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:       end subroutine formfunction
116:       end module ex5f90module

118:       module ex5f90moduleinterfaces
119:         use ex5f90module

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

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

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

146: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: !                   Variable declarations
148: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: !
150: !  Variables:
151: !     snes        - nonlinear solver
152: !     x, r        - solution, residual vectors
153: !     J           - Jacobian matrix
154: !     its         - iterations for convergence
155: !     Nx, Ny      - number of preocessors in x- and y- directions
156: !     matrix_free - flag - 1 indicates matrix-free version
157: !
158:       SNES             snes
159:       Vec              x,r
160:       Mat              J
161:       PetscErrorCode   ierr
162:       PetscInt         its
163:       PetscBool        flg,matrix_free
164:       PetscInt         ione,nfour
165:       PetscReal lambda_max,lambda_min
166:       type (userctx)   user
167:       DM               da

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

173: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174: !  Initialize program
175: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176:       PetscCallA(PetscInitialize(ierr))
177:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr))

179: !  Initialize problem parameters
180:       lambda_max  = 6.81
181:       lambda_min  = 0.0
182:       user%lambda = 6.0
183:       ione = 1
184:       nfour = 4
185:       PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',user%lambda,flg,ierr))
186:       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')

188: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189: !  Create nonlinear solver context
190: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191:       PetscCallA(SNESCreate(PETSC_COMM_WORLD,snes,ierr))

193: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: !  Create vector data structures; set function evaluation routine
195: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

199: ! This really needs only the star-type stencil, but we use the box
200: ! stencil temporarily.
201:       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_ARRAY,PETSC_NULL_INTEGER_ARRAY,da,ierr))
202:       PetscCallA(DMSetFromOptions(da,ierr))
203:       PetscCallA(DMSetUp(da,ierr))

205:       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_ENUM,PETSC_NULL_ENUM,PETSC_NULL_ENUM,PETSC_NULL_ENUM,ierr))

207: !
208: !   Visualize the distribution of the array across the processors
209: !
210: !     PetscCallA(DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr))

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

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

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

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

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

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

238: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
239: !  Create matrix data structure; set Jacobian evaluation routine
240: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

269: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
270: !  Customize nonlinear solver; set runtime options
271: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
272: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
273:       PetscCallA(SNESSetDM(snes,da,ierr))
274:       PetscCallA(SNESSetFromOptions(snes,ierr))

276: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
277: !  Evaluate initial guess; then solve nonlinear system.
278: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
279: !  Note: The user should initialize the vector, x, with the initial guess
280: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
281: !  to employ an initial guess of zero, the user should explicitly set
282: !  this vector to zero by calling VecSet().

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

292: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
293: !  Free work space.  All PETSc objects should be destroyed when they
294: !  are no longer needed.
295: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
296:       if (.not. matrix_free) PetscCallA(MatDestroy(J,ierr))
297:       PetscCallA(VecDestroy(x,ierr))
298:       PetscCallA(VecDestroy(r,ierr))
299:       PetscCallA(SNESDestroy(snes,ierr))
300:       PetscCallA(DMDestroy(da,ierr))

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

305: ! ---------------------------------------------------------------------
306: !
307: !  FormInitialGuess - Forms initial approximation.
308: !
309: !  Input Parameters:
310: !  X - vector
311: !
312: !  Output Parameter:
313: !  X - vector
314: !
315: !  Notes:
316: !  This routine serves as a wrapper for the lower-level routine
317: !  "InitialGuessLocal", where the actual computations are
318: !  done using the standard Fortran style of treating the local
319: !  vector data as a multidimensional array over the local mesh.
320: !  This routine merely handles ghost point scatters and accesses
321: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
322: !
323:       subroutine FormInitialGuess(snes,X,ierr)
324:       use ex5f90module
325:       use ex5f90moduleinterfaces
326:       implicit none

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

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

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

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

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

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

356: !  Insert values into global vector

358:       end

360: ! ---------------------------------------------------------------------
361: !
362: !  InitialGuessLocal - Computes initial approximation, called by
363: !  the higher level routine FormInitialGuess().
364: !
365: !  Input Parameter:
366: !  x - local vector data
367: !
368: !  Output Parameters:
369: !  x - local vector data
370: !  ierr - error code
371: !
372: !  Notes:
373: !  This routine uses standard Fortran-style computations over a 2-dim array.
374: !
375:       subroutine InitialGuessLocal(user,x,ierr)
376:       use ex5f90module
377:       implicit none

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

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

389: !  Set parameters

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

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

408:       end

410: ! ---------------------------------------------------------------------
411: !
412: !  FormFunctionLocal - Computes nonlinear function, called by
413: !  the higher level routine FormFunction().
414: !
415: !  Input Parameter:
416: !  x - local vector data
417: !
418: !  Output Parameters:
419: !  f - local vector data, f(x)
420: !  ierr - error code
421: !
422: !  Notes:
423: !  This routine uses standard Fortran-style computations over a 2-dim array.
424: !
425:       subroutine FormFunctionLocal(x,f,user,ierr)
426:       use ex5f90module

428:       implicit none

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

436: !  Local variables:
437:       PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
438:       PetscScalar u,uxx,uyy
439:       PetscInt  i,j

