Actual source code: plate2f.F

petsc-master 2016-08-23
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  1: !  Program usage: mpiexec -n <proc> plate2f [all TAO options]
  2: !
  3: !  This example demonstrates use of the TAO package to solve a bound constrained
  4: !  minimization problem.  This example is based on a problem from the
  5: !  MINPACK-2 test suite.  Given a rectangular 2-D domain and boundary values
  6: !  along the edges of the domain, the objective is to find the surface
  7: !  with the minimal area that satisfies the boundary conditions.
  8: !  The command line options are:
  9: !    -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction
 10: !    -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction
 11: !    -bmx <bxg>, where <bxg> = number of grid points under plate in 1st direction
 12: !    -bmy <byg>, where <byg> = number of grid points under plate in 2nd direction
 13: !    -bheight <ht>, where <ht> = height of the plate
 14: !
 15: !/*T
 16: !   Concepts: TAO^Solving a bound constrained minimization problem
 17: !   Routines: TaoCreate();
 18: !   Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
 19: !   Routines: TaoSetHessianRoutine();
 20: !   Routines: TaoSetVariableBoundsRoutine();
 21: !   Routines: TaoSetInitialVector();
 22: !   Routines: TaoSetFromOptions();
 23: !   Routines: TaoSolve();
 24: !   Routines: TaoDestroy();
 25: !   Processors: n
 26: !T*/



 30:       implicit none

 32: #include "plate2f.h"

 34: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 35: !                   Variable declarations
 36: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 37: !
 38: !  Variables:
 39: !    (common from plate2f.h):
 40: !    Nx, Ny           number of processors in x- and y- directions
 41: !    mx, my           number of grid points in x,y directions
 42: !    N    global dimension of vector

 44:       PetscErrorCode   ierr          ! used to check for functions returning nonzeros
 45:       Vec              x             ! solution vector
 46:       PetscInt         m             ! number of local elements in vector
 47:       Tao              tao           ! Tao solver context
 48:       Mat              H             ! Hessian matrix
 49:       ISLocalToGlobalMapping isltog  ! local to global mapping object
 50:       PetscBool        flg
 51:       PetscInt         i1,i3,i7


 54:       external FormFunctionGradient
 55:       external FormHessian
 56:       external MSA_BoundaryConditions
 57:       external MSA_Plate
 58:       external MSA_InitialPoint
 59: ! Initialize Tao

 61:       i1=1
 62:       i3=3
 63:       i7=7


 66:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)

 68: ! Specify default dimensions of the problem
 69:       mx = 10
 70:       my = 10
 71:       bheight = 0.1

 73: ! Check for any command line arguments that override defaults

 75:       call PetscOptionsGetInt(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,     &
 76:      &                        '-mx',mx,flg,ierr)
 77:       CHKERRQ(ierr)
 78:       call PetscOptionsGetInt(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,     &
 79:      &                        '-my',my,flg,ierr)
 80:       CHKERRQ(ierr)

 82:       bmx = mx/2
 83:       bmy = my/2

 85:       call PetscOptionsGetInt(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,     &
 86:      &                        '-bmx',bmx,flg,ierr)
 87:       CHKERRQ(ierr)
 88:       call PetscOptionsGetInt(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,     &
 89:      &                        '-bmy',bmy,flg,ierr)
 90:       CHKERRQ(ierr)
 91:       call PetscOptionsGetReal(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,    &
 92:      &                         '-bheight',bheight,flg,ierr)
 93:       CHKERRQ(ierr)


 96: ! Calculate any derived values from parameters
 97:       N = mx*my

 99: ! Let Petsc determine the dimensions of the local vectors
100:       Nx = PETSC_DECIDE
101:       NY = PETSC_DECIDE

103: ! A two dimensional distributed array will help define this problem, which
104: ! derives from an elliptic PDE on a two-dimensional domain.  From the
105: ! distributed array, create the vectors

107:       call DMDACreate2d(MPI_COMM_WORLD,DM_BOUNDARY_NONE,                    &
108:      &     DM_BOUNDARY_NONE, DMDA_STENCIL_BOX,                              &
109:      &     mx,my,Nx,Ny,i1,i1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,           &
110:      &     dm,ierr)
111:       CHKERRQ(ierr)


114: ! Extract global and local vectors from DM; The local vectors are
115: ! used solely as work space for the evaluation of the function,
116: ! gradient, and Hessian.  Duplicate for remaining vectors that are
117: ! the same types.

