Actual source code: ex5f.F

  1: ! "$Id: ex5f.F,v 1.80 2001/08/24 16:23:36 bsmith Exp $";
  2: !
  3: !  Description: This example solves a nonlinear system in parallel with SNES.
  4: !  We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
  5: !  domain, using distributed arrays (DAs) to partition the parallel grid.
  6: !  The command line options include:
  7: !    -par <param>, where <param> indicates the nonlinearity of the problem
  8: !       problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)
  9: !
 10: !  Program usage:  mpirun -np <procs> ex5f [-help] [all PETSc options]
 11: !
 12: !/*T
 13: !  Concepts: SNES^parallel Bratu example
 14: !  Concepts: DA^using distributed arrays;
 15: !  Processors: n
 16: !T*/
 17: !
 18: !  --------------------------------------------------------------------------
 19: !
 20: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 21: !  the partial differential equation
 22: !
 23: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
 24: !
 25: !  with boundary conditions
 26: !
 27: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
 28: !
 29: !  A finite difference approximation with the usual 5-point stencil
 30: !  is used to discretize the boundary value problem to obtain a nonlinear
 31: !  system of equations.
 32: !
 33: !  --------------------------------------------------------------------------

 35:       program main
 36:       implicit none
 37: !
 38: !  We place common blocks, variable declarations, and other include files
 39: !  needed for this code in the single file ex5f.h.  We then need to include
 40: !  only this file throughout the various routines in this program.  See
 41: !  additional comments in the file ex5f.h.
 42: !
 43: #include "ex5f.h"

 45: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 46: !                   Variable declarations
 47: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 48: !
 49: !  Variables:
 50: !     snes        - nonlinear solver
 51: !     x, r        - solution, residual vectors
 52: !     J           - Jacobian matrix
 53: !     its         - iterations for convergence
 54: !
 55: !  See additional variable declarations in the file ex5f.h
 56: !
 57:       SNES                   snes
 58:       Vec                    x,r
 59:       Mat                    J,A
 60:       integer                its,flg,ierr
 61:       double precision       lambda_max,lambda_min
 62:       ISColoring             coloring
 63:       PetscTruth             adifor_jacobian,adiformf_jacobian

 65: !  Note: Any user-defined Fortran routines (such as FormJacobianLocal)
 66: !  MUST be declared as external.

 68:       external FormInitialGuess
 69:       external FormFunctionLocal,FormJacobianLocal
 70: #if defined(PETSC_HAVE_ADIFOR)
 71:       external g_FormFunctionLocal,m_FormFunctionLocal
 72: #endif

 74: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 75: !  Initialize program
 76: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 78:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 79:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
 80:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)

 82: !  Initialize problem parameters

 84:       lambda_max = 6.81
 85:       lambda_min = 0.0
 86:       lambda     = 6.0
 87:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par',lambda,                &
 88:      &                           flg,ierr)
 89:       if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
 90:          if (rank .eq. 0) write(6,*) 'Lambda is out of range'
 91:          SETERRQ(1,' ',ierr)
 92:       endif

 94: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 95: !  Create nonlinear solver context
 96: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 98:       call SNESCreate(PETSC_COMM_WORLD,SNES_NONLINEAR_EQUATIONS,                  &
 99:      &                snes,ierr)

101: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102: !  Create vector data structures; set function evaluation routine
103: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

105: !  Create distributed array (DA) to manage parallel grid and vectors

107: ! This really needs only the star-type stencil, but we use the box
108: ! stencil temporarily.
109:       call DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,-4,          &
110:      &     -4,PETSC_DECIDE,PETSC_DECIDE,1,1,PETSC_NULL_INTEGER,                   &
111:      &     PETSC_NULL_INTEGER,da,ierr)

113: !  Extract global and local vectors from DA; then duplicate for remaining
114: !  vectors that are the same types

116:       call DACreateGlobalVector(da,x,ierr)
117:       call VecDuplicate(x,r,ierr)

119: !  Get local grid boundaries (for 2-dimensional DA)

121:       call DAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,            &
122:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
123:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
124:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
125:      &               PETSC_NULL_INTEGER,ierr)
126:       call DAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,                      &
127:      &     PETSC_NULL_INTEGER,ierr)
128:       call DAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,             &
129:      &     PETSC_NULL_INTEGER,ierr)

131: !  Here we shift the starting indices up by one so that we can easily
132: !  use the Fortran convention of 1-based indices (rather 0-based indices).

