Actual source code: ex1f.F

  1: !
  2: !  Description: This example solves a nonlinear system on 1 processor with SNES.
  3: !  We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
  4: !  domain.  The command line options include:
  5: !    -par <parameter>, where <parameter> indicates the nonlinearity of the problem
  6: !       problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)
  7: !    -mx <xg>, where <xg> = number of grid points in the x-direction
  8: !    -my <yg>, where <yg> = number of grid points in the y-direction
  9: !
 10: !/*T
 11: !  Concepts: SNES^sequential Bratu example
 12: !  Processors: 1
 13: !T*/
 14: !
 15: !  --------------------------------------------------------------------------
 16: !
 17: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 18: !  the partial differential equation
 19: !
 20: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
 21: !
 22: !  with boundary conditions
 23: !
 24: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
 25: !
 26: !  A finite difference approximation with the usual 5-point stencil
 27: !  is used to discretize the boundary value problem to obtain a nonlinear
 28: !  system of equations.
 29: !
 30: !  The parallel version of this code is snes/examples/tutorials/ex5f.F
 31: !
 32: !  --------------------------------------------------------------------------

 34:       program main
 35:       implicit none

 37: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 38: !                    Include files
 39: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40: !
 41: !  The following include statements are generally used in SNES Fortran
 42: !  programs:
 43: !     petscsys.h       - base PETSc routines
 44: !     petscvec.h    - vectors
 45: !     petscmat.h    - matrices
 46: !     petscksp.h    - Krylov subspace methods
 47: !     petscpc.h     - preconditioners
 48: !     petscsnes.h   - SNES interface
 49: !  In addition, we need the following for use of PETSc drawing routines
 50: !     petscdraw.h   - drawing routines
 51: !  Other include statements may be needed if using additional PETSc
 52: !  routines in a Fortran program, e.g.,
 53: !     petscviewer.h - viewers
 54: !     petscis.h     - index sets
 55: !
 56:  #include finclude/petscsys.h
 57:  #include finclude/petscvec.h
 58:  #include finclude/petscis.h
 59:  #include finclude/petscdraw.h
 60:  #include finclude/petscmat.h
 61:  #include finclude/petscksp.h
 62:  #include finclude/petscpc.h
 63:  #include finclude/petscsnes.h
 64: !
 65: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 66: !                   Variable declarations
 67: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 68: !
 69: !  Variables:
 70: !     snes        - nonlinear solver
 71: !     x, r        - solution, residual vectors
 72: !     J           - Jacobian matrix
 73: !     its         - iterations for convergence
 74: !     matrix_free - flag - 1 indicates matrix-free version
 75: !     lambda      - nonlinearity parameter
 76: !     draw        - drawing context
 77: !
 78:       SNES               snes
 79:       Vec                x,r
 80:       PetscDraw               draw
 81:       Mat                J
 82:       PetscTruth matrix_free,flg,fd_coloring
 83:       PetscErrorCode ierr
 84:       PetscInt   its,N, mx,my,i5
 85:       PetscMPIInt size,rank
 86:       PetscReal   lambda_max,lambda_min,lambda
 87:       MatFDColoring      fdcoloring
 88:       ISColoring         iscoloring
 89:       MatStructure       str
 90: 
 91:       PetscScalar        lx_v(0:1)
 92:       PetscOffset        lx_i

 94: !  Store parameters in common block

 96:       common /params/ lambda,mx,my

 98: !  Note: Any user-defined Fortran routines (such as FormJacobian)
 99: !  MUST be declared as external.