119:       call DMCreateGlobalVector(dm,x,ierr)
120:       CHKERRQ(ierr)
121:       call DMCreateLocalVector(dm,localX,ierr)
122:       CHKERRQ(ierr)
123:       call VecDuplicate(localX,localV,ierr)
124:       CHKERRQ(ierr)

126: ! Create a matrix data structure to store the Hessian.
127: ! Here we (optionally) also associate the local numbering scheme
128: ! with the matrix so that later we can use local indices for matrix
129: ! assembly

131:       call VecGetLocalSize(x,m,ierr)
132:       CHKERRQ(ierr)
133:       call MatCreateAIJ(MPI_COMM_WORLD,m,m,N,N,i7,PETSC_NULL_INTEGER,   &
134:      &     i3,PETSC_NULL_INTEGER,H,ierr)
135:       CHKERRQ(ierr)

137:       call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)
138:       CHKERRQ(ierr)
139:       call DMGetLocalToGlobalMapping(dm,isltog,ierr)
140:       CHKERRQ(ierr)
141:       call MatSetLocalToGlobalMapping(H,isltog,isltog,ierr)
142:       CHKERRQ(ierr)


145: ! The Tao code begins here
146: ! Create TAO solver and set desired solution method.
147: ! This problems uses bounded variables, so the
148: ! method must either be 'tao_tron' or 'tao_blmvm'

150:       call TaoCreate(PETSC_COMM_WORLD,tao,ierr)
151:       CHKERRQ(ierr)
152:       call TaoSetType(tao,TAOBLMVM,ierr)
153:       CHKERRQ(ierr)

155: !     Set minimization function and gradient, hessian evaluation functions

157:       call TaoSetObjectiveAndGradientRoutine(tao,                       &
158:      &     FormFunctionGradient,PETSC_NULL_OBJECT,ierr)
159:       CHKERRQ(ierr)

161:       call TaoSetHessianRoutine(tao,H,H,FormHessian,                    &
162:      &     PETSC_NULL_OBJECT, ierr)
163:       CHKERRQ(ierr)

165: ! Set Variable bounds
166:       call MSA_BoundaryConditions(ierr)
167:       CHKERRQ(ierr)
168:       call TaoSetVariableBoundsRoutine(tao,MSA_Plate,                   &
169:      &     PETSC_NULL_OBJECT,ierr)
170:       CHKERRQ(ierr)

172: ! Set the initial solution guess
173:       call MSA_InitialPoint(x, ierr)
174:       CHKERRQ(ierr)
175:       call TaoSetInitialVector(tao,x,ierr)
176:       CHKERRQ(ierr)

178: ! Check for any tao command line options
179:       call TaoSetFromOptions(tao,ierr)
180:       CHKERRQ(ierr)

182: ! Solve the application
183:       call TaoSolve(tao,ierr)
184:       CHKERRQ(ierr)

186: ! Free TAO data structures
187:       call TaoDestroy(tao,ierr)
188:       CHKERRQ(ierr)

190: ! Free PETSc data structures
191:       call VecDestroy(x,ierr)
192:       call VecDestroy(Top,ierr)
193:       call VecDestroy(Bottom,ierr)
194:       call VecDestroy(Left,ierr)
195:       call VecDestroy(Right,ierr)
196:       call MatDestroy(H,ierr)
197:       call VecDestroy(localX,ierr)
198:       call VecDestroy(localV,ierr)
199:       call DMDestroy(dm,ierr)

201: ! Finalize TAO

203:       call PetscFinalize(ierr)

205:       end

207: ! ---------------------------------------------------------------------
208: !
209: !  FormFunctionGradient - Evaluates function f(X).
210: !
211: !  Input Parameters:
212: !  tao   - the Tao context
213: !  X     - the input vector
214: !  dummy - optional user-defined context, as set by TaoSetFunction()
215: !          (not used here)
216: !
217: !  Output Parameters:
218: !  fcn     - the newly evaluated function
219: !  G       - the gradient vector
220: !  info  - error code
221: !


224:       subroutine FormFunctionGradient(tao,X,fcn,G,dummy,ierr)
225:       implicit none

227: ! dm, localX, localG, Top, Bottom, Left, Right defined in plate2f.h
228: #include "plate2f.h"

230: ! Input/output variables

232:       Tao        tao
233:       PetscReal      fcn
234:       Vec              X, G
235:       PetscErrorCode   ierr
236:       PetscInt         dummy

238:       PetscInt         i,j,row
239:       PetscInt         xs, xm
240:       PetscInt         gxs, gxm
241:       PetscInt         ys, ym
242:       PetscInt         gys, gym
243:       PetscReal      ft,zero,hx,hy,hydhx,hxdhy
244:       PetscReal      area,rhx,rhy
245:       PetscReal      f1,f2,f3,f4,f5,f6,d1,d2,d3
246:       PetscReal      d4,d5,d6,d7,d8
247:       PetscReal      df1dxc,df2dxc,df3dxc,df4dxc
248:       PetscReal      df5dxc,df6dxc
249:       PetscReal      xc,xl,xr,xt,xb,xlt,xrb


252: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
253: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
254: ! will return an array of doubles referenced by x_array offset by x_index.
255: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
256: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
257:       PetscReal      g_v(0:1),x_v(0:1)
258:       PetscReal      top_v(0:1),left_v(0:1)
259:       PetscReal      right_v(0:1),bottom_v(0:1)
260:       PetscOffset      g_i,left_i,right_i
261:       PetscOffset      bottom_i,top_i,x_i

