 9999
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end if
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! we build an auxiliary matrix consisting of one row at a
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! time; just a small matrix. might be extended to generate
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! a bunch of rows per call.
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!
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allocate(val(20*nbmax),irow(20*nbmax),&
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&icol(20*nbmax),prv(np),stat=info)
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if (info /= 0 ) then
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info=4000
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call psb_errpush(info,name)
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goto 9999
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endif
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tins = 0.d0
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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! loop over rows belonging to current process in a block
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! distribution.
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do glob_row = 1, n
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call parts(glob_row,n,np,prv,nv)
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do inv = 1, nv
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indx_owner = prv(inv)
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if (indx_owner == iam) then
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! local matrix pointer
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element=1
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! compute gridpoint coordinates
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if (mod(glob_row,ipoints*ipoints) == 0) then
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x = glob_row/(ipoints*ipoints)
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else
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x = glob_row/(ipoints*ipoints)+1
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endif
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if (mod((glob_row-(x-1)*ipoints*ipoints),ipoints) == 0) then
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y = (glob_row-(x-1)*ipoints*ipoints)/ipoints
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else
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y = (glob_row-(x-1)*ipoints*ipoints)/ipoints+1
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endif
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z = glob_row-(x-1)*ipoints*ipoints-(y-1)*ipoints
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! glob_x, glob_y, glob_x coordinates
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glob_x=x*deltah
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glob_y=y*deltah
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glob_z=z*deltah
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! check on boundary points
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zt(1) = 0.d0
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! internal point: build discretization
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!
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! term depending on (x-1,y,z)
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!
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if (x==1) then
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val(element)=-b1(glob_x,glob_y,glob_z)&
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& -a1(glob_x,glob_y,glob_z)
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val(element) = val(element)/(deltah*&
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& deltah)
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zt(1) = exp(-glob_y**2-glob_z**2)*(-val(element))
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else
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val(element)=-b1(glob_x,glob_y,glob_z)&
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& -a1(glob_x,glob_y,glob_z)
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val(element) = val(element)/(deltah*&
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& deltah)
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icol(element)=(x-2)*ipoints*ipoints+(y-1)*ipoints+(z)
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element=element+1
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endif
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! term depending on (x,y-1,z)
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if (y==1) then
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val(element)=-b2(glob_x,glob_y,glob_z)&
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& -a2(glob_x,glob_y,glob_z)
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val(element) = val(element)/(deltah*&
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& deltah)
