Actual source code: plate2f.F90

petsc-3.8.4 2018-03-24
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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*/

 28: #include "plate2f.h"

 30: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 31: !                   Variable declarations
 32: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 33: !
 34: !  Variables:
 35: !    (common from plate2f.h):
 36: !    Nx, Ny           number of processors in x- and y- directions
 37: !    mx, my           number of grid points in x,y directions
 38: !    N    global dimension of vector

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


 50:       external FormFunctionGradient
 51:       external FormHessian
 52:       external MSA_BoundaryConditions
 53:       external MSA_Plate
 54:       external MSA_InitialPoint
 55: ! Initialize Tao

 57:       i1=1
 58:       i3=3
 59:       i7=7


 62:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 63:       if (ierr .ne. 0) then
 64:         print*,'Unable to initialize PETSc'
 65:         stop
 66:       endif

 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_OPTIONS,PETSC_NULL_CHARACTER,     &
 76:      &                        '-mx',mx,flg,ierr)
 77:       CHKERRA(ierr)
 78:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,     &
 79:      &                        '-my',my,flg,ierr)
 80:       CHKERRA(ierr)

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

 85:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,     &
 86:      &                        '-bmx',bmx,flg,ierr)
 87:       CHKERRA(ierr)
 88:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,     &
 89:      &                        '-bmy',bmy,flg,ierr)
 90:       CHKERRA(ierr)
 91:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,    &
 92:      &                         '-bheight',bheight,flg,ierr)
 93:       CHKERRA(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:       CHKERRA(ierr)
112:       call DMSetFromOptions(dm,ierr)
113:       call DMSetUp(dm,ierr)

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

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

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

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

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


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

151:       call TaoCreate(PETSC_COMM_WORLD,tao,ierr)
152:       CHKERRA(ierr)
153:       call TaoSetType(tao,TAOBLMVM,ierr)
154:       CHKERRA(ierr)

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

158:       call TaoSetObjectiveAndGradientRoutine(tao,                       &
159:      &     FormFunctionGradient,0,ierr)
160:       CHKERRA(ierr)

162:       call TaoSetHessianRoutine(tao,H,H,FormHessian,                    &
163:      &     0, ierr)
164:       CHKERRA(ierr)

166: ! Set Variable bounds
167:       call MSA_BoundaryConditions(ierr)
168:       CHKERRA(ierr)
169:       call TaoSetVariableBoundsRoutine(tao,MSA_Plate,                   &
170:      &     0,ierr)
171:       CHKERRA(ierr)

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

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

183: ! Solve the application
184:       call TaoSolve(tao,ierr)
185:       CHKERRA(ierr)

187: ! Free TAO data structures
188:       call TaoDestroy(tao,ierr)
189:       CHKERRA(ierr)

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

202: ! Finalize TAO

204:       call PetscFinalize(ierr)

206:       end

208: ! ---------------------------------------------------------------------
209: !
210: !  FormFunctionGradient - Evaluates function f(X).
211: !
212: !  Input Parameters:
213: !  tao   - the Tao context
214: !  X     - the input vector
215: !  dummy - optional user-defined context, as set by TaoSetFunction()
216: !          (not used here)
217: !
218: !  Output Parameters:
219: !  fcn     - the newly evaluated function
220: !  G       - the gradient vector
221: !  info  - error code
222: !


225:       subroutine FormFunctionGradient(tao,X,fcn,G,dummy,ierr)
226: #include "plate2f.h"

228: ! Input/output variables

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

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


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

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


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

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

282: ! Initialize the vector to zero
283:       call VecSet(localV,zero,ierr)