263:       ft = 0.0
264:       zero = 0.0
265:       hx = 1.0/(mx + 1)
266:       hy = 1.0/(my + 1)
267:       hydhx = hy/hx
268:       hxdhy = hx/hy
269:       area = 0.5 * hx * hy
270:       rhx = mx + 1.0
271:       rhy = my + 1.0


274: ! Get local mesh boundaries
275:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
276:      &                  PETSC_NULL_INTEGER,ierr)
277:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,             &
278:      &                       gxm,gym,PETSC_NULL_INTEGER,ierr)

280: ! Scatter ghost points to local vector
281:       call DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr)
282:       call DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr)

284: ! Initialize the vector to zero
285:       call VecSet(localV,zero,ierr)

287: ! Get arrays to vector data (See note above about using VecGetArray in Fortran)
288:       call VecGetArray(localX,x_v,x_i,ierr)
289:       call VecGetArray(localV,g_v,g_i,ierr)
290:       call VecGetArray(Top,top_v,top_i,ierr)
291:       call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
292:       call VecGetArray(Left,left_v,left_i,ierr)
293:       call VecGetArray(Right,right_v,right_i,ierr)

295: ! Compute function over the locally owned part of the mesh
296:       do j = ys,ys+ym-1
297:          do i = xs,xs+xm-1
298:             row = (j-gys)*gxm + (i-gxs)
299:             xc = x_v(row+x_i)
300:             xt = xc
301:             xb = xc
302:             xr = xc
303:             xl = xc
304:             xrb = xc
305:             xlt = xc

307:             if (i .eq. 0) then !left side
308:                xl = left_v(j - ys + 1 + left_i)
309:                xlt = left_v(j - ys + 2 + left_i)
310:             else
311:                xl = x_v(row - 1 + x_i)
312:             endif

314:             if (j .eq. 0) then !bottom side
315:                xb = bottom_v(i - xs + 1 + bottom_i)
316:                xrb = bottom_v(i - xs + 2 + bottom_i)
317:             else
318:                xb = x_v(row - gxm + x_i)
319:             endif

321:             if (i + 1 .eq. gxs + gxm) then !right side
322:                xr = right_v(j - ys + 1 + right_i)
323:                xrb = right_v(j - ys + right_i)
324:             else
325:                xr = x_v(row + 1 + x_i)
326:             endif

328:             if (j + 1 .eq. gys + gym) then !top side
329:                xt = top_v(i - xs + 1 + top_i)
330:                xlt = top_v(i - xs + top_i)
331:             else
332:                xt = x_v(row + gxm + x_i)
333:             endif

335:             if ((i .gt. gxs ) .and. (j + 1 .lt. gys + gym)) then
336:                xlt = x_v(row - 1 + gxm + x_i)
337:             endif

339:             if ((j .gt. gys) .and. (i + 1 .lt. gxs + gxm)) then
340:                xrb = x_v(row + 1 - gxm + x_i)
341:             endif

343:             d1 = xc-xl
344:             d2 = xc-xr
345:             d3 = xc-xt
346:             d4 = xc-xb
347:             d5 = xr-xrb
348:             d6 = xrb-xb
349:             d7 = xlt-xl
350:             d8 = xt-xlt

352:             df1dxc = d1 * hydhx
353:             df2dxc = d1 * hydhx + d4 * hxdhy
354:             df3dxc = d3 * hxdhy
355:             df4dxc = d2 * hydhx + d3 * hxdhy
356:             df5dxc = d2 * hydhx
357:             df6dxc = d4 * hxdhy

359:             d1 = d1 * rhx
360:             d2 = d2 * rhx
361:             d3 = d3 * rhy
362:             d4 = d4 * rhy
363:             d5 = d5 * rhy
364:             d6 = d6 * rhx
365:             d7 = d7 * rhy
366:             d8 = d8 * rhx

368:             f1 = sqrt(1.0 + d1*d1 + d7*d7)
369:             f2 = sqrt(1.0 + d1*d1 + d4*d4)
370:             f3 = sqrt(1.0 + d3*d3 + d8*d8)
371:             f4 = sqrt(1.0 + d3*d3 + d2*d2)
372:             f5 = sqrt(1.0 + d2*d2 + d5*d5)
373:             f6 = sqrt(1.0 + d4*d4 + d6*d6)

375:             ft = ft + f2 + f4

377:             df1dxc = df1dxc / f1
378:             df2dxc = df2dxc / f2
379:             df3dxc = df3dxc / f3
380:             df4dxc = df4dxc / f4
381:             df5dxc = df5dxc / f5
382:             df6dxc = df6dxc / f6

384:             g_v(row + g_i) = 0.5 * (df1dxc + df2dxc + df3dxc + df4dxc +  &
385:      &                              df5dxc + df6dxc)
386:          enddo
387:       enddo

