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mld2p4-2:

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examples/pdegen/mld_dexample_1lev.f90
 examples/pdegen/mld_dexample_ml.f90
 examples/pdegen/mld_sexample_1lev.f90
 examples/pdegen/mld_sexample_ml.f90
 mlprec/mld_base_prec_type.F90

New scaling options (to be implemented).
Fixed matgen in examples (to be tested).
This commit is contained in:
Salvatore Filippone
2012-02-21 14:35:27 +00:00
parent 34581e785e
commit 9f3f1b1876
5 changed files with 288 additions and 1390 deletions
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examples/pdegen/mld_dexample_1lev.f90
+69 -349
View File
@@ -46,30 +46,20 @@
! - choice = 2, hybrid three-level Schwarz preconditioner (Sec. 6.1, Fig. 3)
! - choice = 3, additive three-level Schwarz preconditioner (Sec. 6.1, Fig. 4)
!
!
! The PDE is a general second order equation in 3d
!
! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0
! 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, on the unit cube 0<=x,y,z<=1.
! with Dirichlet boundary conditions
! u = g
!
! Example taken from:
! C.T.Kelley
! Iterative Methods for Linear and Nonlinear Equations
! SIAM 1995
! on the unit cube 0<=x,y,z<=1.
!
! 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.
!
! Boundary conditions are set in a very simple way, by adding
! equations of the form
!
! u(x,y) = exp(-x^2-y^2-z^2)
!
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
! Note that if b1=b2=b3=c=0., the PDE is the Laplace equation.
!
program mld_dexample_1lev
use psb_base_mod
@@ -91,7 +81,7 @@ program mld_dexample_1lev
type(mld_dprec_type) :: P
! right-hand side, solution and residual vectors
real(psb_dpk_), allocatable , save :: b(:), x(:), r(:)
type(psb_d_vect_type) :: x, b, r
! solver parameters
real(psb_dpk_) :: tol, err
@@ -105,6 +95,7 @@ program mld_dexample_1lev
integer(psb_long_int_k_) :: amatsize, precsize, descsize
integer :: idim, nlev, ierr, ircode
real(psb_dpk_) :: t1, t2, tprec, resmx, resmxp
character(len=5) :: afmt='CSR'
character(len=20) :: name
! initialize the parallel environment
@@ -137,7 +128,8 @@ program mld_dexample_1lev
call psb_barrier(ictxt)
t1 = psb_wtime()
call create_matrix(idim,a,b,x,desc_a,ictxt,info)
call psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,&
& a1,a2,a3,b1,b2,b3,c,g,info)
call psb_barrier(ictxt)
t2 = psb_wtime() - t1
if(info /= psb_success_) then
@@ -172,7 +164,7 @@ program mld_dexample_1lev
! set the initial guess
call psb_geall(x,desc_A,info)
x(:) =0.0
call x%set(dzero)
call psb_geasb(x,desc_A,info)
! solve Ax=b with preconditioned BiCGSTAB
@@ -186,12 +178,12 @@ program mld_dexample_1lev
call psb_amx(ictxt,t2)
call psb_geall(r,desc_A,info)
r(:) =0.0
call r%set(dzero)
call psb_geasb(r,desc_A,info)
call psb_geaxpby(done,b,dzero,r,desc_A,info)
call psb_spmm(-done,A,x,done,r,desc_A,info)
call psb_genrm2s(resmx,r,desc_A,info)
call psb_geamaxs(resmxp,r,desc_A,info)
resmx = psb_genrm2(r,desc_A,info)
resmxp = psb_geamax(r,desc_A,info)
amatsize = a%sizeof()
descsize = desc_a%sizeof()
@@ -259,332 +251,60 @@ contains
call psb_bcast(ictxt,tol)
end subroutine get_parms
!
! subroutine to allocate and fill in the coefficient matrix and
! the rhs
!
subroutine create_matrix(idim,a,b,xv,desc_a,ictxt,info)
!
! Discretize the partial diferential equation
!
! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0
! dxdx dydy dzdz dx dy dz
!
! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
!
! Boundary conditions are set in a very simple way, by adding
! equations of the form
!
! u(x,y) = exp(-x^2-y^2-z^2)
!
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
!
use psb_base_mod
implicit none
integer :: idim
integer, parameter :: nb=20
real(psb_dpk_), allocatable :: b(:),xv(:)
type(psb_desc_type) :: desc_a
integer :: ictxt, info
character :: afmt*5
type(psb_dspmat_type) :: a
real(psb_dpk_) :: zt(nb),x,y,z
integer :: m,n,nnz,glob_row,nlr,i,ii,ib,k
integer :: ix,iy,iz,ia,indx_owner, ipoints
integer :: np, iam, nr, nt
integer :: element
integer, allocatable :: irow(:),icol(:),myidx(:)
real(psb_dpk_), allocatable :: val(:)
! deltah dimension of each grid cell
! deltat discretization time
real(psb_dpk_) :: deltah, deltah2
real(psb_dpk_),parameter :: rhs=0.d0,one=1.d0,zero=0.d0
real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen
real(psb_dpk_) :: a1, a2, a3, a4, b1, b2, b3
external :: a1, a2, a3, a4, b1, b2, b3
integer :: err_act
character(len=20) :: name, ch_err
info = psb_success_
name = 'create_matrix'
call psb_erractionsave(err_act)
call psb_info(ictxt, iam, np)
deltah = 1.d0/(idim-1)
deltah2 = deltah*deltah
! initialize array descriptor and sparse matrix storage. provide an
! estimate of the number of non zeroes
ipoints=idim-2
m = ipoints*ipoints*ipoints
n = m
nnz = ((n*9)/(np))
if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n
!
! Using a simple BLOCK distribution.
