!
!
! MLD2P4 version 2.2
! MultiLevel Domain Decomposition Parallel Preconditioners Package
! based on PSBLAS (Parallel Sparse BLAS version 3.5)
!
! (C) Copyright 2008-2018
!
! Salvatore Filippone
! Pasqua D'Ambra
! Daniela di Serafino
!
! Redistribution and use in source and binary forms, with or without
! modification, are permitted provided that the following conditions
! are met:
! 1. Redistributions of source code must retain the above copyright
! notice, this list of conditions and the following disclaimer.
! 2. Redistributions in binary form must reproduce the above copyright
! notice, this list of conditions, and the following disclaimer in the
! documentation and/or other materials provided with the distribution.
! 3. The name of the MLD2P4 group or the names of its contributors may
! not be used to endorse or promote products derived from this
! software without specific written permission.
!
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
! ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
! TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
! BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
! CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
! SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
! INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
! CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
! POSSIBILITY OF SUCH DAMAGE.
!
!
!
! File: mld_d_pde3d.f90
!
! Program: mld_d_pde3d
! This sample program solves a linear system obtained by discretizing a
! PDE with Dirichlet BCs.
!
!
! The PDE is a general second order equation in 3d
!
! a1 dd(u) a2 dd(u) a3 dd(u) b1 d(u) b2 d(u) b3 d(u)
! - ------ - ------ - ------ + ----- + ------ + ------ + c u = f
! dxdx dydy dzdz dx dy dz
!
! with Dirichlet boundary conditions
! u = g
!
! on the unit cube 0<=x,y,z<=1.
!
!
! Note that if b1=b2=b3=c=0., the PDE is the Laplace equation.
!
! In this sample program the index space of the discretized
! computational domain is first numbered sequentially in a standard way,
! then the corresponding vector is distributed according to a BLOCK
! data distribution.
!
module mld_d_pde3d_mod
contains
!
! functions parametrizing the differential equation
!
function b1(x,y,z)
use psb_base_mod, only : psb_dpk_,done,dzero
real(psb_dpk_) :: b1
real(psb_dpk_), intent(in) :: x,y,z
b1=dzero/sqrt((3*done))
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_dpk_,done,dzero
real(psb_dpk_) :: b2
real(psb_dpk_), intent(in) :: x,y,z
b2=dzero/sqrt((3*done))
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_dpk_,done,dzero
real(psb_dpk_) :: b3
real(psb_dpk_), intent(in) :: x,y,z
b3=dzero/sqrt((3*done))
end function b3
function c(x,y,z)
use psb_base_mod, only : psb_dpk_,done,dzero
real(psb_dpk_) :: c
real(psb_dpk_), intent(in) :: x,y,z
c=dzero
end function c
function a1(x,y,z)
use psb_base_mod, only : psb_dpk_,done,dzero
real(psb_dpk_) :: a1
real(psb_dpk_), intent(in) :: x,y,z
a1=done!/80
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_dpk_,done,dzero
real(psb_dpk_) :: a2
real(psb_dpk_), intent(in) :: x,y,z
a2=done!/80
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_dpk_,done,dzero
real(psb_dpk_) :: a3
real(psb_dpk_), intent(in) :: x,y,z
a3=done!/80
end function a3
function g(x,y,z)
use psb_base_mod, only : psb_dpk_,done,dzero
real(psb_dpk_) :: g
real(psb_dpk_), intent(in) :: x,y,z
g = dzero
if (x == done) then
g = done
else if (x == dzero) then
g = exp(y**2-z**2)
end if
end function g
end module mld_d_pde3d_mod
program mld_d_pde3d
use psb_base_mod
use mld_prec_mod
use psb_krylov_mod
use psb_util_mod
use data_input
use mld_d_pde3d_mod
use mld_d_tlu_solver
implicit none
! input parameters
character(len=20) :: kmethd, ptype
character(len=5) :: afmt
integer(psb_ipk_) :: idim
! miscellaneous
real(psb_dpk_) :: t1, t2, tprec, thier, tslv
! sparse matrix and preconditioner
type(psb_dspmat_type) :: a
type(mld_dprec_type) :: prec
type(mld_d_tlu_solver_type) :: tlusv
! descriptor
type(psb_desc_type) :: desc_a
! dense vectors
type(psb_d_vect_type) :: x,b
! parallel environment
integer(psb_ipk_) :: ctxt, iam, np
! solver parameters
integer(psb_ipk_) :: iter, itmax,itrace, istopc, irst, nlv
integer(psb_epk_) :: amatsize, precsize, descsize
real(psb_dpk_) :: err, eps
! other variables
integer(psb_ipk_) :: info, i
character(len=20) :: name,ch_err
info=psb_success_
call psb_init(ctxt)
call psb_info(ctxt,iam,np)
if (iam < 0) then
! This should not happen, but just in case
call psb_exit(ctxt)
stop
endif
if(psb_get_errstatus() /= 0) goto 9999
name='mld_d_pde3d'
call psb_set_errverbosity(itwo)
!