389: ! Compute triangular areas along the border of the domain.
390:       if (xs .eq. 0) then  ! left side
391:          do j=ys,ys+ym-1
392:             d3 = (left_v(j-ys+1+left_i) - left_v(j-ys+2+left_i))         &
393:      &                 * rhy
394:             d2 = (left_v(j-ys+1+left_i) - x_v((j-gys)*gxm + x_i))        &
395:      &                 * rhx
396:             ft = ft + sqrt(1.0 + d3*d3 + d2*d2)
397:          enddo
398:       endif


401:       if (ys .eq. 0) then !bottom side
402:          do i=xs,xs+xm-1
403:             d2 = (bottom_v(i+1-xs+bottom_i)-bottom_v(i-xs+2+bottom_i))    &
404:      &                    * rhx
405:             d3 = (bottom_v(i-xs+1+bottom_i)-x_v(i-gxs+x_i))*rhy
406:             ft = ft + sqrt(1.0 + d3*d3 + d2*d2)
407:          enddo
408:       endif


411:       if (xs + xm .eq. mx) then ! right side
412:          do j=ys,ys+ym-1
413:             d1 = (x_v((j+1-gys)*gxm-1+x_i)-right_v(j-ys+1+right_i))*rhx
414:             d4 = (right_v(j-ys+right_i) - right_v(j-ys+1+right_i))*rhy
415:             ft = ft + sqrt(1.0 + d1*d1 + d4*d4)
416:          enddo
417:       endif


420:       if (ys + ym .eq. my) then
421:          do i=xs,xs+xm-1
422:             d1 = (x_v((gym-1)*gxm+i-gxs+x_i) - top_v(i-xs+1+top_i))*rhy
423:             d4 = (top_v(i-xs+1+top_i) - top_v(i-xs+top_i))*rhx
424:             ft = ft + sqrt(1.0 + d1*d1 + d4*d4)
425:          enddo
426:       endif


429:       if ((ys .eq. 0) .and. (xs .eq. 0)) then
430:          d1 = (left_v(0 + left_i) - left_v(1 + left_i)) * rhy
431:          d2 = (bottom_v(0+bottom_i)-bottom_v(1+bottom_i))*rhx
432:          ft = ft + sqrt(1.0 + d1*d1 + d2*d2)
433:       endif

435:       if ((ys + ym .eq. my) .and. (xs + xm .eq. mx)) then
436:          d1 = (right_v(ym+1+right_i) - right_v(ym+right_i))*rhy
437:          d2 = (top_v(xm+1+top_i) - top_v(xm + top_i))*rhx
438:          ft = ft + sqrt(1.0 + d1*d1 + d2*d2)
439:       endif

441:       ft = ft * area
442:       call MPI_Allreduce(ft,fcn,1,MPIU_SCALAR,                            &
443:      &             MPIU_SUM,MPI_COMM_WORLD,ierr)


446: ! Restore vectors
447:       call VecRestoreArray(localX,x_v,x_i,ierr)
448:       call VecRestoreArray(localV,g_v,g_i,ierr)
449:       call VecRestoreArray(Left,left_v,left_i,ierr)
450:       call VecRestoreArray(Top,top_v,top_i,ierr)
451:       call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)
452:       call VecRestoreArray(Right,right_v,right_i,ierr)

454: ! Scatter values to global vector
455:       call DMLocalToGlobalBegin(dm,localV,INSERT_VALUES,G,ierr)
456:       call DMLocalToGlobalEnd(dm,localV,INSERT_VALUES,G,ierr)

458:       call PetscLogFlops(70.0d0*xm*ym,ierr)

460:       return
461:       end  !FormFunctionGradient





467: ! ----------------------------------------------------------------------------
468: !
469: !
470: !   FormHessian - Evaluates Hessian matrix.
471: !
472: !   Input Parameters:
473: !.  tao  - the Tao context
474: !.  X    - input vector
475: !.  dummy  - not used
476: !
477: !   Output Parameters:
478: !.  Hessian    - Hessian matrix
479: !.  Hpc    - optionally different preconditioning matrix
480: !.  flag - flag indicating matrix structure
481: !
482: !   Notes:
483: !   Due to mesh point reordering with DMs, we must always work
484: !   with the local mesh points, and then transform them to the new
485: !   global numbering with the local-to-global mapping.  We cannot work
486: !   directly with the global numbers for the original uniprocessor mesh!
487: !
488: !      MatSetValuesLocal(), using the local ordering (including
489: !         ghost points!)
490: !         - Then set matrix entries using the local ordering
491: !           by calling MatSetValuesLocal()

493:       subroutine FormHessian(tao, X, Hessian, Hpc, dummy, ierr)
494:       implicit none

496: ! dm,Top,Left,Right,Bottom,mx,my,localX defined in plate2f.h
497: #include "plate2f.h"

499:       Tao     tao
500:       Vec            X
501:       Mat            Hessian,Hpc
502:       PetscInt       dummy
503:       PetscErrorCode ierr

