Actual source code: ex5f90.F90

  1: !
  2: !  Description: Solves a nonlinear system in parallel with SNES.
  3: !  We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
  4: !  domain, using distributed arrays (DMDAs) to partition the parallel grid.
  5: !  The command line options include:
  6: !    -par <parameter>, where <parameter> indicates the nonlinearity of the problem
  7: !       problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)
  8: !

 10: !
 11: !  --------------------------------------------------------------------------
 12: !
 13: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 14: !  the partial differential equation
 15: !
 16: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
 17: !
 18: !  with boundary conditions
 19: !
 20: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
 21: !
 22: !  A finite difference approximation with the usual 5-point stencil
 23: !  is used to discretize the boundary value problem to obtain a nonlinear
 24: !  system of equations.
 25: !
 26: !  The uniprocessor version of this code is snes/tutorials/ex4f.F
 27: !
 28: !  --------------------------------------------------------------------------
 29: !  The following define must be used before including any PETSc include files
 30: !  into a module or interface. This is because they can't handle declarations
 31: !  in them
 32: !

 34:       module ex5f90module
 35:       use petscsnes
 36:       use petscdmda
 37: #include <petsc/finclude/petscsnes.h>
 38:       type userctx
 39:         PetscInt xs,xe,xm,gxs,gxe,gxm
 40:         PetscInt ys,ye,ym,gys,gye,gym
 41:         PetscInt mx,my
 42:         PetscMPIInt rank
 43:         PetscReal lambda
 44:       end type userctx

 46:       contains
 47: ! ---------------------------------------------------------------------
 48: !
 49: !  FormFunction - Evaluates nonlinear function, F(x).
 50: !
 51: !  Input Parameters:
 52: !  snes - the SNES context
 53: !  X - input vector
 54: !  dummy - optional user-defined context, as set by SNESSetFunction()
 55: !          (not used here)
 56: !
 57: !  Output Parameter:
 58: !  F - function vector
 59: !
 60: !  Notes:
 61: !  This routine serves as a wrapper for the lower-level routine
 62: !  "FormFunctionLocal", where the actual computations are
 63: !  done using the standard Fortran style of treating the local
 64: !  vector data as a multidimensional array over the local mesh.
 65: !  This routine merely handles ghost point scatters and accesses
 66: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
 67: !
 68:       subroutine FormFunction(snes,X,F,user,ierr)
 69:       implicit none

 71: !  Input/output variables:
 72:       SNES           snes
 73:       Vec            X,F
 74:       PetscErrorCode ierr
 75:       type (userctx) user
 76:       DM             da

 78: !  Declarations for use with local arrays:
 79:       PetscScalar,pointer :: lx_v(:),lf_v(:)
 80:       Vec            localX

 82: !  Scatter ghost points to local vector, using the 2-step process
 83: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
 84: !  By placing code between these two statements, computations can
 85: !  be done while messages are in transition.
 86:       PetscCall(SNESGetDM(snes,da,ierr))
 87:       PetscCall(DMGetLocalVector(da,localX,ierr))
 88:       PetscCall(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr))
 89:       PetscCall(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr))

 91: !  Get a pointer to vector data.
 92: !    - For default PETSc vectors, VecGetArrayF90() returns a pointer to
 93: !      the data array. Otherwise, the routine is implementation dependent.
 94: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
 95: !      the array.
 96: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray().

 98:       PetscCall(VecGetArrayF90(localX,lx_v,ierr))
 99:       PetscCall(VecGetArrayF90(F,lf_v,ierr))

101: !  Compute function over the locally owned part of the grid
102:       PetscCall(FormFunctionLocal(lx_v,lf_v,user,ierr))

104: !  Restore vectors
105:       PetscCall(VecRestoreArrayF90(localX,lx_v,ierr))
106:       PetscCall(VecRestoreArrayF90(F,lf_v,ierr))

108: !  Insert values into global vector

110:       PetscCall(DMRestoreLocalVector(da,localX,ierr))
111:       PetscCall(PetscLogFlops(11.0d0*user%ym*user%xm,ierr))

