Actual source code: plate2f.F90

  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: !

 16:       module plate2fmodule
 17: #include "petsc/finclude/petscdmda.h"
 18: #include "petsc/finclude/petsctao.h"
 19:       use petscdmda
 20:       use petsctao

 22:       Vec              localX, localV
 23:       Vec              Top, Left
 24:       Vec              Right, Bottom
 25:       DM               dm
 26:       PetscReal      bheight
 27:       PetscInt         bmx, bmy
 28:       PetscInt         mx, my, Nx, Ny, N
 29:       end module

 31: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 32: !                   Variable declarations
 33: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 34: !
 35: !  Variables:
 36: !    (common from plate2f.h):
 37: !    Nx, Ny           number of processors in x- and y- directions
 38: !    mx, my           number of grid points in x,y directions
 39: !    N    global dimension of vector
 40:       use plate2fmodule
 41:       implicit none

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

 52:       external FormFunctionGradient
 53:       external FormHessian
 54:       external MSA_BoundaryConditions
 55:       external MSA_Plate
 56:       external MSA_InitialPoint
 57: ! Initialize Tao

 59:       i1=1
 60:       i3=3
 61:       i7=7

 63:       PetscCallA(PetscInitialize(ierr))

 65: ! Specify default dimensions of the problem
 66:       mx = 10
 67:       my = 10
 68:       bheight = 0.1

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

 72:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-mx',mx,flg,ierr))
 73:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my',my,flg,ierr))

 75:       bmx = mx/2
 76:       bmy = my/2

 78:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-bmx',bmx,flg,ierr))
 79:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-bmy',bmy,flg,ierr))
 80:       PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-bheight',bheight,flg,ierr))

 82: ! Calculate any derived values from parameters
 83:       N = mx*my

 85: ! Let Petsc determine the dimensions of the local vectors
 86:       Nx = PETSC_DECIDE
 87:       NY = PETSC_DECIDE

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

 93:       PetscCallA(DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE, DMDA_STENCIL_BOX,mx,my,Nx,Ny,i1,i1,PETSC_NULL_INTEGER_ARRAY,PETSC_NULL_INTEGER_ARRAY,dm,ierr))
 94:       PetscCallA(DMSetFromOptions(dm,ierr))
 95:       PetscCallA(DMSetUp(dm,ierr))

 97: ! Extract global and local vectors from DM; The local vectors are
 98: ! used solely as work space for the evaluation of the function,
 99: ! gradient, and Hessian.  Duplicate for remaining vectors that are
100: ! the same types.

102:       PetscCallA(DMCreateGlobalVector(dm,x,ierr))
103:       PetscCallA(DMCreateLocalVector(dm,localX,ierr))
104:       PetscCallA(VecDuplicate(localX,localV,ierr))

106: ! Create a matrix data structure to store the Hessian.
107: ! Here we (optionally) also associate the local numbering scheme
108: ! with the matrix so that later we can use local indices for matrix
109: ! assembly

111:       PetscCallA(VecGetLocalSize(x,m,ierr))
112:       PetscCallA(MatCreateAIJ(PETSC_COMM_WORLD,m,m,N,N,i7,PETSC_NULL_INTEGER_ARRAY,i3,PETSC_NULL_INTEGER_ARRAY,H,ierr))

114:       PetscCallA(MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr))
115:       PetscCallA(DMGetLocalToGlobalMapping(dm,isltog,ierr))
116:       PetscCallA(MatSetLocalToGlobalMapping(H,isltog,isltog,ierr))

118: ! The Tao code begins here
119: ! Create TAO solver and set desired solution method.
120: ! This problems uses bounded variables, so the
121: ! method must either be 'tao_tron' or 'tao_blmvm'

123:       PetscCallA(TaoCreate(PETSC_COMM_WORLD,tao,ierr))
124:       PetscCallA(TaoSetType(tao,TAOBLMVM,ierr))