101:       external FormFunction,FormInitialGuess,FormJacobian

103: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104: !  Initialize program
105: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

107:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
108:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
109:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)

111:       if (size .ne. 1) then
112:          if (rank .eq. 0) then
113:             write(6,*) 'This is a uniprocessor example only!'
114:          endif
115:          SETERRQ(1,' ',ierr)
116:       endif

118: !  Initialize problem parameters
119:       i5 = 5
120:       lambda_max = 6.81
121:       lambda_min = 0.0
122:       lambda     = 6.0
123:       mx         = 4
124:       my         = 4
125:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-mx',mx,flg,ierr)
126:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-my',my,flg,ierr)
127:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par',lambda,      &
128:      &     flg,ierr)
129:       if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
130:          if (rank .eq. 0) write(6,*) 'Lambda is out of range'
131:          SETERRQ(1,' ',ierr)
132:       endif
133:       N       = mx*my

135: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: !  Create nonlinear solver context
137: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

139:       call SNESCreate(PETSC_COMM_WORLD,snes,ierr)

141: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: !  Create vector data structures; set function evaluation routine
143: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

145:       call VecCreate(PETSC_COMM_WORLD,x,ierr)
146:       call VecSetSizes(x,PETSC_DECIDE,N,ierr)
147:       call VecSetFromOptions(x,ierr)
148:       call VecDuplicate(x,r,ierr)

150: !  Set function evaluation routine and vector.  Whenever the nonlinear
151: !  solver needs to evaluate the nonlinear function, it will call this
152: !  routine.
153: !   - Note that the final routine argument is the user-defined
154: !     context that provides application-specific data for the
155: !     function evaluation routine.

157:       call SNESSetFunction(snes,r,FormFunction,PETSC_NULL_OBJECT,ierr)

159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: !  Create matrix data structure; set Jacobian evaluation routine
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

163: !  Create matrix. Here we only approximately preallocate storage space
164: !  for the Jacobian.  See the users manual for a discussion of better
165: !  techniques for preallocating matrix memory.

167:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf',         &
168:      &     matrix_free,ierr)
169:       if (.not. matrix_free) then
170:         call MatCreateSeqAIJ(PETSC_COMM_WORLD,N,N,i5,PETSC_NULL_INTEGER, &
171:      &        J,ierr)
172:       endif

174: !
175: !     This option will cause the Jacobian to be computed via finite differences
176: !    efficiently using a coloring of the columns of the matrix.
177: !
178:       fd_coloring = .false.
179:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_fd_coloring',     &
180:      &                    fd_coloring,ierr)
181:       if (fd_coloring) then
182: 
183: !
184: !      This initializes the nonzero structure of the Jacobian. This is artificial
185: !      because clearly if we had a routine to compute the Jacobian we won't need
186: !      to use finite differences.
187: !
188:         call FormJacobian(snes,x,J,J,str,0,ierr)
189: !
190: !       Color the matrix, i.e. determine groups of columns that share no common
191: !      rows. These columns in the Jacobian can all be computed simulataneously.
192: !
193:         call MatGetColoring(J,MATCOLORING_NATURAL,iscoloring,ierr)
194: 
195: !
196: !       Create the data structure that SNESDefaultComputeJacobianColor() uses
197: !       to compute the actual Jacobians via finite differences.
198: !
199:         call MatFDColoringCreate(J,iscoloring,fdcoloring,ierr)
200:         call MatFDColoringSetFunction(fdcoloring,FormFunction,                &
201:      &                                PETSC_NULL_OBJECT,ierr)
202:         call MatFDColoringSetFromOptions(fdcoloring,ierr)
203: !
204: !        Tell SNES to use the routine SNESDefaultComputeJacobianColor()
205: !      to compute Jacobians.
206: !
207:         call SNESSetJacobian(snes,J,J,SNESDefaultComputeJacobianColor,    &
208:      &                     fdcoloring,ierr)
209:         call ISColoringDestroy(iscoloring,ierr)

211:       else if (.not. matrix_free) then

213: !  Set Jacobian matrix data structure and default Jacobian evaluation
214: !  routine.  Whenever the nonlinear solver needs to compute the
215: !  Jacobian matrix, it will call this routine.
216: !   - Note that the final routine argument is the user-defined
217: !     context that provides application-specific data for the
218: !     Jacobian evaluation routine.
219: !   - The user can override with:
220: !      -snes_fd : default finite differencing approximation of Jacobian
221: !      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
222: !                 (unless user explicitly sets preconditioner)
223: !      -snes_mf_operator : form preconditioning matrix as set by the user,
224: !                          but use matrix-free approx for Jacobian-vector
225: !                          products within Newton-Krylov method
226: !
227:         call SNESSetJacobian(snes,J,J,FormJacobian,PETSC_NULL_OBJECT,   &
228:      &        ierr)
229:       endif

