Actual source code: ex1f.F90

  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: !

 11: !
 12: !  --------------------------------------------------------------------------
 13: !
 14: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 15: !  the partial differential equation
 16: !
 17: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
 18: !
 19: !  with boundary conditions
 20: !
 21: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
 22: !
 23: !  A finite difference approximation with the usual 5-point stencil
 24: !  is used to discretize the boundary value problem to obtain a nonlinear
 25: !  system of equations.
 26: !
 27: !  The parallel version of this code is snes/tutorials/ex5f.F
 28: !
 29: !  --------------------------------------------------------------------------
 30:       subroutine postcheck(snes,x,y,w,changed_y,changed_w,ctx,ierr)
 31: #include <petsc/finclude/petscsnes.h>
 32:       use petscsnes
 33:       implicit none
 34:       SNES           snes
 35:       PetscReal      norm
 36:       Vec            tmp,x,y,w
 37:       PetscBool      changed_w,changed_y
 38:       PetscErrorCode ierr
 39:       PetscInt       ctx
 40:       PetscScalar    mone

 42:       PetscCallA(VecDuplicate(x,tmp,ierr))
 43:       mone = -1.0
 44:       PetscCallA(VecWAXPY(tmp,mone,x,w,ierr))
 45:       PetscCallA(VecNorm(tmp,NORM_2,norm,ierr))
 46:       PetscCallA(VecDestroy(tmp,ierr))
 47:       print*, 'Norm of search step ',norm
 48:       changed_y = PETSC_FALSE
 49:       changed_w = PETSC_FALSE
 50:       return
 51:       end

 53:       program main
 54: #include <petsc/finclude/petscdraw.h>
 55:       use petscsnes
 56:       implicit none
 57:       interface SNESSetJacobian
 58:       subroutine SNESSetJacobian1(a,b,c,d,e,z)
 59:        use petscsnes
 60:        SNES a
 61:        Mat b
 62:        Mat c
 63:        external d
 64:        MatFDColoring e
 65:        PetscErrorCode z
 66:       end subroutine
 67:       subroutine SNESSetJacobian2(a,b,c,d,e,z)
 68:        use petscsnes
 69:        SNES a
 70:        Mat b
 71:        Mat c
 72:        external d
 73:        integer e
 74:        PetscErrorCode z
 75:       end subroutine
 76:       end interface
 77: !
 78: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 79: !                   Variable declarations
 80: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 81: !
 82: !  Variables:
 83: !     snes        - nonlinear solver
 84: !     x, r        - solution, residual vectors
 85: !     J           - Jacobian matrix
 86: !     its         - iterations for convergence
 87: !     matrix_free - flag - 1 indicates matrix-free version
 88: !     lambda      - nonlinearity parameter
 89: !     draw        - drawing context
 90: !
 91:       SNES               snes
 92:       MatColoring        mc
 93:       Vec                x,r
 94:       PetscDraw               draw
 95:       Mat                J
 96:       PetscBool  matrix_free,flg,fd_coloring
 97:       PetscErrorCode ierr
 98:       PetscInt   its,N, mx,my,i5
 99:       PetscMPIInt size,rank
100:       PetscReal   lambda_max,lambda_min,lambda
101:       MatFDColoring      fdcoloring
102:       ISColoring         iscoloring
103:       PetscBool          pc
104:       external           postcheck

106:       PetscScalar        lx_v(0:1)
107:       PetscOffset        lx_i

109: !  Store parameters in common block

111:       common /params/ lambda,mx,my,fd_coloring

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

116:       external FormFunction,FormInitialGuess,FormJacobian

118: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119: !  Initialize program
120: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

122:       PetscCallA(PetscInitialize(ierr))
123:       PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD,size,ierr))
124:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))

126:       if (size .ne. 1) then; SETERRA(PETSC_COMM_SELF,PETSC_ERR_WRONG_MPI_SIZE,'This is a uniprocessor example only'); endif

128: !  Initialize problem parameters
129:       i5 = 5
130:       lambda_max = 6.81
131:       lambda_min = 0.0
132:       lambda     = 6.0
133:       mx         = 4
134:       my         = 4
135:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-mx',mx,flg,ierr))
136:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my',my,flg,ierr))
137:       PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,flg,ierr))
138:       if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then; SETERRA(PETSC_COMM_SELF,PETSC_ERR_USER,'Lambda out of range '); endif
139:       N  = mx*my
140:       pc = PETSC_FALSE
141:       PetscCallA(PetscOptionsGetBool(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-pc',pc,PETSC_NULL_BOOL,ierr))

143: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144: !  Create nonlinear solver context
145: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

147:       PetscCallA(SNESCreate(PETSC_COMM_WORLD,snes,ierr))