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

128:       PetscCallA(TaoSetObjectiveAndGradient(tao,PETSC_NULL_VEC,FormFunctionGradient,0,ierr))

130:       PetscCallA(TaoSetHessian(tao,H,H,FormHessian,0, ierr))

132: ! Set Variable bounds
133:       PetscCallA(MSA_BoundaryConditions(ierr))
134:       PetscCallA(TaoSetVariableBoundsRoutine(tao,MSA_Plate,0,ierr))

136: ! Set the initial solution guess
137:       PetscCallA(MSA_InitialPoint(x, ierr))
138:       PetscCallA(TaoSetSolution(tao,x,ierr))

140: ! Check for any tao command line options
141:       PetscCallA(TaoSetFromOptions(tao,ierr))

143: ! Solve the application
144:       PetscCallA(TaoSolve(tao,ierr))

146: ! Free TAO data structures
147:       PetscCallA(TaoDestroy(tao,ierr))

149: ! Free PETSc data structures
150:       PetscCallA(VecDestroy(x,ierr))
151:       PetscCallA(VecDestroy(Top,ierr))
152:       PetscCallA(VecDestroy(Bottom,ierr))
153:       PetscCallA(VecDestroy(Left,ierr))
154:       PetscCallA(VecDestroy(Right,ierr))
155:       PetscCallA(MatDestroy(H,ierr))
156:       PetscCallA(VecDestroy(localX,ierr))
157:       PetscCallA(VecDestroy(localV,ierr))
158:       PetscCallA(DMDestroy(dm,ierr))

160: ! Finalize TAO

162:       PetscCallA(PetscFinalize(ierr))

164:       end

166: ! ---------------------------------------------------------------------
167: !
168: !  FormFunctionGradient - Evaluates function f(X).
169: !
170: !  Input Parameters:
171: !  tao   - the Tao context
172: !  X     - the input vector
173: !  dummy - optional user-defined context, as set by TaoSetFunction()
174: !          (not used here)
175: !
176: !  Output Parameters:
177: !  fcn     - the newly evaluated function
178: !  G       - the gradient vector
179: !  info  - error code
180: !

182:       subroutine FormFunctionGradient(tao,X,fcn,G,dummy,ierr)
183:       use plate2fmodule
184:       implicit none

186: ! Input/output variables

188:       Tao        tao
189:       PetscReal      fcn
190:       Vec              X, G
191:       PetscErrorCode   ierr
192:       PetscInt         dummy

194:       PetscInt         i,j,row
195:       PetscInt         xs, xm
196:       PetscInt         gxs, gxm
197:       PetscInt         ys, ym
198:       PetscInt         gys, gym
199:       PetscReal      ft,zero,hx,hy,hydhx,hxdhy
200:       PetscReal      area,rhx,rhy
201:       PetscReal      f1,f2,f3,f4,f5,f6,d1,d2,d3
202:       PetscReal      d4,d5,d6,d7,d8
203:       PetscReal      df1dxc,df2dxc,df3dxc,df4dxc
204:       PetscReal      df5dxc,df6dxc
205:       PetscReal      xc,xl,xr,xt,xb,xlt,xrb

207:       PetscReal, pointer :: g_v(:),x_v(:)
208:       PetscReal, pointer :: top_v(:),left_v(:)
209:       PetscReal, pointer :: right_v(:),bottom_v(:)

211:       ft = 0.0
212:       zero = 0.0
213:       hx = 1.0/real(mx + 1)
214:       hy = 1.0/real(my + 1)
215:       hydhx = hy/hx
216:       hxdhy = hx/hy
217:       area = 0.5 * hx * hy
218:       rhx = real(mx) + 1.0
219:       rhy = real(my) + 1.0

221: ! Get local mesh boundaries
222:       PetscCall(DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr))
223:       PetscCall(DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr))

225: ! Scatter ghost points to local vector
226:       PetscCall(DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr))
227:       PetscCall(DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr))