231: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
232: !  Customize nonlinear solver; set runtime options
233: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

235: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)

237:       call SNESSetFromOptions(snes,ierr)

239: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
240: !  Evaluate initial guess; then solve nonlinear system.
241: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

243: !  Note: The user should initialize the vector, x, with the initial guess
244: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
245: !  to employ an initial guess of zero, the user should explicitly set
246: !  this vector to zero by calling VecSet().

248:       call FormInitialGuess(x,ierr)
249:       call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
250:       call SNESGetIterationNumber(snes,its,ierr);
251:       if (rank .eq. 0) then
252:          write(6,100) its
253:       endif
254:   100 format('Number of Newton iterations = ',i1)

256: !  PetscDraw contour plot of solution

258: !      call PetscDrawOpenX(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER,'Solution',
259: !                   300,0,300,300,draw,ierr)
260:       call PetscDrawCreate(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER,          &
261:      &     'Solution',300,0,300,300,draw,ierr)
262:       call PetscDrawSetType(draw,PETSC_DRAW_X,ierr)

264:       call VecGetArray(x,lx_v,lx_i,ierr)
265:       call PetscDrawTensorContour(draw,mx,my,PETSC_NULL_DOUBLE,              &
266:      &     PETSC_NULL_DOUBLE,lx_v(lx_i+1),ierr)
267:       call VecRestoreArray(x,lx_v,lx_i,ierr)

269: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
270: !  Free work space.  All PETSc objects should be destroyed when they
271: !  are no longer needed.
272: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

274:       if (.not. matrix_free) call MatDestroy(J,ierr)
275:       if (fd_coloring) call MatFDColoringDestroy(fdcoloring,ierr)

277:       call VecDestroy(x,ierr)
278:       call VecDestroy(r,ierr)
279:       call SNESDestroy(snes,ierr)
280:       call PetscDrawDestroy(draw,ierr)
281:       call PetscFinalize(ierr)
282:       end

284: ! ---------------------------------------------------------------------
285: !
286: !  FormInitialGuess - Forms initial approximation.
287: !
288: !  Input Parameter:
289: !  X - vector
290: !
291: !  Output Parameters:
292: !  X - vector
293: !  ierr - error code
294: !
295: !  Notes:
296: !  This routine serves as a wrapper for the lower-level routine
297: !  "ApplicationInitialGuess", where the actual computations are
298: !  done using the standard Fortran style of treating the local
299: !  vector data as a multidimensional array over the local mesh.
300: !  This routine merely accesses the local vector data via
301: !  VecGetArray() and VecRestoreArray().
302: !
303:       subroutine FormInitialGuess(X,ierr)
304:       implicit none

306:  #include finclude/petscsys.h
307:  #include finclude/petscvec.h
308:  #include finclude/petscmat.h
309:  #include finclude/petscsnes.h

311: !  Input/output variables:
312:       Vec           X
313:       PetscErrorCode    ierr

315: !  Declarations for use with local arrays:
316:       PetscScalar   lx_v(0:1)
317:       PetscOffset   lx_i

319:       0

321: !  Get a pointer to vector data.
322: !    - For default PETSc vectors, VecGetArray() returns a pointer to
323: !      the data array.  Otherwise, the routine is implementation dependent.
324: !    - You MUST call VecRestoreArray() when you no longer need access to
325: !      the array.
326: !    - Note that the Fortran interface to VecGetArray() differs from the
327: !      C version.  See the users manual for details.