113: !      PetscCallA(VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr))
114: !      PetscCallA(VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr))
115:       return
116:       end subroutine formfunction
117:       end module ex5f90module

119:       module ex5f90moduleinterfaces
120:         use ex5f90module

122:       Interface SNESSetApplicationContext
123:         Subroutine SNESSetApplicationContext(snes,ctx,ierr)
124:         use ex5f90module
125:           SNES snes
126:           type(userctx) ctx
127:           PetscErrorCode ierr
128:         End Subroutine
129:       End Interface SNESSetApplicationContext

131:       Interface SNESGetApplicationContext
132:         Subroutine SNESGetApplicationContext(snes,ctx,ierr)
133:         use ex5f90module
134:           SNES snes
135:           type(userctx), pointer :: ctx
136:           PetscErrorCode ierr
137:         End Subroutine
138:       End Interface SNESGetApplicationContext
139:       end module ex5f90moduleinterfaces

141:       program main
142:       use ex5f90module
143:       use ex5f90moduleinterfaces
144:       implicit none
145: !

147: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: !                   Variable declarations
149: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: !
151: !  Variables:
152: !     snes        - nonlinear solver
153: !     x, r        - solution, residual vectors
154: !     J           - Jacobian matrix
155: !     its         - iterations for convergence
156: !     Nx, Ny      - number of preocessors in x- and y- directions
157: !     matrix_free - flag - 1 indicates matrix-free version
158: !
159:       SNES             snes
160:       Vec              x,r
161:       Mat              J
162:       PetscErrorCode   ierr
163:       PetscInt         its
164:       PetscBool        flg,matrix_free
165:       PetscInt         ione,nfour
166:       PetscReal lambda_max,lambda_min
167:       type (userctx)   user
168:       DM               da

170: !  Note: Any user-defined Fortran routines (such as FormJacobian)
171: !  MUST be declared as external.
172:       external FormInitialGuess,FormJacobian

174: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: !  Initialize program
176: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177:       PetscCallA(PetscInitialize(ierr))
178:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr))

180: !  Initialize problem parameters
181:       lambda_max  = 6.81
182:       lambda_min  = 0.0
183:       user%lambda = 6.0
184:       ione = 1
185:       nfour = 4
186:       PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',user%lambda,flg,ierr))
187:       PetscCheckA(user%lambda .lt. lambda_max .and. user%lambda .gt. lambda_min,PETSC_COMM_SELF,PETSC_ERR_USER,'Lambda provided with -par is out of range')

189: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: !  Create nonlinear solver context
191: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
192:       PetscCallA(SNESCreate(PETSC_COMM_WORLD,snes,ierr))

194: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195: !  Create vector data structures; set function evaluation routine
196: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

198: !  Create distributed array (DMDA) to manage parallel grid and vectors

200: ! This really needs only the star-type stencil, but we use the box
201: ! stencil temporarily.
202:       PetscCallA(DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,ione,ione,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr))
203:       PetscCallA(DMSetFromOptions(da,ierr))
204:       PetscCallA(DMSetUp(da,ierr))

206:       PetscCallA(DMDAGetInfo(da,PETSC_NULL_INTEGER,user%mx,user%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))

208: !
209: !   Visualize the distribution of the array across the processors
210: !
211: !     PetscCallA(DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr))

213: !  Extract global and local vectors from DMDA; then duplicate for remaining
214: !  vectors that are the same types
215:       PetscCallA(DMCreateGlobalVector(da,x,ierr))
216:       PetscCallA(VecDuplicate(x,r,ierr))

218: !  Get local grid boundaries (for 2-dimensional DMDA)
219:       PetscCallA(DMDAGetCorners(da,user%xs,user%ys,PETSC_NULL_INTEGER,user%xm,user%ym,PETSC_NULL_INTEGER,ierr))
220:       PetscCallA(DMDAGetGhostCorners(da,user%gxs,user%gys,PETSC_NULL_INTEGER,user%gxm,user%gym,PETSC_NULL_INTEGER,ierr))