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

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

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

464:       end

466: ! ---------------------------------------------------------------------
467: !
468: !  FormJacobian - Evaluates Jacobian matrix.
469: !
470: !  Input Parameters:
471: !  snes     - the SNES context
472: !  x        - input vector
473: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
474: !             (not used here)
475: !
476: !  Output Parameters:
477: !  jac      - Jacobian matrix
478: !  jac_prec - optionally different preconditioning matrix (not used here)
479: !  flag     - flag indicating matrix structure
480: !
481: !  Notes:
482: !  This routine serves as a wrapper for the lower-level routine
483: !  "FormJacobianLocal", where the actual computations are
484: !  done using the standard Fortran style of treating the local
485: !  vector data as a multidimensional array over the local mesh.
486: !  This routine merely accesses the local vector data via
487: !  VecGetArrayF90() and VecRestoreArrayF90().
488: !
489: !  Notes:
490: !  Due to grid point reordering with DMDAs, we must always work
491: !  with the local grid points, and then transform them to the new
492: !  global numbering with the "ltog" mapping
493: !  We cannot work directly with the global numbers for the original
494: !  uniprocessor grid!
495: !
496: !  Two methods are available for imposing this transformation
497: !  when setting matrix entries:
498: !    (A) MatSetValuesLocal(), using the local ordering (including
499: !        ghost points!)
500: !        - Set matrix entries using the local ordering
501: !          by calling MatSetValuesLocal()
502: !    (B) MatSetValues(), using the global ordering

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

513: !  Input/output variables:
514:       SNES         snes
515:       Vec          X
516:       Mat          jac,jac_prec
517:       type(userctx)  user
518:       PetscErrorCode ierr
519:       DM             da

521: !  Declarations for use with local arrays:
522:       PetscScalar,pointer :: lx_v(:)
523:       Vec            localX

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

530:       PetscCallA(SNESGetDM(snes,da,ierr))
531:       PetscCallA(DMGetLocalVector(da,localX,ierr))
532:       PetscCallA(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr))
533:       PetscCallA(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr))

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

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

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

546:       PetscCallA(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr))
547:       if (jac .ne. jac_prec) then
548:          PetscCallA(MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr))
549:       endif
550:       PetscCallA(VecRestoreArrayF90(localX,lx_v,ierr))
551:       PetscCallA(DMRestoreLocalVector(da,localX,ierr))
552:       PetscCallA(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr))
553:       if (jac .ne. jac_prec) then
554:         PetscCallA(MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr))
555:       endif

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

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

562:       end

564: ! ---------------------------------------------------------------------
565: !
566: !  FormJacobianLocal - Computes Jacobian preconditioner matrix,
567: !  called by the higher level routine FormJacobian().
568: !
569: !  Input Parameters:
570: !  x        - local vector data
571: !
572: !  Output Parameters:
573: !  jac_prec - Jacobian preconditioner matrix
574: !  ierr     - error code
575: !
576: !  Notes:
577: !  This routine uses standard Fortran-style computations over a 2-dim array.
578: !
579: !  Notes:
580: !  Due to grid point reordering with DMDAs, we must always work
581: !  with the local grid points, and then transform them to the new
582: !  global numbering with the "ltog" mapping
583: !  We cannot work directly with the global numbers for the original
584: !  uniprocessor grid!
585: !
586: !  Two methods are available for imposing this transformation
587: !  when setting matrix entries:
588: !    (A) MatSetValuesLocal(), using the local ordering (including
589: !        ghost points!)
590: !        - Set matrix entries using the local ordering
591: !          by calling MatSetValuesLocal()
592: !    (B) MatSetValues(), using the global ordering
593: !        - Then apply this map explicitly yourself
594: !        - Set matrix entries using the global ordering by calling
595: !          MatSetValues()
596: !  Option (A) seems cleaner/easier in many cases, and is the procedure
597: !  used in this example.
598: !
599:       subroutine FormJacobianLocal(x,jac_prec,user,ierr)
600:       use ex5f90module
601:       implicit none

603: !  Input/output variables:
604:       type (userctx) user
605:       PetscScalar    x(user%gxs:user%gxe,user%gys:user%gye)
606:       Mat            jac_prec
607:       PetscErrorCode ierr

609: !  Local variables:
610:       PetscInt    row,col(5),i,j
611:       PetscInt    ione,ifive
612:       PetscScalar two,one,hx,hy,hxdhy
613:       PetscScalar hydhx,sc,v(5)

615: !  Set parameters
616:       ione   = 1
617:       ifive  = 5
618:       one    = 1.0
619:       two    = 2.0
620:       hx     = one/(user%mx-1)
621:       hy     = one/(user%my-1)
622:       sc     = hx*hy
623:       hxdhy  = hx/hy
624:       hydhx  = hy/hx

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

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

664:       end

666: !
667: !/*TEST
668: !
669: !   test:
670: !      nsize: 4
671: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
672: !      requires: !single
673: !
674: !   test:
675: !      suffix: 2
676: !      nsize: 4
677: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
678: !      requires: !single
679: !
680: !   test:
681: !      suffix: 3
682: !      nsize: 3
683: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
684: !      requires: !single
685: !
686: !   test:
687: !      suffix: 4
688: !      nsize: 3
689: !      args: -snes_mf_operator -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
690: !      requires: !single
691: !
692: !   test:
693: !      suffix: 5
694: !      requires: !single
695: !
696: !TEST*/