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

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

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

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

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

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

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

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

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

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

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

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

373:             ft = ft + f2 + f4

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

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

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


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


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


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


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

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

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


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

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

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

458:       return
459:       end  !FormFunctionGradient





465: ! ----------------------------------------------------------------------------
466: !
467: !
468: !   FormHessian - Evaluates Hessian matrix.
469: !
470: !   Input Parameters:
471: !.  tao  - the Tao context
472: !.  X    - input vector
473: !.  dummy  - not used
474: !
475: !   Output Parameters:
476: !.  Hessian    - Hessian matrix
477: !.  Hpc    - optionally different preconditioning matrix
478: !.  flag - flag indicating matrix structure
479: !
480: !   Notes:
481: !   Due to mesh point reordering with DMs, we must always work
482: !   with the local mesh points, and then transform them to the new
483: !   global numbering with the local-to-global mapping.  We cannot work
484: !   directly with the global numbers for the original uniprocessor mesh!
485: !
486: !      MatSetValuesLocal(), using the local ordering (including
487: !         ghost points!)
488: !         - Then set matrix entries using the local ordering
489: !           by calling MatSetValuesLocal()

491:       subroutine FormHessian(tao, X, Hessian, Hpc, dummy, ierr)
492: #include "plate2f.h"

494:       Tao     tao
495:       Vec            X
496:       Mat            Hessian,Hpc
497:       PetscInt       dummy
498:       PetscErrorCode ierr

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

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

524:       i1=1

526: ! Set various matrix options
527:       call MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES,              &
528:      &                  PETSC_TRUE,ierr)

530: ! Get local mesh boundaries
531:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
532:      &                  PETSC_NULL_INTEGER,ierr)
533:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,     &
534:      &                       PETSC_NULL_INTEGER,ierr)

536: ! Scatter ghost points to local vectors
537:       call DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr)
538:       call DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr)

540: ! Get pointers to vector data (see note on Fortran arrays above)
541:       call VecGetArray(localX,x_v,x_i,ierr)
542:       call VecGetArray(Top,top_v,top_i,ierr)
543:       call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
544:       call VecGetArray(Left,left_v,left_i,ierr)
545:       call VecGetArray(Right,right_v,right_i,ierr)

547: ! Initialize matrix entries to zero
548:       call MatAssembled(Hessian,assembled,ierr)
549:       if (assembled .eqv. PETSC_TRUE) call MatZeroEntries(Hessian,ierr)


552:       rhx = real(mx + 1.0)
553:       rhy = real(my + 1.0)
554:       hx = 1.0/rhx
555:       hy = 1.0/rhy
556:       hydhx = hy/hx
557:       hxdhy = hx/hy
558: ! compute Hessian over the locally owned part of the mesh

560:       do  i=xs,xs+xm-1
561:          do  j=ys,ys+ym-1
562:             row = (j-gys)*gxm + (i-gxs)

564:             xc = x_v(row + x_i)
565:             xt = xc
566:             xb = xc
567:             xr = xc
568:             xl = xc
569:             xrb = xc
570:             xlt = xc

572:             if (i .eq. gxs) then   ! Left side
573:                xl = left_v(left_i + j - ys + 1)
574:                xlt = left_v(left_i + j - ys + 2)
575:             else
576:                xl = x_v(x_i + row -1 )
577:             endif

579:             if (j .eq. gys) then ! bottom side
580:                xb = bottom_v(bottom_i + i - xs + 1)
581:                xrb = bottom_v(bottom_i + i - xs + 2)
582:             else
583:                xb = x_v(x_i + row - gxm)
584:             endif

586:             if (i+1 .eq. gxs + gxm) then !right side
587:                xr = right_v(right_i + j - ys + 1)
588:                xrb = right_v(right_i + j - ys)
589:             else
590:                xr = x_v(x_i + row + 1)
591:             endif

593:             if (j+1 .eq. gym+gys) then !top side
594:                xt = top_v(top_i +i - xs + 1)
595:                xlt = top_v(top_i + i - xs)
596:             else
597:                xt = x_v(x_i + row + gxm)
598:             endif

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

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

608:             d1 = (xc-xl)*rhx
609:             d2 = (xc-xr)*rhx
610:             d3 = (xc-xt)*rhy
611:             d4 = (xc-xb)*rhy
612:             d5 = (xrb-xr)*rhy
613:             d6 = (xrb-xb)*rhx
614:             d7 = (xlt-xl)*rhy
615:             d8 = (xlt-xt)*rhx