!
nt = (m+np-1)/np
nr = max(0,min(nt,m-(iam*nt)))
nt = nr
call psb_sum(ictxt,nt)
if (nt /= m) write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m
call psb_barrier(ictxt)
t0 = psb_wtime()
call psb_cdall(ictxt,desc_a,info,nl=nr)
if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz)
! define rhs from boundary conditions; also build initial guess
if (info == psb_success_) call psb_geall(b,desc_a,info)
if (info == psb_success_) call psb_geall(xv,desc_a,info)
nlr = psb_cd_get_local_rows(desc_a)
call psb_barrier(ictxt)
talc = psb_wtime()-t0
if (info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='allocation rout.'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
! functions parametrizing the differential equation
!
function b1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b1
real(psb_dpk_), intent(in) :: x,y,z
b1=1.d0/sqrt(3.d0)
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b2
real(psb_dpk_), intent(in) :: x,y,z
b2=1.d0/sqrt(3.d0)
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b3
real(psb_dpk_), intent(in) :: x,y,z
b3=1.d0/sqrt(3.d0)
end function b3
function c(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: c
real(psb_dpk_), intent(in) :: x,y,z
c=0.d0
end function c
function a1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a1
real(psb_dpk_), intent(in) :: x,y,z
a1=1.d0/80
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a2
real(psb_dpk_), intent(in) :: x,y,z
a2=1.d0/80
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a3
real(psb_dpk_), intent(in) :: x,y,z
a3=1.d0/80
end function a3
function g(x,y,z)
use psb_base_mod, only : psb_dpk_, done
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
! we build an auxiliary matrix consisting of one row at a
! time; just a small matrix. might be extended to generate
! a bunch of rows per call.
!
allocate(val(20*nb),irow(20*nb),&
&icol(20*nb),myidx(nlr),stat=info)
if (info /= psb_success_ ) then
info=psb_err_alloc_dealloc_
call psb_errpush(info,name)
goto 9999
endif
do i=1,nlr
myidx(i) = i
end do
call psb_loc_to_glob(myidx,desc_a,info)
! loop over rows belonging to current process in a block
! distribution.
call psb_barrier(ictxt)
t1 = psb_wtime()
do ii=1, nlr,nb
ib = min(nb,nlr-ii+1)
element = 1
do k=1,ib
i=ii+k-1
! local matrix pointer
glob_row=myidx(i)
! compute gridpoint coordinates
if (mod(glob_row,ipoints*ipoints) == 0) then
ix = glob_row/(ipoints*ipoints)
else
ix = glob_row/(ipoints*ipoints)+1
endif
if (mod((glob_row-(ix-1)*ipoints*ipoints),ipoints) == 0) then
iy = (glob_row-(ix-1)*ipoints*ipoints)/ipoints
else
iy = (glob_row-(ix-1)*ipoints*ipoints)/ipoints+1
endif
iz = glob_row-(ix-1)*ipoints*ipoints-(iy-1)*ipoints
! x, y, x coordinates
x=ix*deltah
y=iy*deltah
z=iz*deltah
! check on boundary points
zt(k) = 0.d0
! internal point: build discretization
!
! term depending on (x-1,y,z)
!
if (ix == 1) then
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*(-val(element))
else
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
icol(element) = (ix-2)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y-1,z)
if (iy == 1) then
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-2)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y,z-1)
if (iz == 1) then
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz-1)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y,z)
val(element)=(2*b1(x,y,z) + 2*b2(x,y,z) + 2*b3(x,y,z))/deltah2&
& + (a1(x,y,z) + a2(x,y,z) + a3(x,y,z)+ a4(x,y,z))/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
! term depending on (x,y,z+1)
if (iz == ipoints) then
val(element)=-b1(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b1(x,y,z)/deltah2
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz+1)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y+1,z)
if (iy == ipoints) then
val(element)=-b2(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b2(x,y,z)/deltah2
icol(element) = (ix-1)*ipoints*ipoints+(iy)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x+1,y,z)
if (ix==ipoints) then
val(element)=-b3(x,y,z)/deltah2
zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/deltah2
icol(element) = (ix)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
end do
call psb_spins(element-1,irow,icol,val,a,desc_a,info)
if(info /= psb_success_) exit
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),b,desc_a,info)
if(info /= psb_success_) exit
zt(:)=0.d0
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xv,desc_a,info)
if(info /= psb_success_) exit
end do
tgen = psb_wtime()-t1
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
deallocate(val,irow,icol)
call psb_barrier(ictxt)
t1 = psb_wtime()
call psb_cdasb(desc_a,info)
if (info == psb_success_) &
& call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_)
call psb_barrier(ictxt)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
call psb_geasb(b,desc_a,info)
call psb_geasb(xv,desc_a,info)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
tasb = psb_wtime()-t1
call psb_barrier(ictxt)
ttot = psb_wtime() - t0
call psb_amx(ictxt,talc)
call psb_amx(ictxt,tgen)
call psb_amx(ictxt,tasb)
call psb_amx(ictxt,ttot)
if(iam == psb_root_) then
write(*,'("The matrix has been generated and assembled in ",a3," format.")')&
& a%get_fmt()
write(*,'("-allocation time : ",es12.5)') talc
write(*,'("-coeff. gen. time : ",es12.5)') tgen
write(*,'("-assembly time : ",es12.5)') tasb
write(*,'("-total time : ",es12.5)') ttot
end if
call psb_erractionrestore(err_act)
return
9999 continue
call psb_erractionrestore(err_act)
if (err_act == psb_act_abort_) then
call psb_error(ictxt)
return
end if
return
end subroutine create_matrix
end function g
end program mld_dexample_1lev
!