505:       PetscInt       i,j,k,row
506:       PetscInt       xs,xm,gxs,gxm
507:       PetscInt       ys,ym,gys,gym
508:       PetscInt       col(0:6)
509:       PetscReal    hx,hy,hydhx,hxdhy,rhx,rhy
510:       PetscReal    f1,f2,f3,f4,f5,f6,d1,d2,d3
511:       PetscReal    d4,d5,d6,d7,d8
512:       PetscReal    xc,xl,xr,xt,xb,xlt,xrb
513:       PetscReal    hl,hr,ht,hb,hc,htl,hbr

515: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
516: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
517: ! will return an array of doubles referenced by x_array offset by x_index.
518: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
519: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
520:       PetscReal   right_v(0:1),left_v(0:1)
521:       PetscReal   bottom_v(0:1),top_v(0:1)
522:       PetscReal   x_v(0:1)
523:       PetscOffset   x_i,right_i,left_i
524:       PetscOffset   bottom_i,top_i
525:       PetscReal   v(0:6)
526:       PetscBool     assembled
527:       PetscInt      i1

529:       i1=1

531: ! Set various matrix options
532:       call MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES,              &
533:      &                  PETSC_TRUE,ierr)

535: ! Get local mesh boundaries
536:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
537:      &                  PETSC_NULL_INTEGER,ierr)
538:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,     &
539:      &                       PETSC_NULL_INTEGER,ierr)

541: ! Scatter ghost points to local vectors
542:       call DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr)
543:       call DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr)

545: ! Get pointers to vector data (see note on Fortran arrays above)
546:       call VecGetArray(localX,x_v,x_i,ierr)
547:       call VecGetArray(Top,top_v,top_i,ierr)
548:       call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
549:       call VecGetArray(Left,left_v,left_i,ierr)
550:       call VecGetArray(Right,right_v,right_i,ierr)

552: ! Initialize matrix entries to zero
553:       call MatAssembled(Hessian,assembled,ierr)
554:       if (assembled .eqv. PETSC_TRUE) call MatZeroEntries(Hessian,ierr)


557:       rhx = mx + 1.0
558:       rhy = my + 1.0
559:       hx = 1.0/rhx
560:       hy = 1.0/rhy
561:       hydhx = hy/hx
562:       hxdhy = hx/hy
563: ! compute Hessian over the locally owned part of the mesh

565:       do  i=xs,xs+xm-1
566:          do  j=ys,ys+ym-1
567:             row = (j-gys)*gxm + (i-gxs)

569:             xc = x_v(row + x_i)
570:             xt = xc
571:             xb = xc
572:             xr = xc
573:             xl = xc
574:             xrb = xc
575:             xlt = xc

577:             if (i .eq. gxs) then   ! Left side
578:                xl = left_v(left_i + j - ys + 1)
579:                xlt = left_v(left_i + j - ys + 2)
580:             else
581:                xl = x_v(x_i + row -1 )
582:             endif

584:             if (j .eq. gys) then ! bottom side
585:                xb = bottom_v(bottom_i + i - xs + 1)
586:                xrb = bottom_v(bottom_i + i - xs + 2)
587:             else
588:                xb = x_v(x_i + row - gxm)
589:             endif

591:             if (i+1 .eq. gxs + gxm) then !right side
592:                xr = right_v(right_i + j - ys + 1)
593:                xrb = right_v(right_i + j - ys)
594:             else
595:                xr = x_v(x_i + row + 1)
596:             endif

598:             if (j+1 .eq. gym+gys) then !top side
599:                xt = top_v(top_i +i - xs + 1)
600:                xlt = top_v(top_i + i - xs)
601:             else
602:                xt = x_v(x_i + row + gxm)
603:             endif

605:             if ((i .gt. gxs) .and. (j+1 .lt. gys+gym)) then
606:                xlt = x_v(x_i + row - 1 + gxm)
607:             endif

609:             if ((i+1 .lt. gxs+gxm) .and. (j .gt. gys)) then
610:                xrb = x_v(x_i + row + 1 - gxm)
611:             endif

613:             d1 = (xc-xl)*rhx
614:             d2 = (xc-xr)*rhx
615:             d3 = (xc-xt)*rhy
616:             d4 = (xc-xb)*rhy
617:             d5 = (xrb-xr)*rhy
618:             d6 = (xrb-xb)*rhx
619:             d7 = (xlt-xl)*rhy
620:             d8 = (xlt-xt)*rhx

622:             f1 = sqrt( 1.0 + d1*d1 + d7*d7)
623:             f2 = sqrt( 1.0 + d1*d1 + d4*d4)
624:             f3 = sqrt( 1.0 + d3*d3 + d8*d8)
625:             f4 = sqrt( 1.0 + d3*d3 + d2*d2)
626:             f5 = sqrt( 1.0 + d2*d2 + d5*d5)
627:             f6 = sqrt( 1.0 + d4*d4 + d6*d6)