229: ! Initialize the vector to zero
230:       PetscCall(VecSet(localV,zero,ierr))

232: ! Get arrays to vector data (See note above about using VecGetArrayF90 in Fortran)
233:       PetscCall(VecGetArrayF90(localX,x_v,ierr))
234:       PetscCall(VecGetArrayF90(localV,g_v,ierr))
235:       PetscCall(VecGetArrayF90(Top,top_v,ierr))
236:       PetscCall(VecGetArrayF90(Bottom,bottom_v,ierr))
237:       PetscCall(VecGetArrayF90(Left,left_v,ierr))
238:       PetscCall(VecGetArrayF90(Right,right_v,ierr))

240: ! Compute function over the locally owned part of the mesh
241:       do j = ys,ys+ym-1
242:          do i = xs,xs+xm-1
243:             row = (j-gys)*gxm + (i-gxs)
244:             xc = x_v(1+row)
245:             xt = xc
246:             xb = xc
247:             xr = xc
248:             xl = xc
249:             xrb = xc
250:             xlt = xc

252:             if (i .eq. 0) then !left side
253:                xl = left_v(1+j - ys + 1)
254:                xlt = left_v(1+j - ys + 2)
255:             else
256:                xl = x_v(1+row - 1)
257:             endif

259:             if (j .eq. 0) then !bottom side
260:                xb = bottom_v(1+i - xs + 1)
261:                xrb = bottom_v(1+i - xs + 2)
262:             else
263:                xb = x_v(1+row - gxm)
264:             endif

266:             if (i + 1 .eq. gxs + gxm) then !right side
267:                xr = right_v(1+j - ys + 1)
268:                xrb = right_v(1+j - ys)
269:             else
270:                xr = x_v(1+row + 1)
271:             endif

273:             if (j + 1 .eq. gys + gym) then !top side
274:                xt = top_v(1+i - xs + 1)
275:                xlt = top_v(1+i - xs)
276:             else
277:                xt = x_v(1+row + gxm)
278:             endif

280:             if ((i .gt. gxs) .and. (j + 1 .lt. gys + gym)) then
281:                xlt = x_v(1+row - 1 + gxm)
282:             endif

284:             if ((j .gt. gys) .and. (i + 1 .lt. gxs + gxm)) then
285:                xrb = x_v(1+row + 1 - gxm)
286:             endif

288:             d1 = xc-xl
289:             d2 = xc-xr
290:             d3 = xc-xt
291:             d4 = xc-xb
292:             d5 = xr-xrb
293:             d6 = xrb-xb
294:             d7 = xlt-xl
295:             d8 = xt-xlt

297:             df1dxc = d1 * hydhx
298:             df2dxc = d1 * hydhx + d4 * hxdhy
299:             df3dxc = d3 * hxdhy
300:             df4dxc = d2 * hydhx + d3 * hxdhy
301:             df5dxc = d2 * hydhx
302:             df6dxc = d4 * hxdhy

304:             d1 = d1 * rhx
305:             d2 = d2 * rhx
306:             d3 = d3 * rhy
307:             d4 = d4 * rhy
308:             d5 = d5 * rhy
309:             d6 = d6 * rhx
310:             d7 = d7 * rhy
311:             d8 = d8 * rhx

313:             f1 = sqrt(1.0 + d1*d1 + d7*d7)
314:             f2 = sqrt(1.0 + d1*d1 + d4*d4)
315:             f3 = sqrt(1.0 + d3*d3 + d8*d8)
316:             f4 = sqrt(1.0 + d3*d3 + d2*d2)
317:             f5 = sqrt(1.0 + d2*d2 + d5*d5)
318:             f6 = sqrt(1.0 + d4*d4 + d6*d6)

320:             ft = ft + f2 + f4

322:             df1dxc = df1dxc / f1
323:             df2dxc = df2dxc / f2
324:             df3dxc = df3dxc / f3
325:             df4dxc = df4dxc / f4
326:             df5dxc = df5dxc / f5
327:             df6dxc = df6dxc / f6