! functions parametrizing the differential equation
!
function a1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a1
real(psb_dpk_) :: x,y,z
!a1=1.d0
a1=0.d0
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a2
real(psb_dpk_) :: x,y,z
!a2=2.d1*y
a2=0.d0
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a3
real(psb_dpk_) :: x,y,z
!a3=1.d0
a3=0.d0
end function a3
function a4(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a4
real(psb_dpk_) :: x,y,z
!a4=1.d0
a4=0.d0
end function a4
function b1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b1
real(psb_dpk_) :: x,y,z
b1=1.d0
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b2
real(psb_dpk_) :: x,y,z
b2=1.d0
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b3
real(psb_dpk_) :: x,y,z
b3=1.d0
end function b3
examples/pdegen/mld_dexample_ml.f90
+71 -345
View File
@@ -48,29 +48,23 @@
!
! The PDE is a general second order equation in 3d
!
! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0
! 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, on the unit cube 0<=x,y,z<=1.
! with Dirichlet boundary conditions
! u = g
!
! Example taken from:
! C.T.Kelley
! Iterative Methods for Linear and Nonlinear Equations
! SIAM 1995
! 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.
!
! Boundary conditions are set in a very simple way, by adding
! equations of the form
!
! u(x,y) = exp(-x^2-y^2-z^2)
!
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
!
program mld_dexample_ml
use psb_base_mod
use mld_prec_mod
@@ -92,7 +86,7 @@ program mld_dexample_ml
type(mld_dprec_type) :: P
! right-hand side, solution and residual vectors
real(psb_dpk_), allocatable , save :: b(:), x(:), r(:)
type(psb_d_vect_type) :: x, b, r
! solver and preconditioner parameters
real(psb_dpk_) :: tol, err
@@ -108,6 +102,7 @@ program mld_dexample_ml
integer(psb_long_int_k_) :: amatsize, precsize, descsize
integer :: idim, ierr, ircode
real(psb_dpk_) :: t1, t2, tprec, resmx, resmxp
character(len=5) :: afmt='CSR'
character(len=20) :: name
! initialize the parallel environment
@@ -141,7 +136,8 @@ program mld_dexample_ml
call psb_barrier(ictxt)
t1 = psb_wtime()
call create_matrix(idim,a,b,x,desc_a,ictxt,info)
call psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,&
& a1,a2,a3,b1,b2,b3,c,g,info)
call psb_barrier(ictxt)
t2 = psb_wtime() - t1
if(info /= psb_success_) then
@@ -208,7 +204,7 @@ program mld_dexample_ml
! set the solver parameters and the initial guess
call psb_geall(x,desc_A,info)
x(:) =0.0
call x%set(dzero)
call psb_geasb(x,desc_A,info)
! solve Ax=b with preconditioned BiCGSTAB
@@ -222,12 +218,12 @@ program mld_dexample_ml
call psb_amx(ictxt,t2)
call psb_geall(r,desc_A,info)
r(:) =0.0
call r%set(dzero)
call psb_geasb(r,desc_A,info)
call psb_geaxpby(done,b,dzero,r,desc_A,info)
call psb_spmm(-done,A,x,done,r,desc_A,info)
call psb_genrm2s(resmx,r,desc_A,info)
call psb_geamaxs(resmxp,r,desc_A,info)
resmx = psb_genrm2(r,desc_A,info)
resmxp = psb_geamax(r,desc_A,info)
amatsize = a%sizeof()
descsize = desc_a%sizeof()
@@ -298,331 +294,61 @@ contains
end subroutine get_parms
!
! subroutine to allocate and fill in the coefficient matrix and
! the rhs
!
subroutine create_matrix(idim,a,b,xv,desc_a,ictxt,info)
!
! Discretize the partial diferential equation
!
! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0
! dxdx dydy dzdz dx dy dz
!
! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
!
! Boundary conditions are set in a very simple way, by adding
! equations of the form
!
! u(x,y) = exp(-x^2-y^2-z^2)
!
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
!
use psb_base_mod
implicit none
integer :: idim
integer, parameter :: nb=20
real(psb_dpk_), allocatable :: b(:),xv(:)
type(psb_desc_type) :: desc_a
integer :: ictxt, info
character :: afmt*5
type(psb_dspmat_type) :: a
real(psb_dpk_) :: zt(nb),x,y,z
integer :: m,n,nnz,glob_row,nlr,i,ii,ib,k
integer :: ix,iy,iz,ia,indx_owner, ipoints
integer :: np, iam, nr, nt
integer :: element
integer, allocatable :: irow(:),icol(:),myidx(:)
real(psb_dpk_), allocatable :: val(:)
! deltah dimension of each grid cell
! deltat discretization time
real(psb_dpk_) :: deltah, deltah2
real(psb_dpk_),parameter :: rhs=0.d0,one=1.d0,zero=0.d0
real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen
real(psb_dpk_) :: a1, a2, a3, a4, b1, b2, b3
external :: a1, a2, a3, a4, b1, b2, b3
integer :: err_act
character(len=20) :: name, ch_err
info = psb_success_
name = 'create_matrix'
call psb_erractionsave(err_act)
call psb_info(ictxt, iam, np)
deltah = 1.d0/(idim-1)
deltah2 = deltah*deltah
! initialize array descriptor and sparse matrix storage. provide an
! estimate of the number of non zeroes
ipoints=idim-2
m = ipoints*ipoints*ipoints
n = m
nnz = ((n*9)/(np))
if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n
!
! Using a simple BLOCK distribution.
