Actual source code: ex5f.F90

  1: !
  2: !  This example shows how to avoid Fortran line lengths larger than 132 characters.
  3: !  We recommend starting from src/snes/tutorials/ex5f90.F90 instead of this example
  4: !
  5: !  Description: This example solves a nonlinear system in parallel with SNES.
  6: !  We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
  7: !  domain, using distributed arrays (DMDAs) to partition the parallel grid.
  8: !  The command line options include:
  9: !    -par <param>, where <param> indicates the nonlinearity of the problem
 10: !       problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)
 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: !  --------------------------------------------------------------------------
 28:       module ex5fmodule
 29:       use petscsnes
 30:       use petscdmda
 31: #include <petsc/finclude/petscsnes.h>
 32: #include <petsc/finclude/petscdm.h>
 33: #include <petsc/finclude/petscdmda.h>
 34:       PetscInt xs,xe,xm,gxs,gxe,gxm
 35:       PetscInt ys,ye,ym,gys,gye,gym
 36:       PetscInt mx,my
 37:       PetscMPIInt rank,size
 38:       PetscReal lambda
 39:       end module ex5fmodule

 41:       program main
 42:       use ex5fmodule
 43:       implicit none

 45: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 46: !                   Variable declarations
 47: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 48: !
 49: !  Variables:
 50: !     snes        - nonlinear solver
 51: !     x, r        - solution, residual vectors
 52: !     its         - iterations for convergence
 53: !
 54: !  See additional variable declarations in the file ex5f.h
 55: !
 56:       SNES           snes
 57:       Vec            x,r
 58:       PetscInt       its,i1,i4
 59:       PetscErrorCode ierr
 60:       PetscReal      lambda_max,lambda_min
 61:       PetscBool      flg
 62:       DM             da

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

 67:       external FormInitialGuess
 68:       external FormFunctionLocal,FormJacobianLocal
 69:       external MySNESConverged

 71: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 72: !  Initialize program
 73: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 75:       call PetscInitialize(ierr)
 76:       CHKERRA(ierr)
 77:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
 78:       CHKERRMPIA(ierr)
 79:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
 80:       CHKERRMPIA(ierr)
 81: !  Initialize problem parameters

 83:       i1 = 1
 84:       i4 = 4
 85:       lambda_max = 6.81
 86:       lambda_min = 0.0
 87:       lambda     = 6.0
 88:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,PETSC_NULL_BOOL,ierr)
 89:       CHKERRA(ierr)

 91: ! this statement is split into multiple-lines to keep lines under 132 char limit - required by 'make check'
 92:       if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
 93:         ierr = PETSC_ERR_ARG_OUTOFRANGE; SETERRA(PETSC_COMM_WORLD,ierr,'Lambda')
 94:       endif

 96: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 97: !  Create nonlinear solver context
 98: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

100:       call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
101:       CHKERRA(ierr)

103: !  Set convergence test routine if desired

105:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)
106:       CHKERRA(ierr)
107:       if (flg) then
108:         call SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,ierr)
109:         CHKERRA(ierr)
110:       endif

112: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113: !  Create vector data structures; set function evaluation routine
114: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

118: !     This really needs only the star-type stencil, but we use the box stencil

120:       call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE, &
121:                         i1,i1, PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
122:       CHKERRA(ierr)
123:       call DMSetFromOptions(da,ierr)
124:       CHKERRA(ierr)
125:       call DMSetUp(da,ierr)
126:       CHKERRA(ierr)

128: !  Extract global and local vectors from DMDA; then duplicate for remaining
129: !  vectors that are the same types

131:       call DMCreateGlobalVector(da,x,ierr)
132:       CHKERRA(ierr)
133:       call VecDuplicate(x,r,ierr)
134:       CHKERRA(ierr)

136: !  Get local grid boundaries (for 2-dimensional DMDA)

138:       call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
139:                        PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
140:                        PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
141:       CHKERRA(ierr)
142:       call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)
143:       CHKERRA(ierr)
144:       call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)
145:       CHKERRA(ierr)

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

150:       xs  = xs+1
151:       ys  = ys+1
152:       gxs = gxs+1
153:       gys = gys+1

