Actual source code: ex11f.F

  1: !
  2: !    "$Id: ex11f.F,v 1.31 2001/08/07 03:04:00 balay Exp $";
  3: !
  4: !  Description: Solves a complex linear system in parallel with SLES (Fortran code).
  5: !
  6: !/*T
  7: !  Concepts: SLES^solving a Helmholtz equation
  8: !  Concepts: complex numbers
  9: !  Processors: n
 10: !T*/
 11: !
 12: !  The model problem:
 13: !     Solve Helmholtz equation on the unit square: (0,1) x (0,1)
 14: !          -delta u - sigma1*u + i*sigma2*u = f,
 15: !           where delta = Laplace operator
 16: !     Dirichlet b.c.'s on all sides
 17: !     Use the 2-D, five-point finite difference stencil.
 18: !
 19: !  Compiling the code:
 20: !     This code uses the complex numbers version of PETSc, so one of the
 21: !     following values of BOPT must be used for compiling the PETSc libraries
 22: !     and this example:
 23: !        BOPT=g_complex   - debugging version
 24: !        BOPT=O_complex   - optimized version
 25: !        BOPT=Opg_complex - profiling version
 26: !
 27: ! -----------------------------------------------------------------------

 29:       program main
 30:       implicit none

 32: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 33: !                    Include files
 34: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 35: !
 36: !  The following include statements are required for SLES Fortran programs:
 37: !     petsc.h       - base PETSc routines
 38: !     petscvec.h    - vectors
 39: !     petscmat.h    - matrices
 40: !     petscpc.h     - preconditioners
 41: !     petscksp.h    - Krylov subspace methods
 42: !     petscsles.h   - SLES interface
 43: !  Include the following to use PETSc random numbers:
 44: !     petscsys.h    - system routines
 45: !  Additional include statements may be needed if using other PETSc
 46: !  routines in a Fortran program, e.g.,
 47: !     petscviewer.h - viewers
 48: !     petscis.h     - index sets
 49: !
 50:  #include include/finclude/petsc.h
 51:  #include include/finclude/petscvec.h
 52:  #include include/finclude/petscmat.h
 53:  #include include/finclude/petscpc.h
 54:  #include include/finclude/petscksp.h
 55:  #include include/finclude/petscsles.h
 56:  #include include/finclude/petscsys.h
 57: !
 58: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59: !                   Variable declarations
 60: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 61: !
 62: !  Variables:
 63: !     sles     - linear solver context
 64: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
 65: !     A        - matrix that defines linear system
 66: !     its      - iterations for convergence
 67: !     norm     - norm of error in solution
 68: !     rctx     - random number context
 69: !

 71:       SLES             sles
 72:       Mat              A
 73:       Vec              x,b,u
 74:       PetscRandom      rctx
 75:       double precision norm,h2,sigma1
 76:       PetscScalar      none,sigma2,v,pfive
 77:       integer          dim,flg,its,ierr,n,rank
 78:       integer          Istart,Iend,i,j,II,JJ
 79:       logical          use_random

 81: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 82: !                 Beginning of program
 83: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 85:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 86: #if !defined(PETSC_USE_COMPLEX)
 87:       write(6,*) "This example requires complex numbers."
 88:       goto 200
 89: #endif

 91:       none   = -1.0
 92:       n      = 6
 93:       sigma1 = 100.0
 94:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
 95:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-sigma1',sigma1,      &
 96:      &                       flg,ierr)
 97:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
 98:       dim    = n*n

100: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101: !      Compute the matrix and right-hand-side vector that define
102: !      the linear system, Ax = b.
103: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

105: !  Create parallel matrix, specifying only its global dimensions.
106: !  When using MatCreate(), the matrix format can be specified at
107: !  runtime. Also, the parallel partitioning of the matrix is
108: !  determined by PETSc at runtime.

110:       call MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,dim,    &
111:      &               dim,A,ierr)
112:       call MatSetFromOptions(A,ierr)

114: !  Currently, all PETSc parallel matrix formats are partitioned by
115: !  contiguous chunks of rows across the processors.  Determine which
116: !  rows of the matrix are locally owned.

118:       call MatGetOwnershipRange(A,Istart,Iend,ierr)

120: !  Set matrix elements in parallel.
121: !   - Each processor needs to insert only elements that it owns
122: !     locally (but any non-local elements will be sent to the
123: !     appropriate processor during matrix assembly).
124: !   - Always specify global rows and columns of matrix entries.

126:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-norandom',        &
127:      &     flg,ierr)
128:       if (flg .eq. 1) then
129:          use_random = .false.
130:          sigma2 = 10.0*PETSC_i
131:       else
132:          use_random = .true.
133:          call PetscRandomCreate(PETSC_COMM_WORLD,                       &
134:      &        RANDOM_DEFAULT_IMAGINARY,rctx,ierr)
135:       endif
136:       h2 = 1.0/((n+1)*(n+1))

138:       do 10, II=Istart,Iend-1
139:         v = -1.0
140:         i = II/n
141:         j = II - i*n
142:         if (i.gt.0) then
143:           JJ = II - n
144:           call MatSetValues(A,1,II,1,JJ,v,ADD_VALUES,ierr)
145:         endif
146:         if (i.lt.n-1) then
147:           JJ = II + n
148:           call MatSetValues(A,1,II,1,JJ,v,ADD_VALUES,ierr)
149:         endif
150:         if (j.gt.0) then
151:           JJ = II - 1
152:           call MatSetValues(A,1,II,1,JJ,v,ADD_VALUES,ierr)
153:         endif
154:         if (j.lt.n-1) then
155:           JJ = II + 1
156:           call MatSetValues(A,1,II,1,JJ,v,ADD_VALUES,ierr)
157:         endif
158:         if (use_random) call PetscRandomGetValue(rctx,sigma2,ierr)
159:         v = 4.0 - sigma1*h2 + sigma2*h2
160:         call  MatSetValues(A,1,II,1,II,v,ADD_VALUES,ierr)
161:  10   continue
162:       if (use_random) call PetscRandomDestroy(rctx,ierr)

164: !  Assemble matrix, using the 2-step process:
165: !       MatAssemblyBegin(), MatAssemblyEnd()
166: !  Computations can be done while messages are in transition
167: !  by placing code between these two statements.

169:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
170:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

172: !  Create parallel vectors.
173: !   - Here, the parallel partitioning of the vector is determined by
174: !     PETSc at runtime.  We could also specify the local dimensions
175: !     if desired.
176: !   - Note: We form 1 vector from scratch and then duplicate as needed.

178:       call VecCreate(PETSC_COMM_WORLD,u,ierr)
179:       call VecSetSizes(u,PETSC_DECIDE,dim,ierr)
180:       call VecSetFromOptions(u,ierr)
181:       call VecDuplicate(u,b,ierr)
182:       call VecDuplicate(b,x,ierr)

184: !  Set exact solution; then compute right-hand-side vector.

186:       if (use_random) then
187:          call PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,        &
188:      &                          rctx,ierr)
189:          call VecSetRandom(rctx,u,ierr)
190:       else
191:          pfive = 0.5
192:          call VecSet(pfive,u,ierr)
193:       endif
194:       call MatMult(A,u,b,ierr)

196: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
197: !         Create the linear solver and set various options
198: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

200: !  Create linear solver context

202:       call SLESCreate(PETSC_COMM_WORLD,sles,ierr)

204: !  Set operators. Here the matrix that defines the linear system
205: !  also serves as the preconditioning matrix.

207:       call SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN,         &
208:      &                      ierr)

210: !  Set runtime options, e.g.,
211: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>

213:       call SLESSetFromOptions(sles,ierr)

215: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
216: !                      Solve the linear system
217: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

219:       call SLESSolve(sles,b,x,its,ierr)

221: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
222: !                     Check solution and clean up
223: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

225: !  Check the error

227:       call VecAXPY(none,u,x,ierr)
228:       call VecNorm(x,NORM_2,norm,ierr)
229:       if (rank .eq. 0) then
230:         if (norm .gt. 1.e-12) then
231:            write(6,100) norm,its
232:         else
233:            write(6,110) its
234:         endif
235:       endif
236:   100 format('Norm of error ',e10.4,',iterations ',i5)
237:   110 format('Norm of error < 1.e-12,iterations ',i5)

239: !  Free work space.  All PETSc objects should be destroyed when they
240: !  are no longer needed.

242:       if (use_random) call PetscRandomDestroy(rctx,ierr)
243:       call SLESDestroy(sles,ierr)
244:       call VecDestroy(u,ierr)
245:       call VecDestroy(x,ierr)
246:       call VecDestroy(b,ierr)
247:       call MatDestroy(A,ierr)

249:  200  continue
250:       call PetscFinalize(ierr)
251:       end