329:       call VecGetArray(X,lx_v,lx_i,ierr)

331: !  Compute initial guess

333:       call ApplicationInitialGuess(lx_v(lx_i),ierr)

335: !  Restore vector

337:       call VecRestoreArray(X,lx_v,lx_i,ierr)

339:       return
340:       end

342: ! ---------------------------------------------------------------------
343: !
344: !  ApplicationInitialGuess - Computes initial approximation, called by
345: !  the higher level routine FormInitialGuess().
346: !
347: !  Input Parameter:
348: !  x - local vector data
349: !
350: !  Output Parameters:
351: !  f - local vector data, f(x)
352: !  ierr - error code
353: !
354: !  Notes:
355: !  This routine uses standard Fortran-style computations over a 2-dim array.
356: !
357:       subroutine ApplicationInitialGuess(x,ierr)

359:       implicit none

361: !  Common blocks:
362:       PetscReal   lambda
363:       PetscInt     mx,my
364:       common      /params/ lambda,mx,my

366: !  Input/output variables:
367:       PetscScalar x(mx,my)
368:       PetscErrorCode     ierr

370: !  Local variables:
371:       PetscInt     i,j
372:       PetscScalar temp1,temp,hx,hy,one

374: !  Set parameters

376:       0
377:       one    = 1.0
378:       hx     = one/(dble(mx-1))
379:       hy     = one/(dble(my-1))
380:       temp1  = lambda/(lambda + one)

382:       do 20 j=1,my
383:          temp = dble(min(j-1,my-j))*hy
384:          do 10 i=1,mx
385:             if (i .eq. 1 .or. j .eq. 1                                  &
386:      &             .or. i .eq. mx .or. j .eq. my) then
387:               x(i,j) = 0.0
388:             else
389:               x(i,j) = temp1 *                                          &
390:      &          sqrt(min(dble(min(i-1,mx-i)*hx),dble(temp)))
391:             endif
392:  10      continue
393:  20   continue

395:       return
396:       end

398: ! ---------------------------------------------------------------------
399: !
400: !  FormFunction - Evaluates nonlinear function, F(x).
401: !
402: !  Input Parameters:
403: !  snes  - the SNES context
404: !  X     - input vector
405: !  dummy - optional user-defined context, as set by SNESSetFunction()
406: !          (not used here)
407: !
408: !  Output Parameter:
409: !  F     - vector with newly computed function
410: !
411: !  Notes:
412: !  This routine serves as a wrapper for the lower-level routine
413: !  "ApplicationFunction", where the actual computations are
414: !  done using the standard Fortran style of treating the local
415: !  vector data as a multidimensional array over the local mesh.
416: !  This routine merely accesses the local vector data via
417: !  VecGetArray() and VecRestoreArray().
418: !
419:       subroutine FormFunction(snes,X,F,dummy,ierr)
420:       implicit none

422:  #include finclude/petscsys.h
423:  #include finclude/petscvec.h
424:  #include finclude/petscsnes.h

426: !  Input/output variables:
427:       SNES              snes
428:       Vec               X,F
429:       PetscFortranAddr  dummy
430:       PetscErrorCode          ierr

432: !  Common blocks:
433:       PetscReal         lambda
434:       PetscInt          mx,my
435:       common            /params/ lambda,mx,my

437: !  Declarations for use with local arrays:
438:       PetscScalar       lx_v(0:1),lf_v(0:1)
439:       PetscOffset       lx_i,lf_i

441: !  Get pointers to vector data.
442: !    - For default PETSc vectors, VecGetArray() returns a pointer to
443: !      the data array.  Otherwise, the routine is implementation dependent.
444: !    - You MUST call VecRestoreArray() when you no longer need access to
445: !      the array.
446: !    - Note that the Fortran interface to VecGetArray() differs from the
447: !      C version.  See the Fortran chapter of the users manual for details.