134:       xs  = xs+1
135:       ys  = ys+1
136:       gxs = gxs+1
137:       gys = gys+1

139:       ye  = ys+ym-1
140:       xe  = xs+xm-1
141:       gye = gys+gym-1
142:       gxe = gxs+gxm-1

144: !  Set function evaluation routine and vector

146:       call DASetLocalFunction(da,FormFunctionLocal,ierr)
147:       call DASetLocalJacobian(da,FormJacobianLocal,ierr)
148: #if defined(PETSC_HAVE_ADIFOR)
149:       call DASetLocalAdiforFunction(da,                                             &
150:      &         g_FormFunctionLocal,ierr)
151: #endif
152:       call SNESSetFunction(snes,r,SNESDAFormFunction,da,ierr)

154: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155: !  Create matrix data structure; set Jacobian evaluation routine
156: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

158: !  Set Jacobian matrix data structure and default Jacobian evaluation
159: !  routine. User can override with:
160: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
161: !                (unless user explicitly sets preconditioner)
162: !     -snes_mf_operator : form preconditioning matrix as set by the user,
163: !                         but use matrix-free approx for Jacobian-vector
164: !                         products within Newton-Krylov method
165: !

167:       call DAGetMatrix(da,MATMPIAIJ,J,ierr)

169: #if defined(PETSC_HAVE_ADIFOR)
170:       call PetscOptionsGetLogical(PETSC_NULL_CHARACTER                            &
171:      &     ,'-adiformf_jacobian',                                                 &
172:      &     adiformf_jacobian,PETSC_NULL_INTEGER,ierr)
173:       if (adiformf_jacobian .eq. 1) then
174:         call DASetLocalAdiforMFFunction(da,                                       &
175:      &         m_FormFunctionLocal,ierr)
176:         call MatRegisterDAAD(ierr)
177:         call MatCreateDAAD(da,A,ierr)
178:         call MatDAADSetSNES(A,snes,ierr)
179:       else
180:         A = J
181:       endif
182: #else 
183:       A = J
184: #endif

186:       call SNESSetJacobian(snes,A,J,SNESDAComputeJacobian,                        &
187:      &                       da,ierr)

189: #if defined(PETSC_HAVE_ADIFOR)
190:       call PetscOptionsGetLogical(PETSC_NULL_CHARACTER                            &
191:      &     ,'-adifor_jacobian',                                                   &
192:      &     adifor_jacobian,PETSC_NULL_INTEGER,ierr)
193:       if (adifor_jacobian .eq. 1) then
194:         call SNESSetJacobian(snes,A,J,SNESDAComputeJacobianWithAdifor,            &
195:      &                         da,ierr)
196:       endif
197: #endif


200: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201: !  Customize nonlinear solver; set runtime options
202: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

206:           call SNESSetFromOptions(snes,ierr)

208: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209: !  Evaluate initial guess; then solve nonlinear system.
210: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

217:       call FormInitialGuess(x,ierr)
218:       call SNESSolve(snes,x,its,ierr)
219:       if (rank .eq. 0) then
220:          write(6,100) its
221:       endif
222:   100 format('Number of Newton iterations = ',i5)


225: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: !  Free work space.  All PETSc objects should be destroyed when they
227: !  are no longer needed.
228: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

230:       if (A .ne. J) call MatDestroy(A,ierr)
231:       call MatDestroy(J,ierr)
232:       call VecDestroy(x,ierr)
233:       call VecDestroy(r,ierr)
234:       call SNESDestroy(snes,ierr)
235:       call DADestroy(da,ierr)
236:       call PetscFinalize(ierr)
237:       end

239: ! ---------------------------------------------------------------------
240: !
241: !  FormInitialGuess - Forms initial approximation.
242: !
243: !  Input Parameters:
244: !  X - vector
245: !
246: !  Output Parameter:
247: !  X - vector
248: !
249: !  Notes:
250: !  This routine serves as a wrapper for the lower-level routine
251: !  "ApplicationInitialGuess", where the actual computations are
252: !  done using the standard Fortran style of treating the local
253: !  vector data as a multidimensional array over the local mesh.
254: !  This routine merely handles ghost point scatters and accesses
255: !  the local vector data via VecGetArray() and VecRestoreArray().
256: !
257:       subroutine FormInitialGuess(X,ierr)
258:       implicit none

260: #include "ex5f.h"

262: !  Input/output variables:
263:       Vec      X
264:       integer  ierr

266: !  Declarations for use with local arrays:
267:       PetscScalar lx_v(0:1)
268:       PetscOffset lx_i
269:       Vec         localX

271:       0

273: !  Get a pointer to vector data.
274: !    - For default PETSc vectors, VecGetArray() returns a pointer to
275: !      the data array.  Otherwise, the routine is implementation dependent.
276: !    - You MUST call VecRestoreArray() when you no longer need access to
277: !      the array.
278: !    - Note that the Fortran interface to VecGetArray() differs from the
279: !      C version.  See the users manual for details.