222: !  Here we shift the starting indices up by one so that we can easily
223: !  use the Fortran convention of 1-based indices (rather 0-based indices).
224:       user%xs  = user%xs+1
225:       user%ys  = user%ys+1
226:       user%gxs = user%gxs+1
227:       user%gys = user%gys+1

229:       user%ye  = user%ys+user%ym-1
230:       user%xe  = user%xs+user%xm-1
231:       user%gye = user%gys+user%gym-1
232:       user%gxe = user%gxs+user%gxm-1

234:       PetscCallA(SNESSetApplicationContext(snes,user,ierr))

236: !  Set function evaluation routine and vector
237:       PetscCallA(SNESSetFunction(snes,r,FormFunction,user,ierr))

239: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
240: !  Create matrix data structure; set Jacobian evaluation routine
241: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

243: !  Set Jacobian matrix data structure and default Jacobian evaluation
244: !  routine. User can override with:
245: !     -snes_fd : default finite differencing approximation of Jacobian
246: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
247: !                (unless user explicitly sets preconditioner)
248: !     -snes_mf_operator : form preconditioning matrix as set by the user,
249: !                         but use matrix-free approx for Jacobian-vector
250: !                         products within Newton-Krylov method
251: !
252: !  Note:  For the parallel case, vectors and matrices MUST be partitioned
253: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
254: !     the DMDAs determine the problem partitioning.  We must explicitly
255: !     specify the local matrix dimensions upon its creation for compatibility
256: !     with the vector distribution.  Thus, the generic MatCreate() routine
257: !     is NOT sufficient when working with distributed arrays.
258: !
259: !     Note: Here we only approximately preallocate storage space for the
260: !     Jacobian.  See the users manual for a discussion of better techniques
261: !     for preallocating matrix memory.

263:       PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr))
264:       if (.not. matrix_free) then
265:         PetscCallA(DMSetMatType(da,MATAIJ,ierr))
266:         PetscCallA(DMCreateMatrix(da,J,ierr))
267:         PetscCallA(SNESSetJacobian(snes,J,J,FormJacobian,user,ierr))
268:       endif

270: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
271: !  Customize nonlinear solver; set runtime options
272: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
273: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
274:       PetscCallA(SNESSetDM(snes,da,ierr))
275:       PetscCallA(SNESSetFromOptions(snes,ierr))

277: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
278: !  Evaluate initial guess; then solve nonlinear system.
279: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
280: !  Note: The user should initialize the vector, x, with the initial guess
281: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
282: !  to employ an initial guess of zero, the user should explicitly set
283: !  this vector to zero by calling VecSet().

285:       PetscCallA(FormInitialGuess(snes,x,ierr))
286:       PetscCallA(SNESSolve(snes,PETSC_NULL_VEC,x,ierr))
287:       PetscCallA(SNESGetIterationNumber(snes,its,ierr))
288:       if (user%rank .eq. 0) then
289:          write(6,100) its
290:       endif
291:   100 format('Number of SNES iterations = ',i5)

293: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
294: !  Free work space.  All PETSc objects should be destroyed when they
295: !  are no longer needed.
296: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
297:       if (.not. matrix_free) PetscCallA(MatDestroy(J,ierr))
298:       PetscCallA(VecDestroy(x,ierr))
299:       PetscCallA(VecDestroy(r,ierr))
300:       PetscCallA(SNESDestroy(snes,ierr))
301:       PetscCallA(DMDestroy(da,ierr))

303:       PetscCallA(PetscFinalize(ierr))
304:       end

306: ! ---------------------------------------------------------------------
307: !
308: !  FormInitialGuess - Forms initial approximation.
309: !
310: !  Input Parameters:
311: !  X - vector
312: !
313: !  Output Parameter:
314: !  X - vector
315: !
316: !  Notes:
317: !  This routine serves as a wrapper for the lower-level routine
318: !  "InitialGuessLocal", where the actual computations are
319: !  done using the standard Fortran style of treating the local
320: !  vector data as a multidimensional array over the local mesh.
321: !  This routine merely handles ghost point scatters and accesses
322: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
323: !
324:       subroutine FormInitialGuess(snes,X,ierr)
325:       use ex5f90module
326:       use ex5f90moduleinterfaces
327:       implicit none