155:       ye  = ys+ym-1
156:       xe  = xs+xm-1
157:       gye = gys+gym-1
158:       gxe = gxs+gxm-1

160: !  Set function evaluation routine and vector

162:       call DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)
163:       CHKERRA(ierr)
164:       call DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)
165:       CHKERRA(ierr)
166:       call SNESSetDM(snes,da,ierr)
167:       CHKERRA(ierr)

169: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: !  Customize nonlinear solver; set runtime options
171: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

175:       call SNESSetFromOptions(snes,ierr)
176:       CHKERRA(ierr)
177: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: !  Evaluate initial guess; then solve nonlinear system.
179: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

186:       call FormInitialGuess(x,ierr)
187:       CHKERRA(ierr)
188:       call SNESSolve(snes,PETSC_NULL_VEC,x,ierr)
189:       CHKERRA(ierr)
190:       call SNESGetIterationNumber(snes,its,ierr)
191:       CHKERRA(ierr)
192:       if (rank .eq. 0) then
193:          write(6,100) its
194:       endif
195:   100 format('Number of SNES iterations = ',i5)

197: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198: !  Free work space.  All PETSc objects should be destroyed when they
199: !  are no longer needed.
200: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

202:       call VecDestroy(x,ierr)
203:       CHKERRA(ierr)
204:       call VecDestroy(r,ierr)
205:       CHKERRA(ierr)
206:       call SNESDestroy(snes,ierr)
207:       CHKERRA(ierr)
208:       call DMDestroy(da,ierr)
209:       CHKERRA(ierr)
210:       call PetscFinalize(ierr)
211:       CHKERRA(ierr)
212:       end

214: ! ---------------------------------------------------------------------
215: !
216: !  FormInitialGuess - Forms initial approximation.
217: !
218: !  Input Parameters:
219: !  X - vector
220: !
221: !  Output Parameter:
222: !  X - vector
223: !
224: !  Notes:
225: !  This routine serves as a wrapper for the lower-level routine
226: !  "ApplicationInitialGuess", where the actual computations are
227: !  done using the standard Fortran style of treating the local
228: !  vector data as a multidimensional array over the local mesh.
229: !  This routine merely handles ghost point scatters and accesses
230: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
231: !
232:       subroutine FormInitialGuess(X,ierr)
233:       use ex5fmodule
234:       implicit none

236: !  Input/output variables:
237:       Vec      X
238:       PetscErrorCode  ierr
239: !  Declarations for use with local arrays:
240:       PetscScalar, pointer :: lx_v(:)

242:       ierr = 0

244: !  Get a pointer to vector data.
245: !    - For default PETSc vectors, VecGetArray() returns a pointer to
246: !      the data array.  Otherwise, the routine is implementation dependent.
247: !    - You MUST call VecRestoreArray() when you no longer need access to
248: !      the array.
249: !    - Note that the Fortran interface to VecGetArray() differs from the
250: !      C version.  See the users manual for details.

252:       call VecGetArrayF90(X,lx_v,ierr)
253:       CHKERRQ(ierr)

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

257:       call InitialGuessLocal(lx_v,ierr)
258:       CHKERRQ(ierr)

260: !  Restore vector

262:       call VecRestoreArrayF90(X,lx_v,ierr)
263:       CHKERRQ(ierr)

265:       return
266:       end

268: ! ---------------------------------------------------------------------
269: !
270: !  InitialGuessLocal - Computes initial approximation, called by
271: !  the higher level routine FormInitialGuess().
272: !
273: !  Input Parameter:
274: !  x - local vector data
275: !
276: !  Output Parameters:
277: !  x - local vector data
278: !  ierr - error code
279: !
280: !  Notes:
281: !  This routine uses standard Fortran-style computations over a 2-dim array.
282: !
283:       subroutine InitialGuessLocal(x,ierr)
284:       use ex5fmodule
285:       implicit none

287: !  Input/output variables:
288:       PetscScalar    x(xs:xe,ys:ye)
289:       PetscErrorCode ierr

291: !  Local variables:
292:       PetscInt  i,j
293:       PetscReal temp1,temp,one,hx,hy