630:             hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+                 &
631:      &              (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2)

633:             hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+                 &
634:      &            (-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4)

636:             ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+                 &
637:      &                (-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4)

639:             hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+                 &
640:      &              (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2)

642:             hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6)
643:             htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3)

645:             hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) +                         &
646:      &              hxdhy*(1.0+d8*d8)/(f3*f3*f3) +                      &
647:      &              hydhx*(1.0+d5*d5)/(f5*f5*f5) +                      &
648:      &              hxdhy*(1.0+d6*d6)/(f6*f6*f6) +                      &
649:      &              (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-               &
650:      &              2*d1*d4)/(f2*f2*f2) +  (hxdhy*(1.0+d2*d2)+          &
651:      &              hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4)

653:             hl = hl * 0.5
654:             hr = hr * 0.5
655:             ht = ht * 0.5
656:             hb = hb * 0.5
657:             hbr = hbr * 0.5
658:             htl = htl * 0.5
659:             hc = hc * 0.5

661:             k = 0

663:             if (j .gt. 0) then
664:                v(k) = hb
665:                col(k) = row - gxm
666:                k=k+1
667:             endif

669:             if ((j .gt. 0) .and. (i .lt. mx-1)) then
670:                v(k) = hbr
671:                col(k) = row-gxm+1
672:                k=k+1
673:             endif

675:             if (i .gt. 0) then
676:                v(k) = hl
677:                col(k) = row - 1
678:                k = k+1
679:             endif

681:             v(k) = hc
682:             col(k) = row
683:             k=k+1

685:             if (i .lt. mx-1) then
686:                v(k) = hr
687:                col(k) = row + 1
688:                k=k+1
689:             endif

691:             if ((i .gt. 0) .and. (j .lt. my-1)) then
692:                v(k) = htl
693:                col(k) = row + gxm - 1
694:                k=k+1
695:             endif

697:             if (j .lt. my-1) then
698:                v(k) = ht
699:                col(k) = row + gxm
700:                k=k+1
701:             endif

703: ! Set matrix values using local numbering, defined earlier in main routine
704:             call MatSetValuesLocal(Hessian,i1,row,k,col,v,INSERT_VALUES,      &
705:      &                              ierr)



709:          enddo
710:       enddo

712: ! restore vectors
713:       call VecRestoreArray(localX,x_v,x_i,ierr)
714:       call VecRestoreArray(Left,left_v,left_i,ierr)
715:       call VecRestoreArray(Right,right_v,right_i,ierr)
716:       call VecRestoreArray(Top,top_v,top_i,ierr)
717:       call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)


720: ! Assemble the matrix
721:       call MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY,ierr)
722:       call MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY,ierr)

724:       call PetscLogFlops(199.0d0*xm*ym,ierr)

726:       return
727:       end





733: ! Top,Left,Right,Bottom,bheight,mx,my,bmx,bmy,H, defined in plate2f.h

735: ! ----------------------------------------------------------------------------
736: !
737: !/*
738: !     MSA_BoundaryConditions - calculates the boundary conditions for the region
739: !
740: !
741: !*/

743:       subroutine MSA_BoundaryConditions(ierr)
744:       implicit none

746: ! Top,Left,Right,Bottom,bheight,mx,my,bmx,bmy defined in plate2f.h
747: #include "plate2f.h"

749:       PetscErrorCode   ierr
750:       PetscInt         i,j,k,limit,maxits
751:       PetscInt         xs, xm, gxs, gxm
752:       PetscInt         ys, ym, gys, gym
753:       PetscInt         bsize, lsize
754:       PetscInt         tsize, rsize
755:       PetscReal      one,two,three,tol
756:       PetscReal      scl,fnorm,det,xt
757:       PetscReal      yt,hx,hy,u1,u2,nf1,nf2
758:       PetscReal      njac11,njac12,njac21,njac22
759:       PetscReal      b, t, l, r
760:       PetscReal      boundary_v(0:1)
761:       PetscOffset      boundary_i
762:       logical exitloop
763:       PetscBool flg

765:       limit=0
766:       maxits = 5
767:       tol=1e-10
768:       b=-0.5
769:       t= 0.5
770:       l=-0.5
771:       r= 0.5
772:       xt=0
773:       yt=0
774:       one=1.0
775:       two=2.0
776:       three=3.0


779:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
780:      &                  PETSC_NULL_INTEGER,ierr)
781:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,              &
782:      &                       gxm,gym,PETSC_NULL_INTEGER,ierr)

784:       bsize = xm + 2
785:       lsize = ym + 2
786:       rsize = ym + 2
787:       tsize = xm + 2


790:       call VecCreateMPI(MPI_COMM_WORLD,bsize,PETSC_DECIDE,Bottom,ierr)
791:       call VecCreateMPI(MPI_COMM_WORLD,tsize,PETSC_DECIDE,Top,ierr)
792:       call VecCreateMPI(MPI_COMM_WORLD,lsize,PETSC_DECIDE,Left,ierr)
793:       call VecCreateMPI(MPI_COMM_WORLD,rsize,PETSC_DECIDE,Right,ierr)