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zt(1) = exp(-glob_x**2-glob_z**2)*(-val(element))
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else
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val(element)=-b2(glob_x,glob_y,glob_z)&
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& -a2(glob_x,glob_y,glob_z)
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val(element) = val(element)/(deltah*&
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& deltah)
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icol(element)=(x-1)*ipoints*ipoints+(y-2)*ipoints+(z)
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element=element+1
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endif
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! term depending on (x,y,z-1)
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if (z==1) then
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val(element)=-b3(glob_x,glob_y,glob_z)&
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& -a3(glob_x,glob_y,glob_z)
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val(element) = val(element)/(deltah*&
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& deltah)
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zt(1) = exp(-glob_x**2-glob_y**2)*(-val(element))
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else
|
|
val(element)=-b3(glob_x,glob_y,glob_z)&
|
|
& -a3(glob_x,glob_y,glob_z)
|
|
val(element) = val(element)/(deltah*&
|
|
& deltah)
|
|
icol(element)=(x-1)*ipoints*ipoints+(y-1)*ipoints+(z-1)
|
|
element=element+1
|
|
endif
|
|
! term depending on (x,y,z)
|
|
val(element)=2*b1(glob_x,glob_y,glob_z)&
|
|
& +2*b2(glob_x,glob_y,glob_z)&
|
|
& +2*b3(glob_x,glob_y,glob_z)&
|
|
& +a1(glob_x,glob_y,glob_z)&
|
|
& +a2(glob_x,glob_y,glob_z)&
|
|
& +a3(glob_x,glob_y,glob_z)
|
|
val(element) = val(element)/(deltah*&
|
|
& deltah)
|
|
icol(element)=(x-1)*ipoints*ipoints+(y-1)*ipoints+(z)
|
|
element=element+1
|
|
! term depending on (x,y,z+1)
|
|
if (z==ipoints) then
|
|
val(element)=-b1(glob_x,glob_y,glob_z)
|
|
val(element) = val(element)/(deltah*&
|
|
& deltah)
|
|
zt(1) = exp(-glob_x**2-glob_y**2)*exp(-glob_z)*(-val(element))
|
|
else
|
|
val(element)=-b1(glob_x,glob_y,glob_z)
|
|
val(element) = val(element)/(deltah*&
|
|
& deltah)
|
|
icol(element)=(x-1)*ipoints*ipoints+(y-1)*ipoints+(z+1)
|
|
element=element+1
|
|
endif
|
|
! term depending on (x,y+1,z)
|
|
if (y==ipoints) then
|
|
val(element)=-b2(glob_x,glob_y,glob_z)
|
|
val(element) = val(element)/(deltah*&
|
|
& deltah)
|
|
zt(1) = exp(-glob_x**2-glob_z**2)*exp(-glob_y)*(-val(element))
|
|
else
|
|
val(element)=-b2(glob_x,glob_y,glob_z)
|
|
val(element) = val(element)/(deltah*&
|
|
& deltah)
|
|
icol(element)=(x-1)*ipoints*ipoints+(y)*ipoints+(z)
|
|
element=element+1
|
|
endif
|
|
! term depending on (x+1,y,z)
|
|
if (x==ipoints) then
|
|
val(element)=-b3(glob_x,glob_y,glob_z)
|
|
val(element) = val(element)/(deltah*&
|
|
& deltah)
|
|
zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element))
|
|
else
|
|
val(element)=-b3(glob_x,glob_y,glob_z)
|
|
val(element) = val(element)/(deltah*&
|
|
& deltah)
|
|
icol(element)=(x)*ipoints*ipoints+(y-1)*ipoints+(z)
|
|
element=element+1
|
|
endif
|
|
irow(1:element-1)=glob_row
|
|
ia=glob_row
|
|
|
|
t3 = psb_wtime()
|
|
call psb_spins(element-1,irow,icol,val,a,desc_a,info)
|
|
if(info /= 0) exit
|
|
tins = tins + (psb_wtime()-t3)
|
|
call psb_geins(1,(/ia/),zt(1:1),b,desc_a,info)
|
|
if(info /= 0) exit
|
|
zt(1)=0.d0
|
|
call psb_geins(1,(/ia/),zt(1:1),xv,desc_a,info)
|
|
if(info /= 0) exit
|
|
end if
|
|
end do
|
|
end do
|
|
|
|
call psb_barrier(ictxt)
|
|
t2 = psb_wtime()-t1
|
|
|
|
if(info /= 0) then
|
|
info=4010
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
deallocate(val,irow,icol)
|
|
|
|
t1 = psb_wtime()
|
|
call psb_cdasb(desc_a,info)
|
|
call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_)
|
|
call psb_barrier(ictxt)
|
|
tasb = psb_wtime()-t1
|
|
if(info /= 0) then
|
|
info=4010
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_amx(ictxt,t2)
|
|
call psb_amx(ictxt,tins)
|
|
call psb_amx(ictxt,tasb)
|
|
|
|
if(iam == psb_root_) then
|
|
write(*,'("The matrix has been generated and assembeld in ",a3," format.")')&
|
|
& a%fida(1:3)
|
|
write(*,'("-pspins time : ",es10.4)')tins
|
|
write(*,'("-insert time : ",es10.4)')t2
|
|
write(*,'("-assembly time : ",es10.4)')tasb
|
|
end if
|
|
|
|
call psb_geasb(b,desc_a,info)
|
|
call psb_geasb(xv,desc_a,info)
|
|
if(info /= 0) then
|
|
info=4010
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_erractionrestore(err_act)
|
|
return
|
|
|
|
9999 continue
|
|
call psb_erractionrestore(err_act)
|
|
if (err_act == psb_act_abort_) then
|
|
call psb_error(ictxt)
|
|
return
|
|
end if
|
|
return
|
|
end subroutine create_matrix
|
|
end program mld_sexample_ml
|
|
!
|
|
! 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
|
|
a1=0.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
|
|
a2=0.e0
|
|
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
|
|
a3=0.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
|
|
a4=0.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
|