!
nt = (m+np-1)/np
nr = max(0,min(nt,m-(iam*nt)))
nt = nr
call psb_sum(ictxt,nt)
if (nt /= m) write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m
call psb_barrier(ictxt)
t0 = psb_wtime()
call psb_cdall(ictxt,desc_a,info,nl=nr)
if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz)
! define rhs from boundary conditions; also build initial guess
if (info == psb_success_) call psb_geall(b,desc_a,info)
if (info == psb_success_) call psb_geall(xv,desc_a,info)
nlr = psb_cd_get_local_rows(desc_a)
call psb_barrier(ictxt)
talc = psb_wtime()-t0
if (info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='allocation rout.'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
! functions parametrizing the differential equation
!
function b1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b1
real(psb_dpk_), intent(in) :: x,y,z
b1=1.d0/sqrt(3.d0)
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b2
real(psb_dpk_), intent(in) :: x,y,z
b2=1.d0/sqrt(3.d0)
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b3
real(psb_dpk_), intent(in) :: x,y,z
b3=1.d0/sqrt(3.d0)
end function b3
function c(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: c
real(psb_dpk_), intent(in) :: x,y,z
c=0.d0
end function c
function a1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a1
real(psb_dpk_), intent(in) :: x,y,z
a1=1.d0/80
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a2
real(psb_dpk_), intent(in) :: x,y,z
a2=1.d0/80
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a3
real(psb_dpk_), intent(in) :: x,y,z
a3=1.d0/80
end function a3
function g(x,y,z)
use psb_base_mod, only : psb_dpk_, done
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
! we build an auxiliary matrix consisting of one row at a
! time; just a small matrix. might be extended to generate
! a bunch of rows per call.
!
allocate(val(20*nb),irow(20*nb),&
&icol(20*nb),myidx(nlr),stat=info)
if (info /= psb_success_ ) then
info=psb_err_alloc_dealloc_
call psb_errpush(info,name)
goto 9999
endif
do i=1,nlr
myidx(i) = i
end do
call psb_loc_to_glob(myidx,desc_a,info)
! loop over rows belonging to current process in a block
! distribution.
call psb_barrier(ictxt)
t1 = psb_wtime()
do ii=1, nlr,nb
ib = min(nb,nlr-ii+1)
element = 1
do k=1,ib
i=ii+k-1
! local matrix pointer
glob_row=myidx(i)
! compute gridpoint coordinates
if (mod(glob_row,ipoints*ipoints) == 0) then
ix = glob_row/(ipoints*ipoints)
else
ix = glob_row/(ipoints*ipoints)+1
endif
if (mod((glob_row-(ix-1)*ipoints*ipoints),ipoints) == 0) then
iy = (glob_row-(ix-1)*ipoints*ipoints)/ipoints
else
iy = (glob_row-(ix-1)*ipoints*ipoints)/ipoints+1
endif
iz = glob_row-(ix-1)*ipoints*ipoints-(iy-1)*ipoints
! x, y, x coordinates
x=ix*deltah
y=iy*deltah
z=iz*deltah
! check on boundary points
zt(k) = 0.d0
! internal point: build discretization
!
! term depending on (x-1,y,z)
!
if (ix == 1) then
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*(-val(element))
else
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
icol(element) = (ix-2)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y-1,z)
if (iy == 1) then
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-2)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y,z-1)
if (iz == 1) then
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz-1)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y,z)
val(element)=(2*b1(x,y,z) + 2*b2(x,y,z) + 2*b3(x,y,z))/deltah2&
& + (a1(x,y,z) + a2(x,y,z) + a3(x,y,z)+ a4(x,y,z))/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
! term depending on (x,y,z+1)
if (iz == ipoints) then
val(element)=-b1(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b1(x,y,z)/deltah2
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz+1)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y+1,z)
if (iy == ipoints) then
val(element)=-b2(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b2(x,y,z)/deltah2
icol(element) = (ix-1)*ipoints*ipoints+(iy)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x+1,y,z)
if (ix==ipoints) then
val(element)=-b3(x,y,z)/deltah2
zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/deltah2
icol(element) = (ix)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
end do
call psb_spins(element-1,irow,icol,val,a,desc_a,info)
if(info /= psb_success_) exit
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),b,desc_a,info)
if(info /= psb_success_) exit
zt(:)=0.d0
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xv,desc_a,info)
if(info /= psb_success_) exit
end do
tgen = psb_wtime()-t1
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
deallocate(val,irow,icol)
call psb_barrier(ictxt)
t1 = psb_wtime()
call psb_cdasb(desc_a,info)
if (info == psb_success_) &
& call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_)
call psb_barrier(ictxt)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
call psb_geasb(b,desc_a,info)
call psb_geasb(xv,desc_a,info)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
tasb = psb_wtime()-t1
call psb_barrier(ictxt)
ttot = psb_wtime() - t0
call psb_amx(ictxt,talc)
call psb_amx(ictxt,tgen)
call psb_amx(ictxt,tasb)
call psb_amx(ictxt,ttot)
if(iam == psb_root_) then
write(*,'("The matrix has been generated and assembled in ",a3," format.")')&
& a%get_fmt()
write(*,'("-allocation time : ",es12.5)') talc
write(*,'("-coeff. gen. time : ",es12.5)') tgen
write(*,'("-assembly time : ",es12.5)') tasb
write(*,'("-total time : ",es12.5)') ttot
end if
call psb_erractionrestore(err_act)
return
9999 continue
call psb_erractionrestore(err_act)
if (err_act == psb_act_abort_) then
call psb_error(ictxt)
return
end if
return
end subroutine create_matrix
end function g
end program mld_dexample_ml
!
