!
! This example shows how to avoid Fortran line lengths larger than 132 characters.
! It avoids used of certain macros such as PetscCallA() and PetscCheckA() that
! generate very long lines
!
! We recommend starting from src/snes/tutorials/ex5f90.F90 instead of this example
! because that does not have the restricted formatting that makes this version
! more difficult to read
!
! Description: This example solves a nonlinear system in parallel with SNES.
! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
! domain, using distributed arrays (DMDAs) to partition the parallel grid.
! The command line options include:
! -par , where indicates the nonlinearity of the problem
! problem SFI: = Bratu parameter (0 <= par <= 6.81)
!
! --------------------------------------------------------------------------
!
! Solid Fuel Ignition (SFI) problem. This problem is modeled by
! the partial differential equation
!
! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
!
! with boundary conditions
!
! u = 0 for x = 0, x = 1, y = 0, y = 1.
!
! A finite difference approximation with the usual 5-point stencil
! is used to discretize the boundary value problem to obtain a nonlinear
! system of equations.
!
! --------------------------------------------------------------------------
module ex5fmodule
use petscsnes
use petscdmda
#include
#include
#include
PetscInt xs,xe,xm,gxs,gxe,gxm
PetscInt ys,ye,ym,gys,gye,gym
PetscInt mx,my
PetscMPIInt rank,size
PetscReal lambda
end module ex5fmodule
program main
use ex5fmodule
implicit none
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Variable declarations
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! Variables:
! snes - nonlinear solver
! x, r - solution, residual vectors
! its - iterations for convergence
!
! See additional variable declarations in the file ex5f.h
!
SNES snes
Vec x,r
PetscInt its,i1,i4
PetscErrorCode ierr
PetscReal lambda_max,lambda_min
PetscBool flg
DM da
! Note: Any user-defined Fortran routines (such as FormJacobianLocal)
! MUST be declared as external.
external FormInitialGuess
external FormFunctionLocal,FormJacobianLocal
external MySNESConverged
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Initialize program
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
call PetscInitialize(ierr)
CHKERRA(ierr)
call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
CHKERRMPIA(ierr)
call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
CHKERRMPIA(ierr)
! Initialize problem parameters
i1 = 1
i4 = 4
lambda_max = 6.81
lambda_min = 0.0
lambda = 6.0
call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,PETSC_NULL_BOOL,ierr)
CHKERRA(ierr)
! this statement is split into multiple-lines to keep lines under 132 char limit - required by 'make check'
if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
ierr = PETSC_ERR_ARG_OUTOFRANGE;
SETERRA(PETSC_COMM_WORLD,ierr,'Lambda')
endif
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Create nonlinear solver context
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
CHKERRA(ierr)
! Set convergence test routine if desired
call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)
CHKERRA(ierr)
if (flg) then
call SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,ierr)
CHKERRA(ierr)
endif
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Create vector data structures; set function evaluation routine
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Create distributed array (DMDA) to manage parallel grid and vectors
! This really needs only the star-type stencil, but we use the box stencil
call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE, &
i1,i1, PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
CHKERRA(ierr)
call DMSetFromOptions(da,ierr)
CHKERRA(ierr)
call DMSetUp(da,ierr)
CHKERRA(ierr)
! Extract global and local vectors from DMDA; then duplicate for remaining
! vectors that are the same types
call DMCreateGlobalVector(da,x,ierr)
CHKERRA(ierr)
call VecDuplicate(x,r,ierr)
CHKERRA(ierr)
! Get local grid boundaries (for 2-dimensional DMDA)
call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
CHKERRA(ierr)
call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)
CHKERRA(ierr)
call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)
CHKERRA(ierr)
! Here we shift the starting indices up by one so that we can easily
! use the Fortran convention of 1-based indices (rather 0-based indices).
xs = xs+1
ys = ys+1
gxs = gxs+1
gys = gys+1
ye = ys+ym-1
xe = xs+xm-1
gye = gys+gym-1
gxe = gxs+gxm-1
! Set function evaluation routine and vector
call DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)
CHKERRA(ierr)
call DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)
CHKERRA(ierr)
call SNESSetDM(snes,da,ierr)
CHKERRA(ierr)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Customize nonlinear solver; set runtime options
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Set runtime options (e.g., -snes_monitor -snes_rtol -ksp_type )
call SNESSetFromOptions(snes,ierr)
CHKERRA(ierr)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Evaluate initial guess; then solve nonlinear system.