281:       call DAGetLocalVector(da,localX,ierr)
282:       call VecGetArray(localX,lx_v,lx_i,ierr)

284: !  Compute initial guess over the locally owned part of the grid

286:       call InitialGuessLocal(lx_v(lx_i),ierr)

288: !  Restore vector

290:       call VecRestoreArray(localX,lx_v,lx_i,ierr)

292: !  Insert values into global vector

294:       call DALocalToGlobal(da,localX,INSERT_VALUES,X,ierr)
295:       call DARestoreLocalVector(da,localX,ierr)
296:       return
297:       end

299: ! ---------------------------------------------------------------------
300: !
301: !  InitialGuessLocal - Computes initial approximation, called by
302: !  the higher level routine FormInitialGuess().
303: !
304: !  Input Parameter:
305: !  x - local vector data
306: !
307: !  Output Parameters:
308: !  x - local vector data
309: !  ierr - error code
310: !
311: !  Notes:
312: !  This routine uses standard Fortran-style computations over a 2-dim array.
313: !
314:       subroutine InitialGuessLocal(x,ierr)
315:       implicit none

317: #include "ex5f.h"

319: !  Input/output variables:
320:       PetscScalar  x(gxs:gxe,gys:gye)
321:       integer ierr

323: !  Local variables:
324:       integer  i,j,hxdhy,hydhx
325:       PetscScalar   temp1,temp,hx,hy,sc,one

327: !  Set parameters

329:       ierr   = 0
330:       one    = 1.0
331:       hx     = one/(dble(mx-1))
332:       hy     = one/(dble(my-1))
333:       sc     = hx*hy*lambda
334:       hxdhy  = hx/hy
335:       hydhx  = hy/hx
336:       temp1  = lambda/(lambda + one)

338:       do 20 j=ys,ye
339:          temp = dble(min(j-1,my-j))*hy
340:          do 10 i=xs,xe
341:             if (i .eq. 1 .or. j .eq. 1                                  &
342:      &             .or. i .eq. mx .or. j .eq. my) then
343:               x(i,j) = 0.0
344:             else
345:               x(i,j) = temp1 *                                          &
346:      &          sqrt(min(dble(min(i-1,mx-i)*hx),dble(temp)))
347:             endif
348:  10      continue
349:  20   continue

351:       return
352:       end

354: ! ---------------------------------------------------------------------
355: !
356: !  FormFunctionLocal - Computes nonlinear function, called by
357: !  the higher level routine FormFunction().
358: !
359: !  Input Parameter:
360: !  x - local vector data
361: !
362: !  Output Parameters:
363: !  f - local vector data, f(x)
364: !  ierr - error code
365: !
366: !  Notes:
367: !  This routine uses standard Fortran-style computations over a 2-dim array.
368: !
369: !     Process adifor: FormFunctionLocal
370: !
371:       subroutine FormFunctionLocal(info,x,f,dummy,ierr)

373:       implicit none

375: #include "ex5f.h"

377: !  Input/output variables:
378:       DALocalInfo info(DA_LOCAL_INFO_SIZE)
379:       PetscScalar x(gxs:gxe,gys:gye)
380:       PetscScalar f(xs:xe,ys:ye)
381:       integer     ierr
382:       PetscObject dummy

384: !  Local variables:
385:       PetscScalar   two,one,hx,hy,hxdhy,hydhx,sc
386:       PetscScalar   u,uxx,uyy
387:       integer  i,j


390:       xs     = info(DA_LOCAL_INFO_XS)+1
391:       xe     = xs+info(DA_LOCAL_INFO_XM)-1
392:       ys     = info(DA_LOCAL_INFO_YS)+1
393:       ye     = ys+info(DA_LOCAL_INFO_YM)-1
394:       mx     = info(DA_LOCAL_INFO_MX)
395:       my     = info(DA_LOCAL_INFO_MY)

397:       one    = 1.0
398:       two    = 2.0
399:       hx     = one/dble(mx-1)
400:       hy     = one/dble(my-1)
401:       sc     = hx*hy*lambda
402:       hxdhy  = hx/hy
403:       hydhx  = hy/hx