329: !  Input/output variables:
330:       SNES           snes
331:       type(userctx), pointer:: puser
332:       Vec            X
333:       PetscErrorCode ierr
334:       DM             da

336: !  Declarations for use with local arrays:
337:       PetscScalar,pointer :: lx_v(:)

339:       ierr = 0
340:       PetscCallA(SNESGetDM(snes,da,ierr))
341:       PetscCallA(SNESGetApplicationContext(snes,puser,ierr))
342: !  Get a pointer to vector data.
343: !    - For default PETSc vectors, VecGetArrayF90() returns a pointer to
344: !      the data array. Otherwise, the routine is implementation dependent.
345: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
346: !      the array.
347: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray().

349:       PetscCallA(VecGetArrayF90(X,lx_v,ierr))

351: !  Compute initial guess over the locally owned part of the grid
352:       PetscCallA(InitialGuessLocal(puser,lx_v,ierr))

354: !  Restore vector
355:       PetscCallA(VecRestoreArrayF90(X,lx_v,ierr))

357: !  Insert values into global vector

359:       return
360:       end

362: ! ---------------------------------------------------------------------
363: !
364: !  InitialGuessLocal - Computes initial approximation, called by
365: !  the higher level routine FormInitialGuess().
366: !
367: !  Input Parameter:
368: !  x - local vector data
369: !
370: !  Output Parameters:
371: !  x - local vector data
372: !  ierr - error code
373: !
374: !  Notes:
375: !  This routine uses standard Fortran-style computations over a 2-dim array.
376: !
377:       subroutine InitialGuessLocal(user,x,ierr)
378:       use ex5f90module
379:       implicit none

381: !  Input/output variables:
382:       type (userctx)         user
383:       PetscScalar  x(user%xs:user%xe,user%ys:user%ye)
384:       PetscErrorCode ierr

386: !  Local variables:
387:       PetscInt  i,j
388:       PetscReal   temp1,temp,hx,hy
389:       PetscReal   one

391: !  Set parameters

393:       ierr   = 0
394:       one    = 1.0
395:       hx     = one/(user%mx-1)
396:       hy     = one/(user%my-1)
397:       temp1  = user%lambda/(user%lambda + one)

399:       do 20 j=user%ys,user%ye
400:          temp = min(j-1,user%my-j)*hy
401:          do 10 i=user%xs,user%xe
402:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
403:               x(i,j) = 0.0
404:             else
405:               x(i,j) = temp1 * sqrt(min(hx*min(i-1,user%mx-i),temp))
406:             endif
407:  10      continue
408:  20   continue

410:       return
411:       end

413: ! ---------------------------------------------------------------------
414: !
415: !  FormFunctionLocal - Computes nonlinear function, called by
416: !  the higher level routine FormFunction().
417: !
418: !  Input Parameter:
419: !  x - local vector data
420: !
421: !  Output Parameters:
422: !  f - local vector data, f(x)
423: !  ierr - error code
424: !
425: !  Notes:
426: !  This routine uses standard Fortran-style computations over a 2-dim array.
427: !
428:       subroutine FormFunctionLocal(x,f,user,ierr)
429:       use ex5f90module

431:       implicit none

433: !  Input/output variables:
434:       type (userctx) user
435:       PetscScalar  x(user%gxs:user%gxe,user%gys:user%gye)
436:       PetscScalar  f(user%xs:user%xe,user%ys:user%ye)
437:       PetscErrorCode ierr

439: !  Local variables:
440:       PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
441:       PetscScalar u,uxx,uyy
442:       PetscInt  i,j

444:       one    = 1.0
445:       two    = 2.0
446:       hx     = one/(user%mx-1)
447:       hy     = one/(user%my-1)
448:       sc     = hx*hy*user%lambda
449:       hxdhy  = hx/hy
450:       hydhx  = hy/hx