295: !  Set parameters

297:       ierr   = 0
298:       one    = 1.0
299:       hx     = one/((mx-1))
300:       hy     = one/((my-1))
301:       temp1  = lambda/(lambda + one)

303:       do 20 j=ys,ye
304:          temp = (min(j-1,my-j))*hy
305:          do 10 i=xs,xe
306:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
307:               x(i,j) = 0.0
308:             else
309:               x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,(temp)))
310:             endif
311:  10      continue
312:  20   continue

314:       return
315:       end

317: ! ---------------------------------------------------------------------
318: !
319: !  FormFunctionLocal - Computes nonlinear function, called by
320: !  the higher level routine FormFunction().
321: !
322: !  Input Parameter:
323: !  x - local vector data
324: !
325: !  Output Parameters:
326: !  f - local vector data, f(x)
327: !  ierr - error code
328: !
329: !  Notes:
330: !  This routine uses standard Fortran-style computations over a 2-dim array.
331: !
332: !
333:       subroutine FormFunctionLocal(info,x,f,da,ierr)
334:       use ex5fmodule
335:       implicit none

337:       DM da

339: !  Input/output variables:
340:       DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
341:       PetscScalar x(gxs:gxe,gys:gye)
342:       PetscScalar f(xs:xe,ys:ye)
343:       PetscErrorCode     ierr

345: !  Local variables:
346:       PetscScalar two,one,hx,hy
347:       PetscScalar hxdhy,hydhx,sc
348:       PetscScalar u,uxx,uyy
349:       PetscInt  i,j

351:       xs     = info(DMDA_LOCAL_INFO_XS)+1
352:       xe     = xs+info(DMDA_LOCAL_INFO_XM)-1
353:       ys     = info(DMDA_LOCAL_INFO_YS)+1
354:       ye     = ys+info(DMDA_LOCAL_INFO_YM)-1
355:       mx     = info(DMDA_LOCAL_INFO_MX)
356:       my     = info(DMDA_LOCAL_INFO_MY)

358:       one    = 1.0
359:       two    = 2.0
360:       hx     = one/(mx-1)
361:       hy     = one/(my-1)
362:       sc     = hx*hy*lambda
363:       hxdhy  = hx/hy
364:       hydhx  = hy/hx

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

368:       do 20 j=ys,ye
369:          do 10 i=xs,xe
370:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
371:                f(i,j) = x(i,j)
372:             else
373:                u = x(i,j)
374:                uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
375:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
376:                f(i,j) = uxx + uyy - sc*exp(u)
377:             endif
378:  10      continue
379:  20   continue

381:       call PetscLogFlops(11.0d0*ym*xm,ierr)
382:       CHKERRQ(ierr)

384:       return
385:       end

387: ! ---------------------------------------------------------------------
388: !
389: !  FormJacobianLocal - Computes Jacobian matrix, called by
390: !  the higher level routine FormJacobian().
391: !
392: !  Input Parameters:
393: !  x        - local vector data
394: !
395: !  Output Parameters:
396: !  jac      - Jacobian matrix
397: !  jac_prec - optionally different preconditioning matrix (not used here)
398: !  ierr     - error code
399: !
400: !  Notes:
401: !  This routine uses standard Fortran-style computations over a 2-dim array.
402: !
403: !  Notes:
404: !  Due to grid point reordering with DMDAs, we must always work
405: !  with the local grid points, and then transform them to the new
406: !  global numbering with the "ltog" mapping
407: !  We cannot work directly with the global numbers for the original
408: !  uniprocessor grid!
409: !
410: !  Two methods are available for imposing this transformation
411: !  when setting matrix entries:
412: !    (A) MatSetValuesLocal(), using the local ordering (including
413: !        ghost points!)
414: !          by calling MatSetValuesLocal()
415: !    (B) MatSetValues(), using the global ordering
416: !        - Use DMDAGetGlobalIndices() to extract the local-to-global map
417: !        - Then apply this map explicitly yourself
418: !        - Set matrix entries using the global ordering by calling
419: !          MatSetValues()
420: !  Option (A) seems cleaner/easier in many cases, and is the procedure
421: !  used in this example.
422: !
423:       subroutine FormJacobianLocal(info,x,A,jac,da,ierr)
424:       use ex5fmodule
425:       implicit none