149:       if (pc .eqv. PETSC_TRUE) then
150:         PetscCallA(SNESSetType(snes,SNESNEWTONTR,ierr))
151:         PetscCallA(SNESNewtonTRSetPostCheck(snes, postcheck,snes,ierr))
152:       endif

154: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155: !  Create vector data structures; set function evaluation routine
156: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

158:       PetscCallA(VecCreate(PETSC_COMM_WORLD,x,ierr))
159:       PetscCallA(VecSetSizes(x,PETSC_DECIDE,N,ierr))
160:       PetscCallA(VecSetFromOptions(x,ierr))
161:       PetscCallA(VecDuplicate(x,r,ierr))

163: !  Set function evaluation routine and vector.  Whenever the nonlinear
164: !  solver needs to evaluate the nonlinear function, it will call this
165: !  routine.
166: !   - Note that the final routine argument is the user-defined
167: !     context that provides application-specific data for the
168: !     function evaluation routine.

170:       PetscCallA(SNESSetFunction(snes,r,FormFunction,fdcoloring,ierr))

172: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
173: !  Create matrix data structure; set Jacobian evaluation routine
174: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

180:       PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr))
181:       if (.not. matrix_free) then
182:         PetscCallA(MatCreateSeqAIJ(PETSC_COMM_WORLD,N,N,i5,PETSC_NULL_INTEGER,J,ierr))
183:       endif

185: !
186: !     This option will cause the Jacobian to be computed via finite differences
187: !    efficiently using a coloring of the columns of the matrix.
188: !
189:       fd_coloring = .false.
190:       PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-snes_fd_coloring',fd_coloring,ierr))
191:       if (fd_coloring) then

193: !
194: !      This initializes the nonzero structure of the Jacobian. This is artificial
195: !      because clearly if we had a routine to compute the Jacobian we won't need
196: !      to use finite differences.
197: !
198:         PetscCallA(FormJacobian(snes,x,J,J,0,ierr))
199: !
200: !       Color the matrix, i.e. determine groups of columns that share no common
201: !      rows. These columns in the Jacobian can all be computed simultaneously.
202: !
203:         PetscCallA(MatColoringCreate(J,mc,ierr))
204:         PetscCallA(MatColoringSetType(mc,MATCOLORINGNATURAL,ierr))
205:         PetscCallA(MatColoringSetFromOptions(mc,ierr))
206:         PetscCallA(MatColoringApply(mc,iscoloring,ierr))
207:         PetscCallA(MatColoringDestroy(mc,ierr))
208: !
209: !       Create the data structure that SNESComputeJacobianDefaultColor() uses
210: !       to compute the actual Jacobians via finite differences.
211: !
212:         PetscCallA(MatFDColoringCreate(J,iscoloring,fdcoloring,ierr))
213:         PetscCallA(MatFDColoringSetFunction(fdcoloring,FormFunction,fdcoloring,ierr))
214:         PetscCallA(MatFDColoringSetFromOptions(fdcoloring,ierr))
215:         PetscCallA(MatFDColoringSetUp(J,iscoloring,fdcoloring,ierr))
216: !
217: !        Tell SNES to use the routine SNESComputeJacobianDefaultColor()
218: !      to compute Jacobians.
219: !
220:         PetscCallA(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,fdcoloring,ierr))
221:         PetscCallA(ISColoringDestroy(iscoloring,ierr))

223:       else if (.not. matrix_free) then

225: !  Set Jacobian matrix data structure and default Jacobian evaluation
226: !  routine.  Whenever the nonlinear solver needs to compute the
227: !  Jacobian matrix, it will call this routine.
228: !   - Note that the final routine argument is the user-defined
229: !     context that provides application-specific data for the
230: !     Jacobian evaluation routine.
231: !   - The user can override with:
232: !      -snes_fd : default finite differencing approximation of Jacobian
233: !      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
234: !                 (unless user explicitly sets preconditioner)
235: !      -snes_mf_operator : form preconditioning matrix as set by the user,
236: !                          but use matrix-free approx for Jacobian-vector
237: !                          products within Newton-Krylov method
238: !
239:         PetscCallA(SNESSetJacobian(snes,J,J,FormJacobian,0,ierr))
240:       endif

242: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
243: !  Customize nonlinear solver; set runtime options
244: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

248:       PetscCallA(SNESSetFromOptions(snes,ierr))

250: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
251: !  Evaluate initial guess; then solve nonlinear system.
252: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

259:       PetscCallA(FormInitialGuess(x,ierr))
260:       PetscCallA(SNESSolve(snes,PETSC_NULL_VEC,x,ierr))
261:       PetscCallA(SNESGetIterationNumber(snes,its,ierr))
262:       if (rank .eq. 0) then
263:          write(6,100) its
264:       endif
265:   100 format('Number of SNES iterations = ',i1)

