Actual source code: ex1f.F

petsc-3.6.4 2016-04-12
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  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 <petsc/finclude/petscsys.h>
 57: #include <petsc/finclude/petscvec.h>
 58: #include <petsc/finclude/petscis.h>
 59: #include <petsc/finclude/petscdraw.h>
 60: #include <petsc/finclude/petscmat.h>
 61: #include <petsc/finclude/petscksp.h>
 62: #include <petsc/finclude/petscpc.h>
 63: #include <petsc/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:       MatColoring        mc
 80:       Vec                x,r
 81:       PetscDraw               draw
 82:       Mat                J
 83:       PetscBool  matrix_free,flg,fd_coloring
 84:       PetscErrorCode ierr
 85:       PetscInt   its,N, mx,my,i5
 86:       PetscMPIInt size,rank
 87:       PetscReal   lambda_max,lambda_min,lambda
 88:       MatFDColoring      fdcoloring
 89:       ISColoring         iscoloring

 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(PETSC_COMM_SELF,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(PETSC_COMM_SELF,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

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,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 MatColoringCreate(J,mc,ierr)
194:         call MatColoringSetType(mc,MATCOLORINGNATURAL,ierr)
195:         call MatColoringSetFromOptions(mc,ierr)
196:         call MatColoringApply(mc,iscoloring,ierr)
197:         call MatColoringDestroy(mc,ierr)
198: !
199: !       Create the data structure that SNESComputeJacobianDefaultColor() uses
200: !       to compute the actual Jacobians via finite differences.
201: !
202:         call MatFDColoringCreate(J,iscoloring,fdcoloring,ierr)
203:         call MatFDColoringSetFunction(fdcoloring,FormFunction,                &
204:      &                                PETSC_NULL_OBJECT,ierr)
205:         call MatFDColoringSetFromOptions(fdcoloring,ierr)
206:         call MatFDColoringSetUp(J,iscoloring,fdcoloring,ierr)
207: !
208: !        Tell SNES to use the routine SNESComputeJacobianDefaultColor()
209: !      to compute Jacobians.
210: !
211:         call SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,    &
212:      &                     fdcoloring,ierr)
213:         call ISColoringDestroy(iscoloring,ierr)

215:       else if (.not. matrix_free) then

217: !  Set Jacobian matrix data structure and default Jacobian evaluation
218: !  routine.  Whenever the nonlinear solver needs to compute the
219: !  Jacobian matrix, it will call this routine.
220: !   - Note that the final routine argument is the user-defined
221: !     context that provides application-specific data for the
222: !     Jacobian evaluation routine.
223: !   - The user can override with:
224: !      -snes_fd : default finite differencing approximation of Jacobian
225: !      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
226: !                 (unless user explicitly sets preconditioner)
227: !      -snes_mf_operator : form preconditioning matrix as set by the user,
228: !                          but use matrix-free approx for Jacobian-vector
229: !                          products within Newton-Krylov method
230: !
231:         call SNESSetJacobian(snes,J,J,FormJacobian,PETSC_NULL_OBJECT,   &
232:      &        ierr)
233:       endif

235: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
236: !  Customize nonlinear solver; set runtime options
237: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

241:       call SNESSetFromOptions(snes,ierr)

243: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
244: !  Evaluate initial guess; then solve nonlinear system.
245: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

252:       call FormInitialGuess(x,ierr)
253:       call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
254:       call SNESGetIterationNumber(snes,its,ierr);
255:       if (rank .eq. 0) then
256:          write(6,100) its
257:       endif
258:   100 format('Number of SNES iterations = ',i1)

260: !  PetscDraw contour plot of solution

262:       call PetscDrawCreate(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER,          &
263:      &     'Solution',300,0,300,300,draw,ierr)
264:       call PetscDrawSetFromOptions(draw,ierr)