452: !  Compute function over the locally owned part of the grid

454:       do 20 j=user%ys,user%ye
455:          do 10 i=user%xs,user%xe
456:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
457:                f(i,j) = x(i,j)
458:             else
459:                u = x(i,j)
460:                uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
461:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
462:                f(i,j) = uxx + uyy - sc*exp(u)
463:             endif
464:  10      continue
465:  20   continue

467:       return
468:       end

470: ! ---------------------------------------------------------------------
471: !
472: !  FormJacobian - Evaluates Jacobian matrix.
473: !
474: !  Input Parameters:
475: !  snes     - the SNES context
476: !  x        - input vector
477: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
478: !             (not used here)
479: !
480: !  Output Parameters:
481: !  jac      - Jacobian matrix
482: !  jac_prec - optionally different preconditioning matrix (not used here)
483: !  flag     - flag indicating matrix structure
484: !
485: !  Notes:
486: !  This routine serves as a wrapper for the lower-level routine
487: !  "FormJacobianLocal", where the actual computations are
488: !  done using the standard Fortran style of treating the local
489: !  vector data as a multidimensional array over the local mesh.
490: !  This routine merely accesses the local vector data via
491: !  VecGetArrayF90() and VecRestoreArrayF90().
492: !
493: !  Notes:
494: !  Due to grid point reordering with DMDAs, we must always work
495: !  with the local grid points, and then transform them to the new
496: !  global numbering with the "ltog" mapping
497: !  We cannot work directly with the global numbers for the original
498: !  uniprocessor grid!
499: !
500: !  Two methods are available for imposing this transformation
501: !  when setting matrix entries:
502: !    (A) MatSetValuesLocal(), using the local ordering (including
503: !        ghost points!)
504: !        - Set matrix entries using the local ordering
505: !          by calling MatSetValuesLocal()
506: !    (B) MatSetValues(), using the global ordering

508: !        - Set matrix entries using the global ordering by calling
509: !          MatSetValues()
510: !  Option (A) seems cleaner/easier in many cases, and is the procedure
511: !  used in this example.
512: !
513:       subroutine FormJacobian(snes,X,jac,jac_prec,user,ierr)
514:       use ex5f90module
515:       implicit none

517: !  Input/output variables:
518:       SNES         snes
519:       Vec          X
520:       Mat          jac,jac_prec
521:       type(userctx)  user
522:       PetscErrorCode ierr
523:       DM             da

525: !  Declarations for use with local arrays:
526:       PetscScalar,pointer :: lx_v(:)
527:       Vec            localX

529: !  Scatter ghost points to local vector, using the 2-step process
530: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
531: !  Computations can be done while messages are in transition,
532: !  by placing code between these two statements.

534:       PetscCallA(SNESGetDM(snes,da,ierr))
535:       PetscCallA(DMGetLocalVector(da,localX,ierr))
536:       PetscCallA(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr))
537:       PetscCallA(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr))

539: !  Get a pointer to vector data
540:       PetscCallA(VecGetArrayF90(localX,lx_v,ierr))

542: !  Compute entries for the locally owned part of the Jacobian preconditioner.
543:       PetscCallA(FormJacobianLocal(lx_v,jac_prec,user,ierr))

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

550:       PetscCallA(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr))
551:       if (jac .ne. jac_prec) then
552:          PetscCallA(MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr))
553:       endif
554:       PetscCallA(VecRestoreArrayF90(localX,lx_v,ierr))
555:       PetscCallA(DMRestoreLocalVector(da,localX,ierr))
556:       PetscCallA(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr))
557:       if (jac .ne. jac_prec) then
558:         PetscCallA(MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr))
559:       endif

561: !  Tell the matrix we will never add a new nonzero location to the
562: !  matrix. If we do it will generate an error.