617:             f1 = sqrt( 1.0 + d1*d1 + d7*d7)
618:             f2 = sqrt( 1.0 + d1*d1 + d4*d4)
619:             f3 = sqrt( 1.0 + d3*d3 + d8*d8)
620:             f4 = sqrt( 1.0 + d3*d3 + d2*d2)
621:             f5 = sqrt( 1.0 + d2*d2 + d5*d5)
622:             f6 = sqrt( 1.0 + d4*d4 + d6*d6)


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

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

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

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

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

640:             hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) +                         &
641:      &              hxdhy*(1.0+d8*d8)/(f3*f3*f3) +                      &
642:      &              hydhx*(1.0+d5*d5)/(f5*f5*f5) +                      &
643:      &              hxdhy*(1.0+d6*d6)/(f6*f6*f6) +                      &
644:      &              (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-               &
645:      &              2*d1*d4)/(f2*f2*f2) +  (hxdhy*(1.0+d2*d2)+          &
646:      &              hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4)

648:             hl = hl * 0.5
649:             hr = hr * 0.5
650:             ht = ht * 0.5
651:             hb = hb * 0.5
652:             hbr = hbr * 0.5
653:             htl = htl * 0.5
654:             hc = hc * 0.5

656:             k = 0

658:             if (j .gt. 0) then
659:                v(k) = hb
660:                col(k) = row - gxm
661:                k=k+1
662:             endif

664:             if ((j .gt. 0) .and. (i .lt. mx-1)) then
665:                v(k) = hbr
666:                col(k) = row-gxm+1
667:                k=k+1
668:             endif

670:             if (i .gt. 0) then
671:                v(k) = hl
672:                col(k) = row - 1
673:                k = k+1
674:             endif

676:             v(k) = hc
677:             col(k) = row
678:             k=k+1

680:             if (i .lt. mx-1) then
681:                v(k) = hr
682:                col(k) = row + 1
683:                k=k+1
684:             endif

686:             if ((i .gt. 0) .and. (j .lt. my-1)) then
687:                v(k) = htl
688:                col(k) = row + gxm - 1
689:                k=k+1
690:             endif

692:             if (j .lt. my-1) then
693:                v(k) = ht
694:                col(k) = row + gxm
695:                k=k+1
696:             endif

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



704:          enddo
705:       enddo

707: ! restore vectors
708:       call VecRestoreArray(localX,x_v,x_i,ierr)
709:       call VecRestoreArray(Left,left_v,left_i,ierr)
710:       call VecRestoreArray(Right,right_v,right_i,ierr)
711:       call VecRestoreArray(Top,top_v,top_i,ierr)
712:       call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)


715: ! Assemble the matrix
716:       call MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY,ierr)
717:       call MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY,ierr)

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

721:       return
722:       end





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

730: ! ----------------------------------------------------------------------------
731: !
732: !/*
733: !     MSA_BoundaryConditions - calculates the boundary conditions for the region
734: !
735: !
736: !*/

738:       subroutine MSA_BoundaryConditions(ierr)
739: #include "plate2f.h"

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

757:       limit=0
758:       maxits = 5
759:       tol=1e-10
760:       b=-0.5
761:       t= 0.5
762:       l=-0.5
763:       r= 0.5
764:       xt=0
765:       yt=0
766:       one=1.0
767:       two=2.0
768:       three=3.0


771:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
772:      &                  PETSC_NULL_INTEGER,ierr)
773:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,              &
774:      &                       gxm,gym,PETSC_NULL_INTEGER,ierr)

776:       bsize = xm + 2
777:       lsize = ym + 2
778:       rsize = ym + 2
779:       tsize = xm + 2


782:       call VecCreateMPI(MPI_COMM_WORLD,bsize,PETSC_DECIDE,Bottom,ierr)
783:       call VecCreateMPI(MPI_COMM_WORLD,tsize,PETSC_DECIDE,Top,ierr)
784:       call VecCreateMPI(MPI_COMM_WORLD,lsize,PETSC_DECIDE,Left,ierr)
785:       call VecCreateMPI(MPI_COMM_WORLD,rsize,PETSC_DECIDE,Right,ierr)

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

790:       do j=0,3

792:          if (j.eq.0) then
793:             yt=b
794:             xt=l+hx*xs
795:             limit=bsize
796:             call VecGetArray(Bottom,boundary_v,boundary_i,ierr)