795:       hx= (r-l)/(mx+1)
796:       hy= (t-b)/(my+1)

798:       do j=0,3

800:          if (j.eq.0) then
801:             yt=b
802:             xt=l+hx*xs
803:             limit=bsize
804:             call VecGetArray(Bottom,boundary_v,boundary_i,ierr)


807:          elseif (j.eq.1) then
808:             yt=t
809:             xt=l+hx*xs
810:             limit=tsize
811:             call VecGetArray(Top,boundary_v,boundary_i,ierr)

813:          elseif (j.eq.2) then
814:             yt=b+hy*ys
815:             xt=l
816:             limit=lsize
817:             call VecGetArray(Left,boundary_v,boundary_i,ierr)

819:          elseif (j.eq.3) then
820:             yt=b+hy*ys
821:             xt=r
822:             limit=rsize
823:             call VecGetArray(Right,boundary_v,boundary_i,ierr)
824:          endif


827:          do i=0,limit-1

829:             u1=xt
830:             u2=-yt
831:             k = 0
832:             exitloop = .false.
833:             do while (k .lt. maxits .and. (.not. exitloop) )

835:                nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt
836:                nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt
837:                fnorm=sqrt(nf1*nf1+nf2*nf2)
838:                if (fnorm .gt. tol) then
839:                   njac11=one+u2*u2-u1*u1
840:                   njac12=two*u1*u2
841:                   njac21=-two*u1*u2
842:                   njac22=-one - u1*u1 + u2*u2
843:                   det = njac11*njac22-njac21*njac12
844:                   u1 = u1-(njac22*nf1-njac12*nf2)/det
845:                   u2 = u2-(njac11*nf2-njac21*nf1)/det
846:                else
847:                   exitloop = .true.
848:                endif
849:                k=k+1
850:             enddo

852:             boundary_v(i + boundary_i) = u1*u1-u2*u2
853:             if ((j .eq. 0) .or. (j .eq. 1)) then
854:                xt = xt + hx
855:             else
856:                yt = yt + hy
857:             endif

859:          enddo


862:          if (j.eq.0) then
863:             call VecRestoreArray(Bottom,boundary_v,boundary_i,ierr)
864:          elseif (j.eq.1) then
865:             call VecRestoreArray(Top,boundary_v,boundary_i,ierr)
866:          elseif (j.eq.2) then
867:             call VecRestoreArray(Left,boundary_v,boundary_i,ierr)
868:          elseif (j.eq.3) then
869:             call VecRestoreArray(Right,boundary_v,boundary_i,ierr)
870:          endif

872:       enddo


875: ! Scale the boundary if desired
876:       call PetscOptionsGetReal(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,          &
877:      &                         '-bottom',scl,flg,ierr)
878:       if (flg .eqv. PETSC_TRUE) then
879:          call VecScale(scl,Bottom,ierr)
880:       endif

882:       call PetscOptionsGetReal(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,          &
883:      &                         '-top',scl,flg,ierr)
884:       if (flg .eqv. PETSC_TRUE) then
885:          call VecScale(scl,Top,ierr)
886:       endif

888:       call PetscOptionsGetReal(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,          &
889:      &                         '-right',scl,flg,ierr)
890:       if (flg .eqv. PETSC_TRUE) then
891:          call VecScale(scl,Right,ierr)
892:       endif

894:       call PetscOptionsGetReal(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,          &
895:      &                         '-left',scl,flg,ierr)
896:       if (flg .eqv. PETSC_TRUE) then
897:          call VecScale(scl,Left,ierr)
898:       endif


901:       return
902:       end

904: ! ----------------------------------------------------------------------------
905: !
906: !/*
907: !     MSA_Plate - Calculates an obstacle for surface to stretch over
908: !
909: !     Output Parameter:
910: !.    xl - lower bound vector
911: !.    xu - upper bound vector
912: !
913: !*/

915:       subroutine MSA_Plate(tao,xl,xu,dummy,ierr)
916:       implicit none
917: ! mx,my,bmx,bmy,dm,bheight defined in plate2f.h
918: #include "plate2f.h"
919:       Tao        tao
920:       Vec              xl,xu
921:       PetscErrorCode   ierr
922:       PetscInt         i,j,row
923:       PetscInt         xs, xm, ys, ym
924:       PetscReal      lb,ub
925:       PetscInt         dummy

927: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
928: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
929: ! will return an array of doubles referenced by x_array offset by x_index.
930: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
931: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
932:       PetscReal      xl_v(0:1)
933:       PetscOffset      xl_i

935:       print *,'msa_plate'