! functions parametrizing the differential equation
!
function a1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a1
real(psb_dpk_) :: x,y,z
! a1=1.d0
a1=0.d0
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a2
real(psb_dpk_) :: x,y,z
! a2=2.d1*y
a2=0.d0
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a3
real(psb_dpk_) :: x,y,z
! a3=1.d0
a3=0.d0
end function a3
function a4(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a4
real(psb_dpk_) :: x,y,z
! a4=1.d0
a4=0.d0
end function a4
function b1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b1
real(psb_dpk_) :: x,y,z
b1=1.d0
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b2
real(psb_dpk_) :: x,y,z
b2=1.d0
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b3
real(psb_dpk_) :: x,y,z
b3=1.d0
end function b3
examples/pdegen/mld_sexample_1lev.f90
+70 -346
View File
@@ -48,29 +48,23 @@
!
! The PDE is a general second order equation in 3d
!
! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0
! 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, on the unit cube 0<=x,y,z<=1.
! with Dirichlet boundary conditions
! u = g
!
! Example taken from:
! C.T.Kelley
! Iterative Methods for Linear and Nonlinear Equations
! SIAM 1995
! 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.
!
! Boundary conditions are set in a very simple way, by adding
! equations of the form
!
! u(x,y) = exp(-x^2-y^2-z^2)
!
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
!
program mld_sexample_1lev
use psb_base_mod
use mld_prec_mod
@@ -91,7 +85,7 @@ program mld_sexample_1lev
type(mld_sprec_type) :: P
! right-hand side, solution and residual vectors
real(psb_spk_), allocatable , save :: b(:), x(:), r(:)
type(psb_s_vect_type) :: x, b, r
! solver parameters
real(psb_spk_) :: tol, err
@@ -106,6 +100,7 @@ program mld_sexample_1lev
integer :: idim, nlev, ierr, ircode
real(psb_dpk_) :: t1, t2, tprec
real(psb_spk_) :: resmx, resmxp
character(len=5) :: afmt='CSR'
character(len=20) :: name
! initialize the parallel environment
@@ -138,7 +133,8 @@ program mld_sexample_1lev
call psb_barrier(ictxt)
t1 = psb_wtime()
call create_matrix(idim,a,b,x,desc_a,ictxt,info)
call psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,&
& a1,a2,a3,b1,b2,b3,c,g,info)
call psb_barrier(ictxt)
t2 = psb_wtime() - t1
if(info /= psb_success_) then
@@ -173,7 +169,7 @@ program mld_sexample_1lev
! set the initial guess
call psb_geall(x,desc_A,info)
x(:) =0.0
call x%set(szero)
call psb_geasb(x,desc_A,info)
! solve Ax=b with preconditioned BiCGSTAB
@@ -187,12 +183,12 @@ program mld_sexample_1lev
call psb_amx(ictxt,t2)
call psb_geall(r,desc_A,info)
r(:) =0.0
call r%set(szero)
call psb_geasb(r,desc_A,info)
call psb_geaxpby(sone,b,szero,r,desc_A,info)
call psb_spmm(-sone,A,x,sone,r,desc_A,info)
call psb_genrm2s(resmx,r,desc_A,info)
call psb_geamaxs(resmxp,r,desc_A,info)
resmx = psb_genrm2(r,desc_A,info)
resmxp = psb_geamax(r,desc_A,info)
amatsize = a%sizeof()
descsize = desc_a%sizeof()
@@ -260,332 +256,60 @@ contains
call psb_bcast(ictxt,tol)
end subroutine get_parms
!
! subroutine to allocate and fill in the coefficient matrix and
! the rhs
!
subroutine create_matrix(idim,a,b,xv,desc_a,ictxt,info)
!
! Discretize the partial diferential equation
!
! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0
! dxdx dydy dzdz dx dy dz
!
! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
!
! Boundary conditions are set in a very simple way, by adding
! equations of the form
!
! u(x,y) = exp(-x^2-y^2-z^2)
!
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
!
use psb_base_mod
implicit none
integer :: idim
integer, parameter :: nb=20
real(psb_spk_), allocatable :: b(:),xv(:)
type(psb_desc_type) :: desc_a
integer :: ictxt, info
character :: afmt*5
type(psb_sspmat_type) :: a
real(psb_spk_) :: zt(nb),x,y,z
integer :: m,n,nnz,glob_row,nlr,i,ii,ib,k
integer :: ix,iy,iz,ia,indx_owner, ipoints
integer :: np, iam, nr, nt
integer :: element
integer, allocatable :: irow(:),icol(:),myidx(:)
real(psb_spk_), allocatable :: val(:)
! deltah dimension of each grid cell
! deltat discretization time
real(psb_spk_) :: deltah, deltah2
real(psb_spk_),parameter :: rhs=0.0,one=1.0,zero=0.0
real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen
real(psb_spk_) :: a1, a2, a3, a4, b1, b2, b3
external :: a1, a2, a3, a4, b1, b2, b3
integer :: err_act
character(len=20) :: name, ch_err
info = psb_success_
name = 'create_matrix'
call psb_erractionsave(err_act)
call psb_info(ictxt, iam, np)
deltah = 1.d0/(idim-1)
deltah2 = deltah*deltah
! initialize array descriptor and sparse matrix storage. provide an
! estimate of the number of non zeroes
ipoints=idim-2
m = ipoints*ipoints*ipoints
n = m
nnz = ((n*9)/(np))
if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n
!
! Using a simple BLOCK distribution.