329:             g_v(1+row) = 0.5 * (df1dxc + df2dxc + df3dxc + df4dxc + df5dxc + df6dxc)
330:          enddo
331:       enddo

333: ! Compute triangular areas along the border of the domain.
334:       if (xs .eq. 0) then  ! left side
335:          do j=ys,ys+ym-1
336:             d3 = (left_v(1+j-ys+1) - left_v(1+j-ys+2)) * rhy
337:             d2 = (left_v(1+j-ys+1) - x_v(1+(j-gys)*gxm)) * rhx
338:             ft = ft + sqrt(1.0 + d3*d3 + d2*d2)
339:          enddo
340:       endif

342:       if (ys .eq. 0) then !bottom side
343:          do i=xs,xs+xm-1
344:             d2 = (bottom_v(1+i+1-xs)-bottom_v(1+i-xs+2)) * rhx
345:             d3 = (bottom_v(1+i-xs+1)-x_v(1+i-gxs))*rhy
346:             ft = ft + sqrt(1.0 + d3*d3 + d2*d2)
347:          enddo
348:       endif

350:       if (xs + xm .eq. mx) then ! right side
351:          do j=ys,ys+ym-1
352:             d1 = (x_v(1+(j+1-gys)*gxm-1)-right_v(1+j-ys+1))*rhx
353:             d4 = (right_v(1+j-ys) - right_v(1+j-ys+1))*rhy
354:             ft = ft + sqrt(1.0 + d1*d1 + d4*d4)
355:          enddo
356:       endif

358:       if (ys + ym .eq. my) then
359:          do i=xs,xs+xm-1
360:             d1 = (x_v(1+(gym-1)*gxm+i-gxs) - top_v(1+i-xs+1))*rhy
361:             d4 = (top_v(1+i-xs+1) - top_v(1+i-xs))*rhx
362:             ft = ft + sqrt(1.0 + d1*d1 + d4*d4)
363:          enddo
364:       endif

366:       if ((ys .eq. 0) .and. (xs .eq. 0)) then
367:          d1 = (left_v(1+0) - left_v(1+1)) * rhy
368:          d2 = (bottom_v(1+0)-bottom_v(1+1))*rhx
369:          ft = ft + sqrt(1.0 + d1*d1 + d2*d2)
370:       endif

372:       if ((ys + ym .eq. my) .and. (xs + xm .eq. mx)) then
373:          d1 = (right_v(1+ym+1) - right_v(1+ym))*rhy
374:          d2 = (top_v(1+xm+1) - top_v(1+xm))*rhx
375:          ft = ft + sqrt(1.0 + d1*d1 + d2*d2)
376:       endif

378:       ft = ft * area
379:       PetscCallMPI(MPI_Allreduce(ft,fcn,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD,ierr))

381: ! Restore vectors
382:       PetscCall(VecRestoreArrayF90(localX,x_v,ierr))
383:       PetscCall(VecRestoreArrayF90(localV,g_v,ierr))
384:       PetscCall(VecRestoreArrayF90(Left,left_v,ierr))
385:       PetscCall(VecRestoreArrayF90(Top,top_v,ierr))
386:       PetscCall(VecRestoreArrayF90(Bottom,bottom_v,ierr))
387:       PetscCall(VecRestoreArrayF90(Right,right_v,ierr))

389: ! Scatter values to global vector
390:       PetscCall(DMLocalToGlobalBegin(dm,localV,INSERT_VALUES,G,ierr))
391:       PetscCall(DMLocalToGlobalEnd(dm,localV,INSERT_VALUES,G,ierr))

393:       PetscCall(PetscLogFlops(70.0d0*xm*ym,ierr))