449:       call VecGetArray(X,lx_v,lx_i,ierr)
450:       call VecGetArray(F,lf_v,lf_i,ierr)

452: !  Compute function

454:       call ApplicationFunction(lx_v(lx_i),lf_v(lf_i),ierr)

456: !  Restore vectors

458:       call VecRestoreArray(X,lx_v,lx_i,ierr)
459:       call VecRestoreArray(F,lf_v,lf_i,ierr)

461:       call PetscLogFlops(11.0d0*mx*my,ierr)

463:       return
464:       end

466: ! ---------------------------------------------------------------------
467: !
468: !  ApplicationFunction - Computes nonlinear function, called by
469: !  the higher level routine FormFunction().
470: !
471: !  Input Parameter:
472: !  x    - local vector data
473: !
474: !  Output Parameters:
475: !  f    - local vector data, f(x)
476: !  ierr - error code
477: !
478: !  Notes:
479: !  This routine uses standard Fortran-style computations over a 2-dim array.
480: !
481:       subroutine ApplicationFunction(x,f,ierr)

483:       implicit none

485: !  Common blocks:
486:       PetscReal      lambda
487:       PetscInt        mx,my
488:       common         /params/ lambda,mx,my

490: !  Input/output variables:
491:       PetscScalar    x(mx,my),f(mx,my)
492:       PetscErrorCode       ierr

494: !  Local variables:
495:       PetscScalar    two,one,hx,hy
496:       PetscScalar    hxdhy,hydhx,sc
497:       PetscScalar    u,uxx,uyy
498:       PetscInt        i,j

500:       0
501:       one    = 1.0
502:       two    = 2.0
503:       hx     = one/dble(mx-1)
504:       hy     = one/dble(my-1)
505:       sc     = hx*hy*lambda
506:       hxdhy  = hx/hy
507:       hydhx  = hy/hx

509: !  Compute function

511:       do 20 j=1,my
512:          do 10 i=1,mx
513:             if (i .eq. 1 .or. j .eq. 1                                  &
514:      &             .or. i .eq. mx .or. j .eq. my) then
515:                f(i,j) = x(i,j)
516:             else
517:                u = x(i,j)
518:                uxx = hydhx * (two*u                                     &
519:      &                - x(i-1,j) - x(i+1,j))
520:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
521:                f(i,j) = uxx + uyy - sc*exp(u)
522:             endif
523:  10      continue
524:  20   continue

526:       return
527:       end

529: ! ---------------------------------------------------------------------
530: !
531: !  FormJacobian - Evaluates Jacobian matrix.
532: !
533: !  Input Parameters:
534: !  snes    - the SNES context
535: !  x       - input vector
536: !  dummy   - optional user-defined context, as set by SNESSetJacobian()
537: !            (not used here)
538: !
539: !  Output Parameters:
540: !  jac      - Jacobian matrix
541: !  jac_prec - optionally different preconditioning matrix (not used here)
542: !  flag     - flag indicating matrix structure
543: !
544: !  Notes:
545: !  This routine serves as a wrapper for the lower-level routine
546: !  "ApplicationJacobian", where the actual computations are
547: !  done using the standard Fortran style of treating the local
548: !  vector data as a multidimensional array over the local mesh.
549: !  This routine merely accesses the local vector data via
550: !  VecGetArray() and VecRestoreArray().
551: !
552:       subroutine FormJacobian(snes,X,jac,jac_prec,flag,dummy,ierr)
553:       implicit none

555:  #include finclude/petscsys.h
556:  #include finclude/petscvec.h
557:  #include finclude/petscmat.h
558:  #include finclude/petscpc.h
559:  #include finclude/petscsnes.h

561: !  Input/output variables:
562:       SNES          snes
563:       Vec           X
564:       Mat           jac,jac_prec
565:       MatStructure  flag
566:       PetscErrorCode      ierr
567:       integer dummy

569: !  Common blocks:
570:       PetscReal     lambda
571:       PetscInt       mx,my
572:       common        /params/ lambda,mx,my

574: !  Declarations for use with local array:
575:       PetscScalar   lx_v(0:1)
576:       PetscOffset   lx_i

578: !  Get a pointer to vector data

580:       call VecGetArray(X,lx_v,lx_i,ierr)

582: !  Compute Jacobian entries

584:       call ApplicationJacobian(lx_v(lx_i),jac,jac_prec,ierr)