564:       PetscCallA(MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr))

566:       return
567:       end

569: ! ---------------------------------------------------------------------
570: !
571: !  FormJacobianLocal - Computes Jacobian preconditioner matrix,
572: !  called by the higher level routine FormJacobian().
573: !
574: !  Input Parameters:
575: !  x        - local vector data
576: !
577: !  Output Parameters:
578: !  jac_prec - Jacobian preconditioner matrix
579: !  ierr     - error code
580: !
581: !  Notes:
582: !  This routine uses standard Fortran-style computations over a 2-dim array.
583: !
584: !  Notes:
585: !  Due to grid point reordering with DMDAs, we must always work
586: !  with the local grid points, and then transform them to the new
587: !  global numbering with the "ltog" mapping
588: !  We cannot work directly with the global numbers for the original
589: !  uniprocessor grid!
590: !
591: !  Two methods are available for imposing this transformation
592: !  when setting matrix entries:
593: !    (A) MatSetValuesLocal(), using the local ordering (including
594: !        ghost points!)
595: !        - Set matrix entries using the local ordering
596: !          by calling MatSetValuesLocal()
597: !    (B) MatSetValues(), using the global ordering
598: !        - Then apply this map explicitly yourself
599: !        - Set matrix entries using the global ordering by calling
600: !          MatSetValues()
601: !  Option (A) seems cleaner/easier in many cases, and is the procedure
602: !  used in this example.
603: !
604:       subroutine FormJacobianLocal(x,jac_prec,user,ierr)
605:       use ex5f90module
606:       implicit none

608: !  Input/output variables:
609:       type (userctx) user
610:       PetscScalar    x(user%gxs:user%gxe,user%gys:user%gye)
611:       Mat            jac_prec
612:       PetscErrorCode ierr

614: !  Local variables:
615:       PetscInt    row,col(5),i,j
616:       PetscInt    ione,ifive
617:       PetscScalar two,one,hx,hy,hxdhy
618:       PetscScalar hydhx,sc,v(5)

620: !  Set parameters
621:       ione   = 1
622:       ifive  = 5
623:       one    = 1.0
624:       two    = 2.0
625:       hx     = one/(user%mx-1)
626:       hy     = one/(user%my-1)
627:       sc     = hx*hy
628:       hxdhy  = hx/hy
629:       hydhx  = hy/hx

631: !  Compute entries for the locally owned part of the Jacobian.
632: !   - Currently, all PETSc parallel matrix formats are partitioned by
633: !     contiguous chunks of rows across the processors.
634: !   - Each processor needs to insert only elements that it owns
635: !     locally (but any non-local elements will be sent to the
636: !     appropriate processor during matrix assembly).
637: !   - Here, we set all entries for a particular row at once.
638: !   - We can set matrix entries either using either
639: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
640: !   - Note that MatSetValues() uses 0-based row and column numbers
641: !     in Fortran as well as in C.

643:       do 20 j=user%ys,user%ye
644:          row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
645:          do 10 i=user%xs,user%xe
646:             row = row + 1
647: !           boundary points
648:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
649:                col(1) = row
650:                v(1)   = one
651:                PetscCallA(MatSetValuesLocal(jac_prec,ione,row,ione,col,v,INSERT_VALUES,ierr))
652: !           interior grid points
653:             else
654:                v(1) = -hxdhy
655:                v(2) = -hydhx
656:                v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j))
657:                v(4) = -hydhx
658:                v(5) = -hxdhy
659:                col(1) = row - user%gxm
660:                col(2) = row - 1
661:                col(3) = row
662:                col(4) = row + 1
663:                col(5) = row + user%gxm
664:                PetscCallA(MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,INSERT_VALUES,ierr))
665:             endif
666:  10      continue
667:  20   continue

669:       return
670:       end

672: !
673: !/*TEST
674: !
675: !   test:
676: !      nsize: 4
677: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
678: !      requires: !single
679: !
680: !   test:
681: !      suffix: 2
682: !      nsize: 4
683: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
684: !      requires: !single
685: !
686: !   test:
687: !      suffix: 3
688: !      nsize: 3
689: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
690: !      requires: !single
691: !
692: !   test:
693: !      suffix: 4
694: !      nsize: 3
695: !      args: -snes_mf_operator -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
696: !      requires: !single
697: !
698: !   test:
699: !      suffix: 5
700: !      requires: !single
701: !
702: !TEST*/