937:       lb = PETSC_NINFINITY
938:       ub = PETSC_INFINITY

940:       if (bmy .lt. 0) bmy = 0
941:       if (bmy .gt. my) bmy = my
942:       if (bmx .lt. 0) bmx = 0
943:       if (bmx .gt. mx) bmx = mx


946:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
947:      &             PETSC_NULL_INTEGER,ierr)

949:       call VecSet(xl,lb,ierr)
950:       call VecSet(xu,ub,ierr)

952:       call VecGetArray(xl,xl_v,xl_i,ierr)


955:       do i=xs,xs+xm-1

957:          do j=ys,ys+ym-1

959:             row=(j-ys)*xm + (i-xs)

961:             if (i.ge.((mx-bmx)/2) .and. i.lt.(mx-(mx-bmx)/2) .and.           &
962:      &          j.ge.((my-bmy)/2) .and. j.lt.(my-(my-bmy)/2)) then
963:                xl_v(xl_i+row) = bheight

965:             endif

967:          enddo
968:       enddo


971:       call VecRestoreArray(xl,xl_v,xl_i,ierr)

973:       return
974:       end





980: ! ----------------------------------------------------------------------------
981: !
982: !/*
983: !     MSA_InitialPoint - Calculates an obstacle for surface to stretch over
984: !
985: !     Output Parameter:
986: !.    X - vector for initial guess
987: !
988: !*/

990:       subroutine MSA_InitialPoint(X, ierr)
991:       implicit none

993: ! mx,my,localX,dm,Top,Left,Bottom,Right defined in plate2f.h
994: #include "plate2f.h"
995:       Vec               X
996:       PetscErrorCode    ierr
997:       PetscInt          start,i,j
998:       PetscInt          row
999:       PetscInt          xs,xm,gxs,gxm
1000:       PetscInt          ys,ym,gys,gym
1001:       PetscReal       zero, np5

1003: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
1004: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (integer) x_index, ierr)
1005: ! will return an array of doubles referenced by x_array offset by x_index.
1006: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
1007: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
1008:       PetscReal   left_v(0:1),right_v(0:1)
1009:       PetscReal   bottom_v(0:1),top_v(0:1)
1010:       PetscReal   x_v(0:1)
1011:       PetscOffset   left_i, right_i, top_i
1012:       PetscOffset   bottom_i,x_i
1013:       PetscBool     flg
1014:       PetscRandom   rctx

1016:       zero = 0.0
1017:       np5 = -0.5

1019:       call PetscOptionsGetInt(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,        &
1020:      &                        '-start', start,flg,ierr)

1022:       if ((flg .eqv. PETSC_TRUE) .and. (start .eq. 0)) then  ! the zero vector is reasonable
1023:          call VecSet(X,zero,ierr)

1025:       elseif ((flg .eqv. PETSC_TRUE) .and. (start .gt. 0)) then  ! random start -0.5 < xi < 0.5
1026:          call PetscRandomCreate(MPI_COMM_WORLD,rctx,ierr)
1027:          do i=0,start-1
1028:             call VecSetRandom(X,rctx,ierr)
1029:          enddo

1031:          call PetscRandomDestroy(rctx,ierr)
1032:          call VecShift(X,np5,ierr)

1034:       else   ! average of boundary conditions

1036: !        Get Local mesh boundaries
1037:          call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,             &
1038:      &                     PETSC_NULL_INTEGER,ierr)
1039:          call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,    &
1040:      &                     PETSC_NULL_INTEGER,ierr)



1044: !        Get pointers to vector data
1045:          call VecGetArray(Top,top_v,top_i,ierr)
1046:          call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
1047:          call VecGetArray(Left,left_v,left_i,ierr)
1048:          call VecGetArray(Right,right_v,right_i,ierr)

1050:          call VecGetArray(localX,x_v,x_i,ierr)

1052: !        Perform local computations
1053:          do  j=ys,ys+ym-1
1054:             do i=xs,xs+xm-1
1055:                row = (j-gys)*gxm  + (i-gxs)
1056:                x_v(x_i + row) = ((j+1)*bottom_v(bottom_i +i-xs+1)/my        &
1057:      &             + (my-j+1)*top_v(top_i+i-xs+1)/(my+2) +                  &
1058:      &              (i+1)*left_v(left_i+j-ys+1)/mx       +                  &
1059:      &              (mx-i+1)*right_v(right_i+j-ys+1)/(mx+2))*0.5
1060:             enddo
1061:          enddo

1063: !        Restore vectors
1064:          call VecRestoreArray(localX,x_v,x_i,ierr)

1066:          call VecRestoreArray(Left,left_v,left_i,ierr)
1067:          call VecRestoreArray(Top,top_v,top_i,ierr)
1068:          call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)
1069:          call VecRestoreArray(Right,right_v,right_i,ierr)

1071:          call DMLocalToGlobalBegin(dm,localX,INSERT_VALUES,X,ierr)
1072:          call DMLocalToGlobalEnd(dm,localX,INSERT_VALUES,X,ierr)

1074:       endif

1076:       return
1077:       end