!
nt = (m+np-1)/np
nr = max(0,min(nt,m-(iam*nt)))
nt = nr
call psb_sum(ictxt,nt)
if (nt /= m) write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m
call psb_barrier(ictxt)
t0 = psb_wtime()
call psb_cdall(ictxt,desc_a,info,nl=nr)
if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz)
! define rhs from boundary conditions; also build initial guess
if (info == psb_success_) call psb_geall(b,desc_a,info)
if (info == psb_success_) call psb_geall(xv,desc_a,info)
nlr = psb_cd_get_local_rows(desc_a)
call psb_barrier(ictxt)
talc = psb_wtime()-t0
if (info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='allocation rout.'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
! functions parametrizing the differential equation
!
function b1(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b1
real(psb_spk_), intent(in) :: x,y,z
b1=1.e0/sqrt(3.e0)
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b2
real(psb_spk_), intent(in) :: x,y,z
b2=1.e0/sqrt(3.e0)
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b3
real(psb_spk_), intent(in) :: x,y,z
b3=1.e0/sqrt(3.e0)
end function b3
function c(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: c
real(psb_spk_), intent(in) :: x,y,z
c=0.e0
end function c
function a1(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a1
real(psb_spk_), intent(in) :: x,y,z
a1=1.e0/80
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a2
real(psb_spk_), intent(in) :: x,y,z
a2=1.e0/80
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a3
real(psb_spk_), intent(in) :: x,y,z
a3=1.e0/80
end function a3
function g(x,y,z)
use psb_base_mod, only : psb_spk_, sone
real(psb_spk_) :: g
real(psb_spk_), intent(in) :: x,y,z
g = szero
if (x == sone) then
g = sone
else if (x == szero) then
g = exp(y**2-z**2)
end if
! we build an auxiliary matrix consisting of one row at a
! time; just a small matrix. might be extended to generate
! a bunch of rows per call.
!
allocate(val(20*nb),irow(20*nb),&
&icol(20*nb),myidx(nlr),stat=info)
if (info /= psb_success_ ) then
info=psb_err_alloc_dealloc_
call psb_errpush(info,name)
goto 9999
endif
do i=1,nlr
myidx(i) = i
end do
call psb_loc_to_glob(myidx,desc_a,info)
! loop over rows belonging to current process in a block
! distribution.
call psb_barrier(ictxt)
t1 = psb_wtime()
do ii=1, nlr,nb
ib = min(nb,nlr-ii+1)
element = 1
do k=1,ib
i=ii+k-1
! local matrix pointer
glob_row=myidx(i)
! compute gridpoint coordinates
if (mod(glob_row,ipoints*ipoints) == 0) then
ix = glob_row/(ipoints*ipoints)
else
ix = glob_row/(ipoints*ipoints)+1
endif
if (mod((glob_row-(ix-1)*ipoints*ipoints),ipoints) == 0) then
iy = (glob_row-(ix-1)*ipoints*ipoints)/ipoints
else
iy = (glob_row-(ix-1)*ipoints*ipoints)/ipoints+1
endif
iz = glob_row-(ix-1)*ipoints*ipoints-(iy-1)*ipoints
! x, y, x coordinates
x=ix*deltah
y=iy*deltah
z=iz*deltah
! check on boundary points
zt(k) = 0.d0
! internal point: build discretization
!
! term depending on (x-1,y,z)
!
if (ix == 1) then
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*(-val(element))
else
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
icol(element) = (ix-2)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y-1,z)
if (iy == 1) then
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-2)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y,z-1)
if (iz == 1) then
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz-1)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y,z)
val(element)=(2*b1(x,y,z) + 2*b2(x,y,z) + 2*b3(x,y,z))/deltah2&
& + (a1(x,y,z) + a2(x,y,z) + a3(x,y,z)+ a4(x,y,z))/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
! term depending on (x,y,z+1)
if (iz == ipoints) then
val(element)=-b1(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b1(x,y,z)/deltah2
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz+1)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y+1,z)
if (iy == ipoints) then
val(element)=-b2(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b2(x,y,z)/deltah2
icol(element) = (ix-1)*ipoints*ipoints+(iy)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x+1,y,z)
if (ix==ipoints) then
val(element)=-b3(x,y,z)/deltah2
zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/deltah2
icol(element) = (ix)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
end do
call psb_spins(element-1,irow,icol,val,a,desc_a,info)
if(info /= psb_success_) exit
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),b,desc_a,info)
if(info /= psb_success_) exit
zt(:)=0.d0
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xv,desc_a,info)
if(info /= psb_success_) exit
end do
tgen = psb_wtime()-t1
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
deallocate(val,irow,icol)
call psb_barrier(ictxt)
t1 = psb_wtime()
call psb_cdasb(desc_a,info)
if (info == psb_success_) &
& call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_)
call psb_barrier(ictxt)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
call psb_geasb(b,desc_a,info)
call psb_geasb(xv,desc_a,info)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
tasb = psb_wtime()-t1
call psb_barrier(ictxt)
ttot = psb_wtime() - t0
call psb_amx(ictxt,talc)
call psb_amx(ictxt,tgen)
call psb_amx(ictxt,tasb)
call psb_amx(ictxt,ttot)
if(iam == psb_root_) then
write(*,'("The matrix has been generated and assembled in ",a3," format.")')&
& a%get_fmt()
write(*,'("-allocation time : ",es12.5)') talc
write(*,'("-coeff. gen. time : ",es12.5)') tgen
write(*,'("-assembly time : ",es12.5)') tasb
write(*,'("-total time : ",es12.5)') ttot
end if
call psb_erractionrestore(err_act)
return
9999 continue
call psb_erractionrestore(err_act)
if (err_act == psb_act_abort_) then
call psb_error(ictxt)
return
end if
return
end subroutine create_matrix
end function g
end program mld_sexample_1lev
!
! 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
examples/pdegen/mld_sexample_ml.f90
+71 -346
View File
@@ -48,29 +48,23 @@
!
! The PDE is a general second order equation in 3d
!
! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0
! 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, on the unit cube 0<=x,y,z<=1.
! with Dirichlet boundary conditions
! u = g
!
! Example taken from:
! C.T.Kelley
! Iterative Methods for Linear and Nonlinear Equations
! SIAM 1995
! 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.
!