266:       call VecGetArrayRead(x,lx_v,lx_i,ierr)
267:       call PetscDrawTensorContour(draw,mx,my,PETSC_NULL_REAL,              &
268:      &     PETSC_NULL_REAL,lx_v(lx_i+1),ierr)
269:       call VecRestoreArrayRead(x,lx_v,lx_i,ierr)

271: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
272: !  Free work space.  All PETSc objects should be destroyed when they
273: !  are no longer needed.
274: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

276:       if (.not. matrix_free) call MatDestroy(J,ierr)
277:       if (fd_coloring) call MatFDColoringDestroy(fdcoloring,ierr)

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

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

308: #include <petsc/finclude/petscsys.h>
309: #include <petsc/finclude/petscvec.h>
310: #include <petsc/finclude/petscmat.h>
311: #include <petsc/finclude/petscsnes.h>

313: !  Input/output variables:
314:       Vec           X
315:       PetscErrorCode    ierr

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

321:       0

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

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

333: !  Compute initial guess

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

337: !  Restore vector

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

341:       return
342:       end

344: ! ---------------------------------------------------------------------
345: !
346: !  ApplicationInitialGuess - Computes initial approximation, called by
347: !  the higher level routine FormInitialGuess().
348: !
349: !  Input Parameter:
350: !  x - local vector data
351: !
352: !  Output Parameters:
353: !  f - local vector data, f(x)
354: !  ierr - error code
355: !
356: !  Notes:
357: !  This routine uses standard Fortran-style computations over a 2-dim array.
358: !
359:       subroutine ApplicationInitialGuess(x,ierr)

361:       implicit none

363: !  Common blocks:
364:       PetscReal   lambda
365:       PetscInt     mx,my
366:       common      /params/ lambda,mx,my

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

372: !  Local variables:
373:       PetscInt     i,j
374:       PetscScalar temp1,temp,hx,hy,one

376: !  Set parameters

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

384:       do 20 j=1,my
385:          temp = dble(min(j-1,my-j))*hy
386:          do 10 i=1,mx
387:             if (i .eq. 1 .or. j .eq. 1                                  &
388:      &             .or. i .eq. mx .or. j .eq. my) then
389:               x(i,j) = 0.0
390:             else
391:               x(i,j) = temp1 *                                          &
392:      &          sqrt(min(dble(min(i-1,mx-i)*hx),dble(temp)))
393:             endif
394:  10      continue
395:  20   continue

397:       return
398:       end

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

424: #include <petsc/finclude/petscsys.h>
425: #include <petsc/finclude/petscvec.h>
426: #include <petsc/finclude/petscsnes.h>

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

434: !  Common blocks:
435:       PetscReal         lambda
436:       PetscInt          mx,my
437:       common            /params/ lambda,mx,my

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

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

451:       call VecGetArrayRead(X,lx_v,lx_i,ierr)
452:       call VecGetArray(F,lf_v,lf_i,ierr)

454: !  Compute function

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

458: !  Restore vectors

460:       call VecRestoreArrayRead(X,lx_v,lx_i,ierr)
461:       call VecRestoreArray(F,lf_v,lf_i,ierr)

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

465:       return
466:       end

468: ! ---------------------------------------------------------------------
469: !
470: !  ApplicationFunction - Computes nonlinear function, called by
471: !  the higher level routine FormFunction().
472: !
473: !  Input Parameter:
474: !  x    - local vector data
475: !
476: !  Output Parameters:
477: !  f    - local vector data, f(x)
478: !  ierr - error code
479: !
480: !  Notes:
481: !  This routine uses standard Fortran-style computations over a 2-dim array.
482: !
483:       subroutine ApplicationFunction(x,f,ierr)

485:       implicit none

487: !  Common blocks:
488:       PetscReal      lambda
489:       PetscInt        mx,my
490:       common         /params/ lambda,mx,my

