Actual source code: ex5f.F90

petsc-master 2020-02-25
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```  1: !
2: !  Description: This example 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 <param>, where <param> indicates the nonlinearity of the problem
7: !       problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)
8: !
9: !
10: !!/*T
11: !  Concepts: SNES^parallel Bratu example
12: !  Concepts: DMDA^using distributed arrays;
13: !  Processors: n
14: !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:  #include <petsc/finclude/petscsnes.h>
37:       use petscdmda
38:       use petscsnes
39:       implicit none
40: !
41: !  We place common blocks, variable declarations, and other include files
42: !  needed for this code in the single file ex5f.h.  We then need to include
43: !  only this file throughout the various routines in this program.  See
45: !
46: #include "ex5f.h"

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

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

70:       external FormInitialGuess
71:       external FormFunctionLocal,FormJacobianLocal
72:       external MySNESConverged

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

78:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
79:       if (ierr .ne. 0) then
80:         print*,'Unable to initialize PETSc'
81:         stop
82:       endif
83:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
84:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)

86: !  Initialize problem parameters

88:       i1 = 1
89:       i4 = 4
90:       lambda_max = 6.81
91:       lambda_min = 0.0
92:       lambda     = 6.0
93:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,PETSC_NULL_BOOL,ierr)
94: ! this statement is split into multiple-lines to keep lines under 132 char limit - required by 'make check'
95:       if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
96:         PETSC_ERR_ARG_OUTOFRANGE; SETERRA(PETSC_COMM_WORLD,ierr,'Lambda')
97:       endif

99: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100: !  Create nonlinear solver context
101: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

103:       call SNESCreate(PETSC_COMM_WORLD,snes,ierr)

105: !  Set convergence test routine if desired

107:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)
108:       if (flg) then
109:         call SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,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
119: ! stencil temporarily.
120:       call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,      &
121:      &     DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE,i1,i1,                &
122:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
123:       call DMSetFromOptions(da,ierr)
124:       call DMSetUp(da,ierr)

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

129:       call DMCreateGlobalVector(da,x,ierr)
130:       call VecDuplicate(x,r,ierr)

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

134:       call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,            &
135:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
136:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
137:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
138:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
139:      &               PETSC_NULL_INTEGER,ierr)
140:       call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)
141:       call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)

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

146:       xs  = xs+1
147:       ys  = ys+1
148:       gxs = gxs+1
149:       gys = gys+1

151:       ye  = ys+ym-1
152:       xe  = xs+xm-1
153:       gye = gys+gym-1
154:       gxe = gxs+gxm-1

156: !  Set function evaluation routine and vector

158:       call DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)
159:       call DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)
160:       call SNESSetDM(snes,da,ierr)

162: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: !  Customize nonlinear solver; set runtime options
164: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

168:           call SNESSetFromOptions(snes,ierr)
169: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: !  Evaluate initial guess; then solve nonlinear system.
171: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

178:       call FormInitialGuess(x,ierr)
179:       call SNESSolve(snes,PETSC_NULL_VEC,x,ierr)
180:       call SNESGetIterationNumber(snes,its,ierr)
181:       if (rank .eq. 0) then
182:          write(6,100) its
183:       endif
184:   100 format('Number of SNES iterations = ',i5)

187: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: !  Free work space.  All PETSc objects should be destroyed when they
189: !  are no longer needed.
190: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

192:       call VecDestroy(x,ierr)
193:       call VecDestroy(r,ierr)
194:       call SNESDestroy(snes,ierr)
195:       call DMDestroy(da,ierr)
196:       call PetscFinalize(ierr)
197:       end

199: ! ---------------------------------------------------------------------
200: !
201: !  FormInitialGuess - Forms initial approximation.
202: !
203: !  Input Parameters:
204: !  X - vector
205: !
206: !  Output Parameter:
207: !  X - vector
208: !
209: !  Notes:
210: !  This routine serves as a wrapper for the lower-level routine
211: !  "ApplicationInitialGuess", where the actual computations are
212: !  done using the standard Fortran style of treating the local
213: !  vector data as a multidimensional array over the local mesh.
214: !  This routine merely handles ghost point scatters and accesses
215: !  the local vector data via VecGetArray() and VecRestoreArray().
216: !
217:       subroutine FormInitialGuess(X,ierr)
218:       use petscsnes
219:       implicit none