427:       DM da

429: !  Input/output variables:
430:       PetscScalar x(gxs:gxe,gys:gye)
431:       Mat         A,jac
432:       PetscErrorCode  ierr
433:       DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)

435: !  Local variables:
436:       PetscInt  row,col(5),i,j,i1,i5
437:       PetscScalar two,one,hx,hy,v(5)
438:       PetscScalar hxdhy,hydhx,sc

440: !  Set parameters

442:       i1     = 1
443:       i5     = 5
444:       one    = 1.0
445:       two    = 2.0
446:       hx     = one/(mx-1)
447:       hy     = one/(my-1)
448:       sc     = hx*hy
449:       hxdhy  = hx/hy
450:       hydhx  = hy/hx

452: !  Compute entries for the locally owned part of the Jacobian.
453: !   - Currently, all PETSc parallel matrix formats are partitioned by
454: !     contiguous chunks of rows across the processors.
455: !   - Each processor needs to insert only elements that it owns
456: !     locally (but any non-local elements will be sent to the
457: !     appropriate processor during matrix assembly).
458: !   - Here, we set all entries for a particular row at once.
459: !   - We can set matrix entries either using either
460: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
461: !   - Note that MatSetValues() uses 0-based row and column numbers
462: !     in Fortran as well as in C.

464:       do 20 j=ys,ye
465:          row = (j - gys)*gxm + xs - gxs - 1
466:          do 10 i=xs,xe
467:             row = row + 1
468: !           boundary points
469:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
470: !       Some f90 compilers need 4th arg to be of same type in both calls
471:                col(1) = row
472:                v(1)   = one
473:                call MatSetValuesLocal(jac,i1,row,i1,col,v,INSERT_VALUES,ierr)
474:                CHKERRQ(ierr)
475: !           interior grid points
476:             else
477:                v(1) = -hxdhy
478:                v(2) = -hydhx
479:                v(3) = two*(hydhx + hxdhy) - sc*lambda*exp(x(i,j))
480:                v(4) = -hydhx
481:                v(5) = -hxdhy
482:                col(1) = row - gxm
483:                col(2) = row - 1
484:                col(3) = row
485:                col(4) = row + 1
486:                col(5) = row + gxm
487:                call MatSetValuesLocal(jac,i1,row,i5,col,v, INSERT_VALUES,ierr)
488:                CHKERRQ(ierr)
489:             endif
490:  10      continue
491:  20   continue
492:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
493:       CHKERRQ(ierr)
494:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
495:       CHKERRQ(ierr)
496:       if (A .ne. jac) then
497:          call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
498:          CHKERRQ(ierr)
499:          call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
500:          CHKERRQ(ierr)
501:       endif
502:       return
503:       end

505: !
506: !     Simple convergence test based on the infinity norm of the residual being small
507: !
508:       subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr)
509:       use ex5fmodule
510:       implicit none

512:       SNES snes
513:       PetscInt it,dummy
514:       PetscReal xnorm,snorm,fnorm,nrm
515:       SNESConvergedReason reason
516:       Vec f
517:       PetscErrorCode ierr

519:       call SNESGetFunction(snes,f,PETSC_NULL_FUNCTION,dummy,ierr)
520:       CHKERRQ(ierr)
521:       call VecNorm(f,NORM_INFINITY,nrm,ierr)
522:       CHKERRQ(ierr)
523:       if (nrm .le. 1.e-5) reason = SNES_CONVERGED_FNORM_ABS

525:       end

527: !/*TEST
528: !
529: !   build:
530: !      requires: !complex !single
531: !
532: !   test:
533: !      nsize: 4
534: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short \
535: !            -ksp_gmres_cgs_refinement_type refine_always
536: !
537: !   test:
538: !      suffix: 2
539: !      nsize: 4
540: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
541: !
542: !   test:
543: !      suffix: 3
544: !      nsize: 3
545: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
546: !
547: !   test:
548: !      suffix: 6
549: !      nsize: 1
550: !      args: -snes_monitor_short -my_snes_convergence
551: !
552: !TEST*/