! Boundary conditions are set in a very simple way, by adding
! equations of the form
!
! u(x,y) = exp(-x^2-y^2-z^2)
!
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
!
program mld_sexample_ml
use psb_base_mod
use mld_prec_mod
@@ -92,7 +86,7 @@ program mld_sexample_ml
type(mld_sprec_type) :: P
! right-hand side, solution and residual vectors
real(psb_spk_), allocatable , save :: b(:), x(:), r(:)
type(psb_s_vect_type) :: x, b, r
! solver and preconditioner parameters
real(psb_spk_) :: tol, err
@@ -109,6 +103,7 @@ program mld_sexample_ml
integer :: idim, ierr, ircode
real(psb_dpk_) :: t1, t2, tprec
real(psb_spk_) :: resmx, resmxp
character(len=5) :: afmt='CSR'
character(len=20) :: name
! initialize the parallel environment
@@ -142,7 +137,8 @@ program mld_sexample_ml
call psb_barrier(ictxt)
t1 = psb_wtime()
call create_matrix(idim,a,b,x,desc_a,ictxt,info)
call psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,&
& a1,a2,a3,b1,b2,b3,c,g,info)
call psb_barrier(ictxt)
t2 = psb_wtime() - t1
if(info /= psb_success_) then
@@ -209,7 +205,7 @@ program mld_sexample_ml
! set the solver parameters and the initial guess
call psb_geall(x,desc_A,info)
x(:) =0.0
call x%set(szero)
call psb_geasb(x,desc_A,info)
! solve Ax=b with preconditioned BiCGSTAB
@@ -223,12 +219,12 @@ program mld_sexample_ml
call psb_amx(ictxt,t2)
call psb_geall(r,desc_A,info)
r(:) =0.0
call r%set(szero)
call psb_geasb(r,desc_A,info)
call psb_geaxpby(sone,b,szero,r,desc_A,info)
call psb_spmm(-sone,A,x,sone,r,desc_A,info)
call psb_genrm2s(resmx,r,desc_A,info)
call psb_geamaxs(resmxp,r,desc_A,info)
resmx = psb_genrm2(r,desc_A,info)
resmxp = psb_geamax(r,desc_A,info)
amatsize = a%sizeof()
descsize = desc_a%sizeof()
@@ -298,332 +294,61 @@ contains
call psb_bcast(ictxt,tol)
end subroutine get_parms
!
! subroutine to allocate and fill in the coefficient matrix and
! the rhs
!
subroutine create_matrix(idim,a,b,xv,desc_a,ictxt,info)
!
! Discretize the partial diferential equation
!
! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0
! dxdx dydy dzdz dx dy dz
!
! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
!
! Boundary conditions are set in a very simple way, by adding
! equations of the form
!
! u(x,y) = exp(-x^2-y^2-z^2)
!
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
!
use psb_base_mod
implicit none
integer :: idim
integer, parameter :: nb=20
real(psb_spk_), allocatable :: b(:),xv(:)
type(psb_desc_type) :: desc_a
integer :: ictxt, info
character :: afmt*5
type(psb_sspmat_type) :: a
real(psb_spk_) :: zt(nb),x,y,z
integer :: m,n,nnz,glob_row,nlr,i,ii,ib,k
integer :: ix,iy,iz,ia,indx_owner, ipoints
integer :: np, iam, nr, nt
integer :: element
integer, allocatable :: irow(:),icol(:),myidx(:)
real(psb_spk_), allocatable :: val(:)
! deltah dimension of each grid cell
! deltat discretization time
real(psb_spk_) :: deltah, deltah2
real(psb_spk_),parameter :: rhs=0.0,one=1.0,zero=0.0
real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen
real(psb_spk_) :: a1, a2, a3, a4, b1, b2, b3
external :: a1, a2, a3, a4, b1, b2, b3
integer :: err_act
character(len=20) :: name, ch_err
info = psb_success_
name = 'create_matrix'
call psb_erractionsave(err_act)
call psb_info(ictxt, iam, np)
deltah = 1.d0/(idim-1)
deltah2 = deltah*deltah
! initialize array descriptor and sparse matrix storage. provide an
! estimate of the number of non zeroes
ipoints=idim-2
m = ipoints*ipoints*ipoints
n = m
nnz = ((n*9)/(np))
if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n
!
! Using a simple BLOCK distribution.
!
nt = (m+np-1)/np
nr = max(0,min(nt,m-(iam*nt)))
nt = nr
call psb_sum(ictxt,nt)
if (nt /= m) write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m
call psb_barrier(ictxt)
t0 = psb_wtime()
call psb_cdall(ictxt,desc_a,info,nl=nr)
if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz)
! define rhs from boundary conditions; also build initial guess
if (info == psb_success_) call psb_geall(b,desc_a,info)
if (info == psb_success_) call psb_geall(xv,desc_a,info)
nlr = psb_cd_get_local_rows(desc_a)
call psb_barrier(ictxt)
talc = psb_wtime()-t0
if (info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='allocation rout.'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
! functions parametrizing the differential equation
!
function b1(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b1
real(psb_spk_), intent(in) :: x,y,z
b1=1.e0/sqrt(3.e0)
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b2
real(psb_spk_), intent(in) :: x,y,z
b2=1.e0/sqrt(3.e0)
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b3
real(psb_spk_), intent(in) :: x,y,z
b3=1.e0/sqrt(3.e0)
end function b3
function c(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: c
real(psb_spk_), intent(in) :: x,y,z
c=0.e0
end function c
function a1(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a1
real(psb_spk_), intent(in) :: x,y,z
a1=1.e0/80
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a2
real(psb_spk_), intent(in) :: x,y,z
a2=1.e0/80
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a3
real(psb_spk_), intent(in) :: x,y,z
a3=1.e0/80
end function a3
function g(x,y,z)
use psb_base_mod, only : psb_spk_, sone
real(psb_spk_) :: g
real(psb_spk_), intent(in) :: x,y,z
g = szero
if (x == sone) then
g = sone
else if (x == szero) then
g = exp(y**2-z**2)
end if
! we build an auxiliary matrix consisting of one row at a
! time; just a small matrix. might be extended to generate
! a bunch of rows per call.