267: !  PetscDraw contour plot of solution

269:       PetscCallA(PetscDrawCreate(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER,'Solution',300,0,300,300,draw,ierr))
270:       PetscCallA(PetscDrawSetFromOptions(draw,ierr))

272:       PetscCallA(VecGetArrayRead(x,lx_v,lx_i,ierr))
273:       PetscCallA(PetscDrawTensorContour(draw,mx,my,PETSC_NULL_REAL,PETSC_NULL_REAL,lx_v(lx_i+1),ierr))
274:       PetscCallA(VecRestoreArrayRead(x,lx_v,lx_i,ierr))

276: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
277: !  Free work space.  All PETSc objects should be destroyed when they
278: !  are no longer needed.
279: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

281:       if (.not. matrix_free) PetscCallA(MatDestroy(J,ierr))
282:       if (fd_coloring) PetscCallA(MatFDColoringDestroy(fdcoloring,ierr))

284:       PetscCallA(VecDestroy(x,ierr))
285:       PetscCallA(VecDestroy(r,ierr))
286:       PetscCallA(SNESDestroy(snes,ierr))
287:       PetscCallA(PetscDrawDestroy(draw,ierr))
288:       PetscCallA(PetscFinalize(ierr))
289:       end

291: ! ---------------------------------------------------------------------
292: !
293: !  FormInitialGuess - Forms initial approximation.
294: !
295: !  Input Parameter:
296: !  X - vector
297: !
298: !  Output Parameters:
299: !  X - vector
300: !  ierr - error code
301: !
302: !  Notes:
303: !  This routine serves as a wrapper for the lower-level routine
304: !  "ApplicationInitialGuess", where the actual computations are
305: !  done using the standard Fortran style of treating the local
306: !  vector data as a multidimensional array over the local mesh.
307: !  This routine merely accesses the local vector data via
308: !  VecGetArray() and VecRestoreArray().
309: !
310:       subroutine FormInitialGuess(X,ierr)
311:       use petscsnes
312:       implicit none

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

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

322:       0

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

332:       PetscCallA(VecGetArray(X,lx_v,lx_i,ierr))

334: !  Compute initial guess

336:       PetscCallA(ApplicationInitialGuess(lx_v(lx_i),ierr))

338: !  Restore vector

340:       PetscCallA(VecRestoreArray(X,lx_v,lx_i,ierr))

342:       return
343:       end

345: !  ApplicationInitialGuess - Computes initial approximation, called by
346: !  the higher level routine FormInitialGuess().
347: !
348: !  Input Parameter:
349: !  x - local vector data
350: !
351: !  Output Parameters:
352: !  f - local vector data, f(x)
353: !  ierr - error code
354: !
355: !  Notes:
356: !  This routine uses standard Fortran-style computations over a 2-dim array.
357: !
358:       subroutine ApplicationInitialGuess(x,ierr)
359:       use petscksp
360:       implicit none

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

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

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

376: !  Set parameters

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

384:       do 20 j=1,my
385:          temp = min(j-1,my-j)*hy
386:          do 10 i=1,mx
387:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
388:               x(i,j) = 0.0
389:             else
390:               x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,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,fdcoloring,ierr)
420:       use petscsnes
421:       implicit none

423: !  Input/output variables:
424:       SNES              snes
425:       Vec               X,F
426:       PetscErrorCode          ierr
427:       MatFDColoring fdcoloring

429: !  Common blocks:
430:       PetscReal         lambda
431:       PetscInt          mx,my
432:       PetscBool         fd_coloring
433:       common            /params/ lambda,mx,my,fd_coloring

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

439:       PetscInt, pointer :: indices(:)

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:       PetscCallA(VecGetArrayRead(X,lx_v,lx_i,ierr))
450:       PetscCallA(VecGetArray(F,lf_v,lf_i,ierr))

452: !  Compute function

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

456: !  Restore vectors

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

461:       PetscCallA(PetscLogFlops(11.0d0*mx*my,ierr))
462: !
463: !     fdcoloring is in the common block and used here ONLY to test the
464: !     calls to MatFDColoringGetPerturbedColumnsF90() and  MatFDColoringRestorePerturbedColumnsF90()
465: !
466:       if (fd_coloring) then
467:          PetscCallA(MatFDColoringGetPerturbedColumnsF90(fdcoloring,indices,ierr))
468:          print*,'Indices from GetPerturbedColumnsF90'
469:          write(*,1000) indices
470:  1000    format(50i4)
471:          PetscCallA(MatFDColoringRestorePerturbedColumnsF90(fdcoloring,indices,ierr))
472:       endif
473:       return
474:       end