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

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

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

511: !  Compute function

513:       do 20 j=1,my
514:          do 10 i=1,mx
515:             if (i .eq. 1 .or. j .eq. 1                                  &
516:      &             .or. i .eq. mx .or. j .eq. my) then
517:                f(i,j) = x(i,j)
518:             else
519:                u = x(i,j)
520:                uxx = hydhx * (two*u                                     &
521:      &                - x(i-1,j) - x(i+1,j))
522:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
523:                f(i,j) = uxx + uyy - sc*exp(u)
524:             endif
525:  10      continue
526:  20   continue

528:       return
529:       end

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

557: #include <petsc/finclude/petscsys.h>
558: #include <petsc/finclude/petscvec.h>
559: #include <petsc/finclude/petscmat.h>
560: #include <petsc/finclude/petscpc.h>
561: #include <petsc/finclude/petscsnes.h>

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

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

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

579: !  Get a pointer to vector data

581:       call VecGetArrayRead(X,lx_v,lx_i,ierr)

583: !  Compute Jacobian entries

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

587: !  Restore vector

589:       call VecRestoreArrayRead(X,lx_v,lx_i,ierr)

591: !  Assemble matrix

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


597:       return
598:       end

600: ! ---------------------------------------------------------------------
601: !
602: !  ApplicationJacobian - Computes Jacobian matrix, called by
603: !  the higher level routine FormJacobian().
604: !
605: !  Input Parameters:
606: !  x        - local vector data
607: !
608: !  Output Parameters:
609: !  jac      - Jacobian matrix
610: !  jac_prec - optionally different preconditioning matrix (not used here)
611: !  ierr     - error code
612: !
613: !  Notes:
614: !  This routine uses standard Fortran-style computations over a 2-dim array.
615: !
616:       subroutine ApplicationJacobian(x,jac,jac_prec,ierr)
617:       implicit none

619: #include <petsc/finclude/petscsys.h>
620: #include <petsc/finclude/petscvec.h>
621: #include <petsc/finclude/petscmat.h>
622: #include <petsc/finclude/petscpc.h>
623: #include <petsc/finclude/petscsnes.h>

625: !  Common blocks:
626:       PetscReal    lambda
627:       PetscInt      mx,my
628:       common       /params/ lambda,mx,my

630: !  Input/output variables:
631:       PetscScalar  x(mx,my)
632:       Mat          jac,jac_prec
633:       PetscErrorCode      ierr

635: !  Local variables:
636:       PetscInt      i,j,row(1),col(5),i1,i5
637:       PetscScalar  two,one, hx,hy
638:       PetscScalar  hxdhy,hydhx,sc,v(5)

640: !  Set parameters

642:       i1     = 1
643:       i5     = 5
644:       one    = 1.0
645:       two    = 2.0
646:       hx     = one/dble(mx-1)
647:       hy     = one/dble(my-1)
648:       sc     = hx*hy
649:       hxdhy  = hx/hy
650:       hydhx  = hy/hx

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

657:       do 20 j=1,my
658:          row(1) = (j-1)*mx - 1
659:          do 10 i=1,mx
660:             row(1) = row(1) + 1
661: !           boundary points
662:             if (i .eq. 1 .or. j .eq. 1                                  &
663:      &             .or. i .eq. mx .or. j .eq. my) then
664:                call MatSetValues(jac_prec,i1,row,i1,row,one,              &
665:      &                           INSERT_VALUES,ierr)
666: !           interior grid points
667:             else
668:                v(1) = -hxdhy
669:                v(2) = -hydhx
670:                v(3) = two*(hydhx + hxdhy)                               &
671:      &                  - sc*lambda*exp(x(i,j))
672:                v(4) = -hydhx
673:                v(5) = -hxdhy
674:                col(1) = row(1) - mx
675:                col(2) = row(1) - 1
676:                col(3) = row(1)
677:                col(4) = row(1) + 1
678:                col(5) = row(1) + mx
679:                call MatSetValues(jac_prec,i1,row,i5,col,v,                &
680:      &                           INSERT_VALUES,ierr)
681:             endif
682:  10      continue
683:  20   continue

685:       return
686:       end