221: #include "ex5f.h"

223: !  Input/output variables:
224:       Vec      X
225:       PetscErrorCode  ierr

227: !  Declarations for use with local arrays:
228:       PetscScalar lx_v(0:1)
229:       PetscOffset lx_i

231:       0

233: !  Get a pointer to vector data.
234: !    - For default PETSc vectors, VecGetArray() returns a pointer to
235: !      the data array.  Otherwise, the routine is implementation dependent.
236: !    - You MUST call VecRestoreArray() when you no longer need access to
237: !      the array.
238: !    - Note that the Fortran interface to VecGetArray() differs from the
239: !      C version.  See the users manual for details.

241:       call VecGetArray(X,lx_v,lx_i,ierr)

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

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

247: !  Restore vector

249:       call VecRestoreArray(X,lx_v,lx_i,ierr)

251:       return
252:       end

254: ! ---------------------------------------------------------------------
255: !
256: !  InitialGuessLocal - Computes initial approximation, called by
257: !  the higher level routine FormInitialGuess().
258: !
259: !  Input Parameter:
260: !  x - local vector data
261: !
262: !  Output Parameters:
263: !  x - local vector data
264: !  ierr - error code
265: !
266: !  Notes:
267: !  This routine uses standard Fortran-style computations over a 2-dim array.
268: !
269:       subroutine InitialGuessLocal(x,ierr)
270:       use petscsnes
271:       implicit none

273: #include "ex5f.h"

275: !  Input/output variables:
276:       PetscScalar    x(xs:xe,ys:ye)
277:       PetscErrorCode ierr

279: !  Local variables:
280:       PetscInt  i,j
281:       PetscReal temp1,temp,one,hx,hy

283: !  Set parameters

285:       0
286:       one    = 1.0
287:       hx     = one/((mx-1))
288:       hy     = one/((my-1))
289:       temp1  = lambda/(lambda + one)

291:       do 20 j=ys,ye
292:          temp = (min(j-1,my-j))*hy
293:          do 10 i=xs,xe
294:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
295:               x(i,j) = 0.0
296:             else
297:               x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,(temp)))
298:             endif
299:  10      continue
300:  20   continue

302:       return
303:       end

305: ! ---------------------------------------------------------------------
306: !
307: !  FormFunctionLocal - Computes nonlinear function, called by
308: !  the higher level routine FormFunction().
309: !
310: !  Input Parameter:
311: !  x - local vector data
312: !
313: !  Output Parameters:
314: !  f - local vector data, f(x)
315: !  ierr - error code
316: !
317: !  Notes:
318: !  This routine uses standard Fortran-style computations over a 2-dim array.
319: !
320: !
321:       subroutine FormFunctionLocal(info,x,f,da,ierr)
322:  #include <petsc/finclude/petscdmda.h>
323:       use petscsnes
324:       implicit none

326: #include "ex5f.h"
327:       DM da

329: !  Input/output variables:
330:       DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
331:       PetscScalar x(gxs:gxe,gys:gye)
332:       PetscScalar f(xs:xe,ys:ye)
333:       PetscErrorCode     ierr

335: !  Local variables:
336:       PetscScalar two,one,hx,hy
337:       PetscScalar hxdhy,hydhx,sc
338:       PetscScalar u,uxx,uyy
339:       PetscInt  i,j

341:       xs     = info(DMDA_LOCAL_INFO_XS)+1
342:       xe     = xs+info(DMDA_LOCAL_INFO_XM)-1
343:       ys     = info(DMDA_LOCAL_INFO_YS)+1
344:       ye     = ys+info(DMDA_LOCAL_INFO_YM)-1
345:       mx     = info(DMDA_LOCAL_INFO_MX)
346:       my     = info(DMDA_LOCAL_INFO_MY)