476: ! ---------------------------------------------------------------------
477: !
478: !  ApplicationFunction - Computes nonlinear function, called by
479: !  the higher level routine FormFunction().
480: !
481: !  Input Parameter:
482: !  x    - local vector data
483: !
484: !  Output Parameters:
485: !  f    - local vector data, f(x)
486: !  ierr - error code
487: !
488: !  Notes:
489: !  This routine uses standard Fortran-style computations over a 2-dim array.
490: !
491:       subroutine ApplicationFunction(x,f,ierr)
492:       use petscsnes
493:       implicit none

495: !  Common blocks:
496:       PetscReal      lambda
497:       PetscInt        mx,my
498:       PetscBool         fd_coloring
499:       common         /params/ lambda,mx,my,fd_coloring

501: !  Input/output variables:
502:       PetscScalar    x(mx,my),f(mx,my)
503:       PetscErrorCode       ierr

505: !  Local variables:
506:       PetscScalar    two,one,hx,hy
507:       PetscScalar    hxdhy,hydhx,sc
508:       PetscScalar    u,uxx,uyy
509:       PetscInt        i,j

511:       0
512:       one    = 1.0
513:       two    = 2.0
514:       hx     = one/(mx-1)
515:       hy     = one/(my-1)
516:       sc     = hx*hy*lambda
517:       hxdhy  = hx/hy
518:       hydhx  = hy/hx

520: !  Compute function

522:       do 20 j=1,my
523:          do 10 i=1,mx
524:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
525:                f(i,j) = x(i,j)
526:             else
527:                u = x(i,j)
528:                uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
529:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
530:                f(i,j) = uxx + uyy - sc*exp(u)
531:             endif
532:  10      continue
533:  20   continue

535:       return
536:       end

538: ! ---------------------------------------------------------------------
539: !
540: !  FormJacobian - Evaluates Jacobian matrix.
541: !
542: !  Input Parameters:
543: !  snes    - the SNES context
544: !  x       - input vector
545: !  dummy   - optional user-defined context, as set by SNESSetJacobian()
546: !            (not used here)
547: !
548: !  Output Parameters:
549: !  jac      - Jacobian matrix
550: !  jac_prec - optionally different preconditioning matrix (not used here)
551: !  flag     - flag indicating matrix structure
552: !
553: !  Notes:
554: !  This routine serves as a wrapper for the lower-level routine
555: !  "ApplicationJacobian", where the actual computations are
556: !  done using the standard Fortran style of treating the local
557: !  vector data as a multidimensional array over the local mesh.
558: !  This routine merely accesses the local vector data via
559: !  VecGetArray() and VecRestoreArray().
560: !
561:       subroutine FormJacobian(snes,X,jac,jac_prec,dummy,ierr)
562:       use petscsnes
563:       implicit none

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

572: !  Common blocks:
573:       PetscReal     lambda
574:       PetscInt       mx,my
575:       PetscBool         fd_coloring
576:       common        /params/ lambda,mx,my,fd_coloring

578: !  Declarations for use with local array:
579:       PetscScalar   lx_v(0:1)
580:       PetscOffset   lx_i

582: !  Get a pointer to vector data

584:       PetscCallA(VecGetArrayRead(X,lx_v,lx_i,ierr))

586: !  Compute Jacobian entries

588:       PetscCallA(ApplicationJacobian(lx_v(lx_i),jac,jac_prec,ierr))

590: !  Restore vector

592:       PetscCallA(VecRestoreArrayRead(X,lx_v,lx_i,ierr))

594: !  Assemble matrix

596:       PetscCallA(MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr))
597:       PetscCallA(MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr))

599:       return
600:       end

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

622: !  Common blocks:
623:       PetscReal    lambda
624:       PetscInt      mx,my
625:       PetscBool         fd_coloring
626:       common       /params/ lambda,mx,my,fd_coloring

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

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

638: !  Set parameters

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

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

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

679:       return
680:       end

682: !
683: !/*TEST
684: !
685: !   build:
686: !      requires: !single
687: !
688: !   test:
689: !      args: -snes_monitor_short -nox -snes_type newtontr -ksp_gmres_cgs_refinement_type refine_always
690: !
691: !   test:
692: !      suffix: 2
693: !      args: -snes_monitor_short -nox -snes_fd -ksp_gmres_cgs_refinement_type refine_always
694: !
695: !   test:
696: !      suffix: 3
697: !      args: -snes_monitor_short -nox -snes_fd_coloring -mat_coloring_type sl -ksp_gmres_cgs_refinement_type refine_always
698: !      filter: sort -b
699: !      filter_output: sort -b
700: !
701: !   test:
702: !     suffix: 4
703: !     args: -pc -par 6.807 -nox
704: !
705: !TEST*/