586: !  Restore vector

588:       call VecRestoreArray(X,lx_v,lx_i,ierr)

590: !  Assemble matrix

592:       call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
593:       call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)

595: !  Set flag to indicate that the Jacobian matrix retains an identical
596: !  nonzero structure throughout all nonlinear iterations (although the
597: !  values of the entries change). Thus, we can save some work in setting
598: !  up the preconditioner (e.g., no need to redo symbolic factorization for
599: !  ILU/ICC preconditioners).
600: !   - If the nonzero structure of the matrix is different during
601: !     successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
602: !     must be used instead.  If you are unsure whether the matrix
603: !     structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
604: !   - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
605: !     believes your assertion and does not check the structure
606: !     of the matrix.  If you erroneously claim that the structure
607: !     is the same when it actually is not, the new preconditioner
608: !     will not function correctly.  Thus, use this optimization
609: !     feature with caution!

611:       flag = SAME_NONZERO_PATTERN

613:       return
614:       end

616: ! ---------------------------------------------------------------------
617: !
618: !  ApplicationJacobian - Computes Jacobian matrix, called by
619: !  the higher level routine FormJacobian().
620: !
621: !  Input Parameters:
622: !  x        - local vector data
623: !
624: !  Output Parameters:
625: !  jac      - Jacobian matrix
626: !  jac_prec - optionally different preconditioning matrix (not used here)
627: !  ierr     - error code
628: !
629: !  Notes:
630: !  This routine uses standard Fortran-style computations over a 2-dim array.
631: !
632:       subroutine ApplicationJacobian(x,jac,jac_prec,ierr)
633:       implicit none

635:  #include finclude/petscsys.h
636:  #include finclude/petscvec.h
637:  #include finclude/petscmat.h
638:  #include finclude/petscpc.h
639:  #include finclude/petscsnes.h

641: !  Common blocks:
642:       PetscReal    lambda
643:       PetscInt      mx,my
644:       common       /params/ lambda,mx,my

646: !  Input/output variables:
647:       PetscScalar  x(mx,my)
648:       Mat          jac,jac_prec
649:       PetscErrorCode      ierr

651: !  Local variables:
652:       PetscInt      i,j,row(1),col(5),i1,i5
653:       PetscScalar  two,one, hx,hy
654:       PetscScalar  hxdhy,hydhx,sc,v(5)

656: !  Set parameters

658:       i1     = 1
659:       i5     = 5
660:       one    = 1.0
661:       two    = 2.0
662:       hx     = one/dble(mx-1)
663:       hy     = one/dble(my-1)
664:       sc     = hx*hy
665:       hxdhy  = hx/hy
666:       hydhx  = hy/hx

668: !  Compute entries of the Jacobian matrix
669: !   - Here, we set all entries for a particular row at once.
670: !   - Note that MatSetValues() uses 0-based row and column numbers
671: !     in Fortran as well as in C.

673:       do 20 j=1,my
674:          row(1) = (j-1)*mx - 1
675:          do 10 i=1,mx
676:             row(1) = row(1) + 1
677: !           boundary points
678:             if (i .eq. 1 .or. j .eq. 1                                  &
679:      &             .or. i .eq. mx .or. j .eq. my) then
680:                call MatSetValues(jac_prec,i1,row,i1,row,one,              &
681:      &                           INSERT_VALUES,ierr)
682: !           interior grid points
683:             else
684:                v(1) = -hxdhy
685:                v(2) = -hydhx
686:                v(3) = two*(hydhx + hxdhy)                               &
687:      &                  - sc*lambda*exp(x(i,j))
688:                v(4) = -hydhx
689:                v(5) = -hxdhy
690:                col(1) = row(1) - mx
691:                col(2) = row(1) - 1
692:                col(3) = row(1)
693:                col(4) = row(1) + 1
694:                col(5) = row(1) + mx
695:                call MatSetValues(jac_prec,i1,row,i5,col,v,                &
696:      &                           INSERT_VALUES,ierr)
697:             endif
698:  10      continue
699:  20   continue

701:       return
702:       end