395:       end  !FormFunctionGradient

397: ! ----------------------------------------------------------------------------
398: !
399: !
400: !   FormHessian - Evaluates Hessian matrix.
401: !
402: !   Input Parameters:
403: !.  tao  - the Tao context
404: !.  X    - input vector
405: !.  dummy  - not used
406: !
407: !   Output Parameters:
408: !.  Hessian    - Hessian matrix
409: !.  Hpc    - optionally different preconditioning matrix
410: !
411: !   Notes:
412: !   Due to mesh point reordering with DMs, we must always work
413: !   with the local mesh points, and then transform them to the new
414: !   global numbering with the local-to-global mapping.  We cannot work
415: !   directly with the global numbers for the original uniprocessor mesh!
416: !
417: !      MatSetValuesLocal(), using the local ordering (including
418: !         ghost points!)
419: !         - Then set matrix entries using the local ordering
420: !           by calling MatSetValuesLocal()

422:       subroutine FormHessian(tao, X, Hessian, Hpc, dummy, ierr)
423:       use plate2fmodule
424:       implicit none

426:       Tao     tao
427:       Vec            X
428:       Mat            Hessian,Hpc
429:       PetscInt       dummy
430:       PetscErrorCode ierr

432:       PetscInt       i,j,k,row
433:       PetscInt       xs,xm,gxs,gxm
434:       PetscInt       ys,ym,gys,gym
435:       PetscInt       col(0:6)
436:       PetscReal    hx,hy,hydhx,hxdhy,rhx,rhy
437:       PetscReal    f1,f2,f3,f4,f5,f6,d1,d2,d3
438:       PetscReal    d4,d5,d6,d7,d8
439:       PetscReal    xc,xl,xr,xt,xb,xlt,xrb
440:       PetscReal    hl,hr,ht,hb,hc,htl,hbr

442:       PetscReal,pointer ::  right_v(:),left_v(:)
443:       PetscReal,pointer ::  bottom_v(:),top_v(:)
444:       PetscReal,pointer ::  x_v(:)
445:       PetscReal   v(0:6)
446:       PetscBool     assembled
447:       PetscInt      i1

449:       i1=1

451: ! Set various matrix options
452:       PetscCall(MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE,ierr))

454: ! Get local mesh boundaries
455:       PetscCall(DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr))
456:       PetscCall(DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr))

458: ! Scatter ghost points to local vectors
459:       PetscCall(DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr))
460:       PetscCall(DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr))

462: ! Get pointers to vector data (see note on Fortran arrays above)
463:       PetscCall(VecGetArrayF90(localX,x_v,ierr))
464:       PetscCall(VecGetArrayF90(Top,top_v,ierr))
465:       PetscCall(VecGetArrayF90(Bottom,bottom_v,ierr))
466:       PetscCall(VecGetArrayF90(Left,left_v,ierr))
467:       PetscCall(VecGetArrayF90(Right,right_v,ierr))

469: ! Initialize matrix entries to zero
470:       PetscCall(MatAssembled(Hessian,assembled,ierr))
471:       if (assembled .eqv. PETSC_TRUE) PetscCall(MatZeroEntries(Hessian,ierr))

473:       rhx = real(mx) + 1.0
474:       rhy = real(my) + 1.0
475:       hx = 1.0/rhx
476:       hy = 1.0/rhy
477:       hydhx = hy/hx
478:       hxdhy = hx/hy
479: ! compute Hessian over the locally owned part of the mesh

481:       do  i=xs,xs+xm-1
482:          do  j=ys,ys+ym-1
483:             row = (j-gys)*gxm + (i-gxs)

485:             xc = x_v(1+row)
486:             xt = xc
487:             xb = xc
488:             xr = xc
489:             xl = xc
490:             xrb = xc
491:             xlt = xc

493:             if (i .eq. gxs) then   ! Left side
494:                xl = left_v(1+j - ys + 1)
495:                xlt = left_v(1+j - ys + 2)
496:             else
497:                xl = x_v(1+row -1)
498:             endif