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Note: The user should initialize the vector, x, with the initial guess
! for the nonlinear solver prior to calling SNESSolve(). In particular,
! to employ an initial guess of zero, the user should explicitly set
! this vector to zero by calling VecSet().
call FormInitialGuess(x,ierr)
CHKERRA(ierr)
call SNESSolve(snes,PETSC_NULL_VEC,x,ierr)
CHKERRA(ierr)
call SNESGetIterationNumber(snes,its,ierr)
CHKERRA(ierr)
if (rank .eq. 0) then
write(6,100) its
endif
100 format('Number of SNES iterations = ',i5)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Free work space. All PETSc objects should be destroyed when they
! are no longer needed.
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
call VecDestroy(x,ierr)
CHKERRA(ierr)
call VecDestroy(r,ierr)
CHKERRA(ierr)
call SNESDestroy(snes,ierr)
CHKERRA(ierr)
call DMDestroy(da,ierr)
CHKERRA(ierr)
call PetscFinalize(ierr)
CHKERRA(ierr)
end
! ---------------------------------------------------------------------
!
! FormInitialGuess - Forms initial approximation.
!
! Input Parameters:
! X - vector
!
! Output Parameter:
! X - vector
!
! Notes:
! This routine serves as a wrapper for the lower-level routine
! "ApplicationInitialGuess", where the actual computations are
! done using the standard Fortran style of treating the local
! vector data as a multidimensional array over the local mesh.
! This routine merely handles ghost point scatters and accesses
! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
!
subroutine FormInitialGuess(X,ierr)
use ex5fmodule
implicit none
! Input/output variables:
Vec X
PetscErrorCode ierr
! Declarations for use with local arrays:
PetscScalar, pointer :: lx_v(:)
ierr = 0
! Get a pointer to vector data.
! - For default PETSc vectors, VecGetArray() returns a pointer to
! the data array. Otherwise, the routine is implementation dependent.
! - You MUST call VecRestoreArray() when you no longer need access to
! the array.
! - Note that the Fortran interface to VecGetArray() differs from the
! C version. See the users manual for details.
call VecGetArrayF90(X,lx_v,ierr)
CHKERRQ(ierr)
! Compute initial guess over the locally owned part of the grid
call InitialGuessLocal(lx_v,ierr)
CHKERRQ(ierr)
! Restore vector
call VecRestoreArrayF90(X,lx_v,ierr)
CHKERRQ(ierr)
end
! ---------------------------------------------------------------------
!
! InitialGuessLocal - Computes initial approximation, called by
! the higher level routine FormInitialGuess().
!
! Input Parameter:
! x - local vector data
!
! Output Parameters:
! x - local vector data
! ierr - error code
!
! Notes:
! This routine uses standard Fortran-style computations over a 2-dim array.
!
subroutine InitialGuessLocal(x,ierr)
use ex5fmodule
implicit none
! Input/output variables:
PetscScalar x(xs:xe,ys:ye)
PetscErrorCode ierr
! Local variables:
PetscInt i,j
PetscReal temp1,temp,one,hx,hy
! Set parameters
ierr = 0
one = 1.0
hx = one/((mx-1))
hy = one/((my-1))
temp1 = lambda/(lambda + one)
do 20 j=ys,ye
temp = (min(j-1,my-j))*hy
do 10 i=xs,xe
if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
x(i,j) = 0.0
else
x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,(temp)))
endif
10 continue
20 continue
end
! ---------------------------------------------------------------------
!
! FormFunctionLocal - Computes nonlinear function, called by
! the higher level routine FormFunction().
!
! Input Parameter:
! x - local vector data
!
! Output Parameters:
! f - local vector data, f(x)
! ierr - error code
!
! Notes:
! This routine uses standard Fortran-style computations over a 2-dim array.
!
!
subroutine FormFunctionLocal(info,x,f,da,ierr)
use ex5fmodule
implicit none
DM da
! Input/output variables:
DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
PetscScalar x(gxs:gxe,gys:gye)
PetscScalar f(xs:xe,ys:ye)
PetscErrorCode ierr
! Local variables:
PetscScalar two,one,hx,hy
PetscScalar hxdhy,hydhx,sc
PetscScalar u,uxx,uyy
PetscInt i,j
xs = info(DMDA_LOCAL_INFO_XS)+1
xe = xs+info(DMDA_LOCAL_INFO_XM)-1
ys = info(DMDA_LOCAL_INFO_YS)+1
ye = ys+info(DMDA_LOCAL_INFO_YM)-1
mx = info(DMDA_LOCAL_INFO_MX)
my = info(DMDA_LOCAL_INFO_MY)
one = 1.0
two = 2.0
hx = one/(mx-1)
hy = one/(my-1)
sc = hx*hy*lambda
hxdhy = hx/hy
hydhx = hy/hx
! Compute function over the locally owned part of the grid
do 20 j=ys,ye
do 10 i=xs,xe
if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
f(i,j) = x(i,j)
else
u = x(i,j)
uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
f(i,j) = uxx + uyy - sc*exp(u)
endif
10 continue
20 continue
call PetscLogFlops(11.0d0*ym*xm,ierr)
CHKERRQ(ierr)
end
! ---------------------------------------------------------------------
!