! Hello world
!
if (iam == psb_root_) then
write(*,*) 'Welcome to MLD2P4 version: ',mld_version_string_
write(*,*) 'This is the ',trim(name),' sample program'
end if
!
! get parameters
!
call get_parms(ctxt,kmethd,afmt,idim,istopc,itmax,itrace,irst,eps)
!
! allocate and fill in the coefficient matrix, rhs and initial guess
!
call psb_barrier(ctxt)
t1 = psb_wtime()
call psb_gen_pde3d(ctxt,idim,a,b,x,desc_a,afmt,&
& a1,a2,a3,b1,b2,b3,c,g,info)
call psb_barrier(ctxt)
t2 = psb_wtime() - t1
if(info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='create_matrix'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
if (iam == psb_root_) &
& write(psb_out_unit,'("Overall matrix creation time : ",es12.5)')t2
if (iam == psb_root_) &
& write(psb_out_unit,'(" ")')
!
! prepare the preconditioner: an ML with defaults, but with TLU solver at
! intermediate levels. All other parameters are at default values.
!
call prec%init('ML', info)
call psb_barrier(ctxt)
t1 = psb_wtime()
call prec%hierarchy_build(a,desc_a,info)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='prec%hierarchy_bld'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
thier = psb_wtime()-t1
nlv = prec%get_nlevs()
call prec%set(tlusv, info,ilev=1,ilmax=max(1,nlv-1))
call psb_barrier(ctxt)
t1 = psb_wtime()
call prec%smoothers_build(a,desc_a,info)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='prec%smoothers_build'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
tprec = psb_wtime()-t1
call psb_amx(ctxt,thier)
call psb_amx(ctxt,tprec)
if (iam == psb_root_) &
& write(psb_out_unit,'("Preconditioner time : ",es12.5)') tprec+thier
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(ctxt)
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(ctxt)
tslv = psb_wtime() - t1
call psb_amx(ctxt,tslv)
amatsize = a%sizeof()
descsize = desc_a%sizeof()
precsize = prec%sizeof()
call psb_sum(ctxt,amatsize)
call psb_sum(ctxt,descsize)
call psb_sum(ctxt,precsize)
if (iam == psb_root_) then
write(psb_out_unit,'(" ")')
write(psb_out_unit,'("Numer of levels of aggr. hierarchy: ",i12)') prec%get_nlevs()
write(psb_out_unit,'("Time to build aggr. hierarchy : ",es12.5)') thier
write(psb_out_unit,'("Time to build smoothers : ",es12.5)') tprec
write(psb_out_unit,'("Total preconditioner time : ",es12.5)') tprec+thier
write(psb_out_unit,'("Time to solve system : ",es12.5)') tslv
write(psb_out_unit,'("Time per iteration : ",es12.5)') tslv/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,'("Storage format for A: ",a)') trim(a%get_fmt())
write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)') descsize
write(psb_out_unit,'("Storage format for DESC_A: ",a)') trim(desc_a%get_fmt())
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(ctxt)
stop
9999 continue
call psb_error(ctxt)
contains
!
! get iteration parameters from standard input
!
subroutine get_parms(ctxt,kmethd,afmt,idim,istopc,itmax,itrace,irst,eps)
integer(psb_ipk_) :: ctxt
character(len=*) :: kmethd, afmt
integer(psb_ipk_) :: idim, istopc,itmax,itrace,irst
integer(psb_ipk_) :: np, iam, info
real(psb_dpk_) :: eps
character(len=20) :: buffer
call psb_info(ctxt, iam, np)
if (iam == psb_root_) then
call read_data(kmethd,psb_inp_unit)
call read_data(afmt,psb_inp_unit)
call read_data(idim,psb_inp_unit)
call read_data(istopc,psb_inp_unit)
call read_data(itmax,psb_inp_unit)
call read_data(itrace,psb_inp_unit)
call read_data(irst,psb_inp_unit)
call read_data(eps,psb_inp_unit)
end if
! broadcast parameters to all processors
call psb_bcast(ctxt,kmethd)
call psb_bcast(ctxt,afmt)
call psb_bcast(ctxt,idim)
call psb_bcast(ctxt,istopc)
call psb_bcast(ctxt,itmax)
call psb_bcast(ctxt,itrace)
call psb_bcast(ctxt,irst)
call psb_bcast(ctxt,eps)
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)') 'ML-TLU'
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_pde3d 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_pde3d