500:             if (j .eq. gys) then ! bottom side
501:                xb = bottom_v(1+i - xs + 1)
502:                xrb = bottom_v(1+i - xs + 2)
503:             else
504:                xb = x_v(1+row - gxm)
505:             endif

507:             if (i+1 .eq. gxs + gxm) then !right side
508:                xr = right_v(1+j - ys + 1)
509:                xrb = right_v(1+j - ys)
510:             else
511:                xr = x_v(1+row + 1)
512:             endif

514:             if (j+1 .eq. gym+gys) then !top side
515:                xt = top_v(1+i - xs + 1)
516:                xlt = top_v(1+i - xs)
517:             else
518:                xt = x_v(1+row + gxm)
519:             endif

521:             if ((i .gt. gxs) .and. (j+1 .lt. gys+gym)) then
522:                xlt = x_v(1+row - 1 + gxm)
523:             endif

525:             if ((i+1 .lt. gxs+gxm) .and. (j .gt. gys)) then
526:                xrb = x_v(1+row + 1 - gxm)
527:             endif

529:             d1 = (xc-xl)*rhx
530:             d2 = (xc-xr)*rhx
531:             d3 = (xc-xt)*rhy
532:             d4 = (xc-xb)*rhy
533:             d5 = (xrb-xr)*rhy
534:             d6 = (xrb-xb)*rhx
535:             d7 = (xlt-xl)*rhy
536:             d8 = (xlt-xt)*rhx

538:             f1 = sqrt(1.0 + d1*d1 + d7*d7)
539:             f2 = sqrt(1.0 + d1*d1 + d4*d4)
540:             f3 = sqrt(1.0 + d3*d3 + d8*d8)
541:             f4 = sqrt(1.0 + d3*d3 + d2*d2)
542:             f5 = sqrt(1.0 + d2*d2 + d5*d5)
543:             f6 = sqrt(1.0 + d4*d4 + d6*d6)

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

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

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

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

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

556:             hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) + hydhx*(1.0+d5*d5)/(f5*f5*f5) +                      &
557:      &           hxdhy*(1.0+d6*d6)/(f6*f6*f6) + (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)- 2*d1*d4)/(f2*f2*f2) +  (hxdhy*(1.0+d2*d2)+   &
558:      &           hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4)

560:             hl = hl * 0.5
561:             hr = hr * 0.5
562:             ht = ht * 0.5
563:             hb = hb * 0.5
564:             hbr = hbr * 0.5
565:             htl = htl * 0.5
566:             hc = hc * 0.5

568:             k = 0

570:             if (j .gt. 0) then
571:                v(k) = hb
572:                col(k) = row - gxm
573:                k=k+1
574:             endif

576:             if ((j .gt. 0) .and. (i .lt. mx-1)) then
577:                v(k) = hbr
578:                col(k) = row-gxm+1
579:                k=k+1
580:             endif

582:             if (i .gt. 0) then
583:                v(k) = hl
584:                col(k) = row - 1
585:                k = k+1
586:             endif

588:             v(k) = hc
589:             col(k) = row
590:             k=k+1

592:             if (i .lt. mx-1) then
593:                v(k) = hr
594:                col(k) = row + 1
595:                k=k+1
596:             endif

598:             if ((i .gt. 0) .and. (j .lt. my-1)) then
599:                v(k) = htl
600:                col(k) = row + gxm - 1
601:                k=k+1
602:             endif

604:             if (j .lt. my-1) then
605:                v(k) = ht
606:                col(k) = row + gxm
607:                k=k+1
608:             endif

610: ! Set matrix values using local numbering, defined earlier in main routine
611:             PetscCall(MatSetValuesLocal(Hessian,i1,[row],k,col,v,INSERT_VALUES,ierr))