! FormJacobianLocal - Computes Jacobian matrix, called by
! the higher level routine FormJacobian().
!
! Input Parameters:
! x - local vector data
!
! Output Parameters:
! jac - Jacobian matrix
! jac_prec - optionally different preconditioning matrix (not used here)
! ierr - error code
!
! Notes:
! This routine uses standard Fortran-style computations over a 2-dim array.
!
! Notes:
! Due to grid point reordering with DMDAs, we must always work
! with the local grid points, and then transform them to the new
! global numbering with the "ltog" mapping
! We cannot work directly with the global numbers for the original
! uniprocessor grid!
!
! Two methods are available for imposing this transformation
! when setting matrix entries:
! (A) MatSetValuesLocal(), using the local ordering (including
! ghost points!)
! by calling MatSetValuesLocal()
! (B) MatSetValues(), using the global ordering
! - Use DMDAGetGlobalIndices() to extract the local-to-global map
! - Then apply this map explicitly yourself
! - Set matrix entries using the global ordering by calling
! MatSetValues()
! Option (A) seems cleaner/easier in many cases, and is the procedure
! used in this example.
!
subroutine FormJacobianLocal(info,x,A,jac,da,ierr)
use ex5fmodule
implicit none
DM da
! Input/output variables:
PetscScalar x(gxs:gxe,gys:gye)
Mat A,jac
PetscErrorCode ierr
DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
! Local variables:
PetscInt row,col(5),i,j,i1,i5
PetscScalar two,one,hx,hy,v(5)
PetscScalar hxdhy,hydhx,sc
! Set parameters
i1 = 1
i5 = 5
one = 1.0
two = 2.0
hx = one/(mx-1)
hy = one/(my-1)
sc = hx*hy
hxdhy = hx/hy
hydhx = hy/hx
! Compute entries for the locally owned part of the Jacobian.
! - Currently, all PETSc parallel matrix formats are partitioned by
! contiguous chunks of rows across the processors.
! - Each processor needs to insert only elements that it owns
! locally (but any non-local elements will be sent to the
! appropriate processor during matrix assembly).
! - Here, we set all entries for a particular row at once.
! - We can set matrix entries either using either
! MatSetValuesLocal() or MatSetValues(), as discussed above.
! - Note that MatSetValues() uses 0-based row and column numbers
! in Fortran as well as in C.
do 20 j=ys,ye
row = (j - gys)*gxm + xs - gxs - 1
do 10 i=xs,xe
row = row + 1
! boundary points
if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
! Some f90 compilers need 4th arg to be of same type in both calls
col(1) = row
v(1) = one
call MatSetValuesLocal(jac,i1,row,i1,col,v,INSERT_VALUES,ierr)
CHKERRQ(ierr)
! interior grid points
else
v(1) = -hxdhy
v(2) = -hydhx
v(3) = two*(hydhx + hxdhy) - sc*lambda*exp(x(i,j))
v(4) = -hydhx
v(5) = -hxdhy
col(1) = row - gxm
col(2) = row - 1
col(3) = row
col(4) = row + 1
col(5) = row + gxm
call MatSetValuesLocal(jac,i1,row,i5,col,v, INSERT_VALUES,ierr)
CHKERRQ(ierr)
endif
10 continue
20 continue
call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
CHKERRQ(ierr)
call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
CHKERRQ(ierr)
if (A .ne. jac) then
call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
CHKERRQ(ierr)
call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
CHKERRQ(ierr)
endif
end
!
! Simple convergence test based on the infinity norm of the residual being small
!
subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr)
use ex5fmodule
implicit none
SNES snes
PetscInt it,dummy
PetscReal xnorm,snorm,fnorm,nrm
SNESConvergedReason reason
Vec f
PetscErrorCode ierr
call SNESGetFunction(snes,f,PETSC_NULL_FUNCTION,dummy,ierr)
CHKERRQ(ierr)
call VecNorm(f,NORM_INFINITY,nrm,ierr)
CHKERRQ(ierr)
if (nrm .le. 1.e-5) reason = SNES_CONVERGED_FNORM_ABS
end
!/*TEST
!
! build:
! requires: !complex !single
!
! test:
! nsize: 4
! args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short \
! -ksp_gmres_cgs_refinement_type refine_always
!
! test:
! suffix: 2
! nsize: 4
! args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
!
! test:
! suffix: 3
! nsize: 3
! args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
!
! test:
! suffix: 6
! nsize: 1
! args: -snes_monitor_short -my_snes_convergence
!
!TEST*/