799:          elseif (j.eq.1) then
800:             yt=t
801:             xt=l+hx*xs
802:             limit=tsize
803:             call VecGetArray(Top,boundary_v,boundary_i,ierr)

805:          elseif (j.eq.2) then
806:             yt=b+hy*ys
807:             xt=l
808:             limit=lsize
809:             call VecGetArray(Left,boundary_v,boundary_i,ierr)

811:          elseif (j.eq.3) then
812:             yt=b+hy*ys
813:             xt=r
814:             limit=rsize
815:             call VecGetArray(Right,boundary_v,boundary_i,ierr)
816:          endif


819:          do i=0,limit-1

821:             u1=xt
822:             u2=-yt
823:             k = 0
824:             exitloop = .false.
825:             do while (k .lt. maxits .and. (.not. exitloop) )

827:                nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt
828:                nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt
829:                fnorm=sqrt(nf1*nf1+nf2*nf2)
830:                if (fnorm .gt. tol) then
831:                   njac11=one+u2*u2-u1*u1
832:                   njac12=two*u1*u2
833:                   njac21=-two*u1*u2
834:                   njac22=-one - u1*u1 + u2*u2
835:                   det = njac11*njac22-njac21*njac12
836:                   u1 = u1-(njac22*nf1-njac12*nf2)/det
837:                   u2 = u2-(njac11*nf2-njac21*nf1)/det
838:                else
839:                   exitloop = .true.
840:                endif
841:                k=k+1
842:             enddo

844:             boundary_v(i + boundary_i) = u1*u1-u2*u2
845:             if ((j .eq. 0) .or. (j .eq. 1)) then
846:                xt = xt + hx
847:             else
848:                yt = yt + hy
849:             endif

851:          enddo


854:          if (j.eq.0) then
855:             call VecRestoreArray(Bottom,boundary_v,boundary_i,ierr)
856:          elseif (j.eq.1) then
857:             call VecRestoreArray(Top,boundary_v,boundary_i,ierr)
858:          elseif (j.eq.2) then
859:             call VecRestoreArray(Left,boundary_v,boundary_i,ierr)
860:          elseif (j.eq.3) then
861:             call VecRestoreArray(Right,boundary_v,boundary_i,ierr)
862:          endif

864:       enddo


867: ! Scale the boundary if desired
868:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,          &
869:      &                         '-bottom',scl,flg,ierr)
870:       if (flg .eqv. PETSC_TRUE) then
871:          call VecScale(Bottom,scl,ierr)
872:       endif

874:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,          &
875:      &                         '-top',scl,flg,ierr)
876:       if (flg .eqv. PETSC_TRUE) then
877:          call VecScale(Top,scl,ierr)
878:       endif

880:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,          &
881:      &                         '-right',scl,flg,ierr)
882:       if (flg .eqv. PETSC_TRUE) then
883:          call VecScale(Right,scl,ierr)
884:       endif

886:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,          &
887:      &                         '-left',scl,flg,ierr)
888:       if (flg .eqv. PETSC_TRUE) then
889:          call VecScale(Left,scl,ierr)
890:       endif


893:       return
894:       end

896: ! ----------------------------------------------------------------------------
897: !
898: !/*
899: !     MSA_Plate - Calculates an obstacle for surface to stretch over
900: !
901: !     Output Parameter:
902: !.    xl - lower bound vector
903: !.    xu - upper bound vector
904: !
905: !*/

907:       subroutine MSA_Plate(tao,xl,xu,dummy,ierr)
908: #include "plate2f.h"

910:       Tao        tao
911:       Vec              xl,xu
912:       PetscErrorCode   ierr
913:       PetscInt         i,j,row
914:       PetscInt         xs, xm, ys, ym
915:       PetscReal      lb,ub
916:       PetscInt         dummy

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

926:       print *,'msa_plate'

928:       lb = PETSC_NINFINITY
929:       ub = PETSC_INFINITY

931:       if (bmy .lt. 0) bmy = 0
932:       if (bmy .gt. my) bmy = my
933:       if (bmx .lt. 0) bmx = 0
934:       if (bmx .gt. mx) bmx = mx


937:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
938:      &             PETSC_NULL_INTEGER,ierr)

940:       call VecSet(xl,lb,ierr)
941:       call VecSet(xu,ub,ierr)

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


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

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

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

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

956:             endif

958:          enddo
959:       enddo


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

964:       return
965:       end





971: ! ----------------------------------------------------------------------------
972: !
973: !/*
974: !     MSA_InitialPoint - Calculates an obstacle for surface to stretch over
975: !
976: !     Output Parameter:
977: !.    X - vector for initial guess
978: !
979: !*/

981:       subroutine MSA_InitialPoint(X, ierr)
982: #include "plate2f.h"

984:       Vec               X
985:       PetscErrorCode    ierr
986:       PetscInt          start,i,j
987:       PetscInt          row
988:       PetscInt          xs,xm,gxs,gxm
989:       PetscInt          ys,ym,gys,gym
990:       PetscReal       zero, np5

992: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
993: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (integer) x_index, ierr)
994: ! will return an array of doubles referenced by x_array offset by x_index.
995: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
996: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
997:       PetscReal   left_v(0:1),right_v(0:1)
998:       PetscReal   bottom_v(0:1),top_v(0:1)
999:       PetscReal   x_v(0:1)
1000:       PetscOffset   left_i, right_i, top_i
1001:       PetscOffset   bottom_i,x_i
1002:       PetscBool     flg
1003:       PetscRandom   rctx

1005:       zero = 0.0
1006:       np5 = -0.5

1008:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,        &
1009:      &                        '-start', start,flg,ierr)

1011:       if ((flg .eqv. PETSC_TRUE) .and. (start .eq. 0)) then  ! the zero vector is reasonable
1012:          call VecSet(X,zero,ierr)

1014:       elseif ((flg .eqv. PETSC_TRUE) .and. (start .gt. 0)) then  ! random start -0.5 < xi < 0.5
1015:          call PetscRandomCreate(MPI_COMM_WORLD,rctx,ierr)
1016:          do i=0,start-1
1017:             call VecSetRandom(X,rctx,ierr)
1018:          enddo

1020:          call PetscRandomDestroy(rctx,ierr)
1021:          call VecShift(X,np5,ierr)

1023:       else   ! average of boundary conditions

1025: !        Get Local mesh boundaries
1026:          call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,             &
1027:      &                     PETSC_NULL_INTEGER,ierr)
1028:          call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,    &
1029:      &                     PETSC_NULL_INTEGER,ierr)



1033: !        Get pointers to vector data
1034:          call VecGetArray(Top,top_v,top_i,ierr)
1035:          call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
1036:          call VecGetArray(Left,left_v,left_i,ierr)
1037:          call VecGetArray(Right,right_v,right_i,ierr)

1039:          call VecGetArray(localX,x_v,x_i,ierr)

1041: !        Perform local computations
1042:          do  j=ys,ys+ym-1
1043:             do i=xs,xs+xm-1
1044:                row = (j-gys)*gxm  + (i-gxs)
1045:                x_v(x_i + row) = ((j+1)*bottom_v(bottom_i +i-xs+1)/my        &
1046:      &             + (my-j+1)*top_v(top_i+i-xs+1)/(my+2) +                  &
1047:      &              (i+1)*left_v(left_i+j-ys+1)/mx       +                  &
1048:      &              (mx-i+1)*right_v(right_i+j-ys+1)/(mx+2))*0.5
1049:             enddo
1050:          enddo

1052: !        Restore vectors
1053:          call VecRestoreArray(localX,x_v,x_i,ierr)

1055:          call VecRestoreArray(Left,left_v,left_i,ierr)
1056:          call VecRestoreArray(Top,top_v,top_i,ierr)
1057:          call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)
1058:          call VecRestoreArray(Right,right_v,right_i,ierr)

1060:          call DMLocalToGlobalBegin(dm,localX,INSERT_VALUES,X,ierr)
1061:          call DMLocalToGlobalEnd(dm,localX,INSERT_VALUES,X,ierr)

1063:       endif

1065:       return
1066:       end