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

407:       do 20 j=ys,ye
408:          do 10 i=xs,xe
409:             if (i .eq. 1 .or. j .eq. 1                                  &
410:      &             .or. i .eq. mx .or. j .eq. my) then
411:                f(i,j) = x(i,j)
412:             else
413:                u = x(i,j)
414:                uxx = hydhx * (two*u                                     &
415:      &                - x(i-1,j) - x(i+1,j))
416:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
417:                f(i,j) = uxx + uyy - sc*exp(u)
418:             endif
419:  10      continue
420:  20   continue

422:       call PetscLogFlops(11*ym*xm,ierr)

424:       return
425:       end

427: ! ---------------------------------------------------------------------
428: !
429: !  FormJacobianLocal - Computes Jacobian matrix, called by
430: !  the higher level routine FormJacobian().
431: !
432: !  Input Parameters:
433: !  x        - local vector data
434: !
435: !  Output Parameters:
436: !  jac      - Jacobian matrix
437: !  jac_prec - optionally different preconditioning matrix (not used here)
438: !  ierr     - error code
439: !
440: !  Notes:
441: !  This routine uses standard Fortran-style computations over a 2-dim array.
442: !
443: !  Notes:
444: !  Due to grid point reordering with DAs, we must always work
445: !  with the local grid points, and then transform them to the new
446: !  global numbering with the "ltog" mapping (via DAGetGlobalIndices()).
447: !  We cannot work directly with the global numbers for the original
448: !  uniprocessor grid!
449: !
450: !  Two methods are available for imposing this transformation
451: !  when setting matrix entries:
452: !    (A) MatSetValuesLocal(), using the local ordering (including
453: !        ghost points!)
454: !        - Use DAGetGlobalIndices() to extract the local-to-global map
455: !        - Associate this map with the matrix by calling
456: !          MatSetLocalToGlobalMapping() once
457: !        - Set matrix entries using the local ordering
458: !          by calling MatSetValuesLocal()
459: !    (B) MatSetValues(), using the global ordering
460: !        - Use DAGetGlobalIndices() to extract the local-to-global map
461: !        - Then apply this map explicitly yourself
462: !        - Set matrix entries using the global ordering by calling
463: !          MatSetValues()
464: !  Option (A) seems cleaner/easier in many cases, and is the procedure
465: !  used in this example.
466: !
467:       subroutine FormJacobianLocal(info,x,jac,ctx,ierr)
468:       implicit none

470: #include "ex5f.h"

472: !  Input/output variables:
473:       PetscScalar x(gxs:gxe,gys:gye)
474:       Mat         jac
475:       integer     ierr,ctx
476:       DALocalInfo info(DA_LOCAL_INFO_SIZE)
477: 

479: !  Local variables:
480:       integer  row,col(5),i,j
481:       PetscScalar   two,one,hx,hy,hxdhy,hydhx,sc,v(5)

483: !  Set parameters

485:       one    = 1.0
486:       two    = 2.0
487:       hx     = one/dble(mx-1)
488:       hy     = one/dble(my-1)
489:       sc     = hx*hy
490:       hxdhy  = hx/hy
491:       hydhx  = hy/hx

493: !  Compute entries for the locally owned part of the Jacobian.
494: !   - Currently, all PETSc parallel matrix formats are partitioned by
495: !     contiguous chunks of rows across the processors.
496: !   - Each processor needs to insert only elements that it owns
497: !     locally (but any non-local elements will be sent to the
498: !     appropriate processor during matrix assembly).
499: !   - Here, we set all entries for a particular row at once.
500: !   - We can set matrix entries either using either
501: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
502: !   - Note that MatSetValues() uses 0-based row and column numbers
503: !     in Fortran as well as in C.

505:       do 20 j=ys,ye
506:          row = (j - gys)*gxm + xs - gxs - 1
507:          do 10 i=xs,xe
508:             row = row + 1
509: !           boundary points
510:             if (i .eq. 1 .or. j .eq. 1                                  &
511:      &             .or. i .eq. mx .or. j .eq. my) then
512:                call MatSetValuesLocal(jac,1,row,1,row,one,              &
513:      &                           INSERT_VALUES,ierr)
514: !           interior grid points
515:             else
516:                v(1) = -hxdhy
517:                v(2) = -hydhx
518:                v(3) = two*(hydhx + hxdhy)                               &
519:      &                  - sc*lambda*exp(x(i,j))
520:                v(4) = -hydhx
521:                v(5) = -hxdhy
522:                col(1) = row - gxm
523:                col(2) = row - 1
524:                col(3) = row
525:                col(4) = row + 1
526:                col(5) = row + gxm
527:                call MatSetValuesLocal(jac,1,row,5,col,v,                &
528:      &                                INSERT_VALUES,ierr)
529:             endif
530:  10      continue
531:  20   continue
532:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
533:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
534:       return
535:       end