348:       one    = 1.0
349:       two    = 2.0
350:       hx     = one/(mx-1)
351:       hy     = one/(my-1)
352:       sc     = hx*hy*lambda
353:       hxdhy  = hx/hy
354:       hydhx  = hy/hx

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

358:       do 20 j=ys,ye
359:          do 10 i=xs,xe
360:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
361:                f(i,j) = x(i,j)
362:             else
363:                u = x(i,j)
364:                uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
365:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
366:                f(i,j) = uxx + uyy - sc*exp(u)
367:             endif
368:  10      continue
369:  20   continue

371:       call PetscLogFlops(11.0d0*ym*xm,ierr)

373:       return
374:       end

376: ! ---------------------------------------------------------------------
377: !
378: !  FormJacobianLocal - Computes Jacobian matrix, called by
379: !  the higher level routine FormJacobian().
380: !
381: !  Input Parameters:
382: !  x        - local vector data
383: !
384: !  Output Parameters:
385: !  jac      - Jacobian matrix
386: !  jac_prec - optionally different preconditioning matrix (not used here)
387: !  ierr     - error code
388: !
389: !  Notes:
390: !  This routine uses standard Fortran-style computations over a 2-dim array.
391: !
392: !  Notes:
393: !  Due to grid point reordering with DMDAs, we must always work
394: !  with the local grid points, and then transform them to the new
395: !  global numbering with the "ltog" mapping
396: !  We cannot work directly with the global numbers for the original
397: !  uniprocessor grid!
398: !
399: !  Two methods are available for imposing this transformation
400: !  when setting matrix entries:
401: !    (A) MatSetValuesLocal(), using the local ordering (including
402: !        ghost points!)
403: !          by calling MatSetValuesLocal()
404: !    (B) MatSetValues(), using the global ordering
405: !        - Use DMDAGetGlobalIndices() to extract the local-to-global map
406: !        - Then apply this map explicitly yourself
407: !        - Set matrix entries using the global ordering by calling
408: !          MatSetValues()
409: !  Option (A) seems cleaner/easier in many cases, and is the procedure
410: !  used in this example.
411: !
412:       subroutine FormJacobianLocal(info,x,A,jac,da,ierr)
413:       use petscsnes
414:       implicit none

416: #include "ex5f.h"
417:       DM da
418:
419: !  Input/output variables:
420:       PetscScalar x(gxs:gxe,gys:gye)
421:       Mat         A,jac
422:       PetscErrorCode  ierr
423:       DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)

426: !  Local variables:
427:       PetscInt  row,col(5),i,j,i1,i5
428:       PetscScalar two,one,hx,hy,v(5)
429:       PetscScalar hxdhy,hydhx,sc

431: !  Set parameters

433:       i1     = 1
434:       i5     = 5
435:       one    = 1.0
436:       two    = 2.0
437:       hx     = one/(mx-1)
438:       hy     = one/(my-1)
439:       sc     = hx*hy
440:       hxdhy  = hx/hy
441:       hydhx  = hy/hx

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

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

490: !
491: !     Simple convergence test based on the infinity norm of the residual being small
492: !
493:       subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr)
494:       use petscsnes
495:       implicit none

497:       SNES snes
498:       PetscInt it,dummy
499:       PetscReal xnorm,snorm,fnorm,nrm
500:       SNESConvergedReason reason
501:       Vec f
502:       PetscErrorCode ierr

504:       call SNESGetFunction(snes,f,PETSC_NULL_FUNCTION,dummy,ierr)
505:       call VecNorm(f,NORM_INFINITY,nrm,ierr)
506:       if (nrm .le. 1.e-5) reason = SNES_CONVERGED_FNORM_ABS

508:       end

510: !/*TEST
511: !
512: !   build:
513: !      requires: !complex !single
514: !
515: !   test:
516: !      nsize: 4
517: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
518: !
519: !   test:
520: !      suffix: 2
521: !      nsize: 4
522: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
523: !
524: !   test:
525: !      suffix: 3
526: !      nsize: 3
527: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
528: !
529: !   test:
530: !      suffix: 6
531: !      nsize: 1
532: !      args: -snes_monitor_short -my_snes_convergence
533: !
534: !TEST*/
```