!
allocate(val(20*nb),irow(20*nb),&
&icol(20*nb),myidx(nlr),stat=info)
if (info /= psb_success_ ) then
info=psb_err_alloc_dealloc_
call psb_errpush(info,name)
goto 9999
endif
do i=1,nlr
myidx(i) = i
end do
call psb_loc_to_glob(myidx,desc_a,info)
! loop over rows belonging to current process in a block
! distribution.
call psb_barrier(ictxt)
t1 = psb_wtime()
do ii=1, nlr,nb
ib = min(nb,nlr-ii+1)
element = 1
do k=1,ib
i=ii+k-1
! local matrix pointer
glob_row=myidx(i)
! compute gridpoint coordinates
if (mod(glob_row,ipoints*ipoints) == 0) then
ix = glob_row/(ipoints*ipoints)
else
ix = glob_row/(ipoints*ipoints)+1
endif
if (mod((glob_row-(ix-1)*ipoints*ipoints),ipoints) == 0) then
iy = (glob_row-(ix-1)*ipoints*ipoints)/ipoints
else
iy = (glob_row-(ix-1)*ipoints*ipoints)/ipoints+1
endif
iz = glob_row-(ix-1)*ipoints*ipoints-(iy-1)*ipoints
! x, y, x coordinates
x=ix*deltah
y=iy*deltah
z=iz*deltah
! check on boundary points
zt(k) = 0.d0
! internal point: build discretization
!
! term depending on (x-1,y,z)
!
if (ix == 1) then
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*(-val(element))
else
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
icol(element) = (ix-2)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y-1,z)
if (iy == 1) then
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-2)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y,z-1)
if (iz == 1) then
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz-1)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y,z)
val(element)=(2*b1(x,y,z) + 2*b2(x,y,z) + 2*b3(x,y,z))/deltah2&
& + (a1(x,y,z) + a2(x,y,z) + a3(x,y,z)+ a4(x,y,z))/deltah
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
! term depending on (x,y,z+1)
if (iz == ipoints) then
val(element)=-b1(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b1(x,y,z)/deltah2
icol(element) = (ix-1)*ipoints*ipoints+(iy-1)*ipoints+(iz+1)
irow(element) = glob_row
element = element+1
endif
! term depending on (x,y+1,z)
if (iy == ipoints) then
val(element)=-b2(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b2(x,y,z)/deltah2
icol(element) = (ix-1)*ipoints*ipoints+(iy)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
! term depending on (x+1,y,z)
if (ix==ipoints) then
val(element)=-b3(x,y,z)/deltah2
zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/deltah2
icol(element) = (ix)*ipoints*ipoints+(iy-1)*ipoints+(iz)
irow(element) = glob_row
element = element+1
endif
end do
call psb_spins(element-1,irow,icol,val,a,desc_a,info)
if(info /= psb_success_) exit
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),b,desc_a,info)
if(info /= psb_success_) exit
zt(:)=0.d0
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xv,desc_a,info)
if(info /= psb_success_) exit
end do
tgen = psb_wtime()-t1
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
deallocate(val,irow,icol)
call psb_barrier(ictxt)
t1 = psb_wtime()
call psb_cdasb(desc_a,info)
if (info == psb_success_) &
& call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_)
call psb_barrier(ictxt)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
call psb_geasb(b,desc_a,info)
call psb_geasb(xv,desc_a,info)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name)
goto 9999
end if
tasb = psb_wtime()-t1
call psb_barrier(ictxt)
ttot = psb_wtime() - t0
call psb_amx(ictxt,talc)
call psb_amx(ictxt,tgen)
call psb_amx(ictxt,tasb)
call psb_amx(ictxt,ttot)
if(iam == psb_root_) then
write(*,'("The matrix has been generated and assembled in ",a3," format.")')&
& a%get_fmt()
write(*,'("-allocation time : ",es12.5)') talc
write(*,'("-coeff. gen. time : ",es12.5)') tgen
write(*,'("-assembly time : ",es12.5)') tasb
write(*,'("-total time : ",es12.5)') ttot
end if
call psb_erractionrestore(err_act)
return
9999 continue
call psb_erractionrestore(err_act)
if (err_act == psb_act_abort_) then
call psb_error(ictxt)
return
end if
return
end subroutine create_matrix
end function g
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
mlprec/mld_base_prec_type.F90
+7 -4
View File
@@ -195,11 +195,14 @@ module mld_base_prec_type
!
! Legal values for entry: mld_ilu_scale_
!
integer, parameter :: mld_ilu_scale_none_ = 0
integer, parameter :: mld_ilu_scale_maxval_ = 1
integer, parameter :: mld_ilu_scale_diag_ = 2
integer, parameter :: mld_ilu_scale_none_ = 0
integer, parameter :: mld_ilu_scale_maxval_ = 1
integer, parameter :: mld_ilu_scale_diag_ = 2
integer, parameter :: mld_ilu_scale_arwsum_ = 3
integer, parameter :: mld_ilu_scale_aclsum_ = 4
integer, parameter :: mld_ilu_scale_dabsum_ = 5
! For the time being enable only maxval scale
integer, parameter :: mld_max_ilu_scale_ = 1
integer, parameter :: mld_max_ilu_scale_ = 1
!
! Legal values for entry: mld_ml_type_
!