613:          enddo
614:       enddo

616: ! restore vectors
617:       PetscCall(VecRestoreArrayF90(localX,x_v,ierr))
618:       PetscCall(VecRestoreArrayF90(Left,left_v,ierr))
619:       PetscCall(VecRestoreArrayF90(Right,right_v,ierr))
620:       PetscCall(VecRestoreArrayF90(Top,top_v,ierr))
621:       PetscCall(VecRestoreArrayF90(Bottom,bottom_v,ierr))

623: ! Assemble the matrix
624:       PetscCall(MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY,ierr))
625:       PetscCall(MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY,ierr))

627:       PetscCall(PetscLogFlops(199.0d0*xm*ym,ierr))

629:       end

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

633: ! ----------------------------------------------------------------------------
634: !
635: !/*
636: !     MSA_BoundaryConditions - calculates the boundary conditions for the region
637: !
638: !
639: !*/

641:       subroutine MSA_BoundaryConditions(ierr)
642:       use plate2fmodule
643:       implicit none

645:       PetscErrorCode   ierr
646:       PetscInt         i,j,k,limit,maxits
647:       PetscInt         xs, xm, gxs, gxm
648:       PetscInt         ys, ym, gys, gym
649:       PetscInt         bsize, lsize
650:       PetscInt         tsize, rsize
651:       PetscReal      one,two,three,tol
652:       PetscReal      scl,fnorm,det,xt
653:       PetscReal      yt,hx,hy,u1,u2,nf1,nf2
654:       PetscReal      njac11,njac12,njac21,njac22
655:       PetscReal      b, t, l, r
656:       PetscReal,pointer :: boundary_v(:)

658:       logical exitloop
659:       PetscBool flg

661:       limit=0
662:       maxits = 5
663:       tol=1e-10
664:       b=-0.5
665:       t= 0.5
666:       l=-0.5
667:       r= 0.5
668:       xt=0
669:       yt=0
670:       one=1.0
671:       two=2.0
672:       three=3.0

674:       PetscCall(DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr))
675:       PetscCall(DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr))

677:       bsize = xm + 2
678:       lsize = ym + 2
679:       rsize = ym + 2
680:       tsize = xm + 2

682:       PetscCall(VecCreateMPI(PETSC_COMM_WORLD,bsize,PETSC_DECIDE,Bottom,ierr))
683:       PetscCall(VecCreateMPI(PETSC_COMM_WORLD,tsize,PETSC_DECIDE,Top,ierr))
684:       PetscCall(VecCreateMPI(PETSC_COMM_WORLD,lsize,PETSC_DECIDE,Left,ierr))
685:       PetscCall(VecCreateMPI(PETSC_COMM_WORLD,rsize,PETSC_DECIDE,Right,ierr))

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

690:       do j=0,3

692:          if (j.eq.0) then
693:             yt=b
694:             xt=l+hx*xs
695:             limit=bsize
696:             PetscCall(VecGetArrayF90(Bottom,boundary_v,ierr))

698:          elseif (j.eq.1) then
699:             yt=t
700:             xt=l+hx*xs
701:             limit=tsize
702:             PetscCall(VecGetArrayF90(Top,boundary_v,ierr))

704:          elseif (j.eq.2) then
705:             yt=b+hy*ys
706:             xt=l
707:             limit=lsize
708:             PetscCall(VecGetArrayF90(Left,boundary_v,ierr))

710:          elseif (j.eq.3) then
711:             yt=b+hy*ys
712:             xt=r
713:             limit=rsize
714:             PetscCall(VecGetArrayF90(Right,boundary_v,ierr))
715:          endif

717:          do i=0,limit-1

719:             u1=xt
720:             u2=-yt
721:             k = 0
722:             exitloop = .false.
723:             do while (k .lt. maxits .and. (.not. exitloop))

725:                nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt
726:                nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt
727:                fnorm=sqrt(nf1*nf1+nf2*nf2)
728:                if (fnorm .gt. tol) then
729:                   njac11=one+u2*u2-u1*u1
730:                   njac12=two*u1*u2
731:                   njac21=-two*u1*u2
732:                   njac22=-one - u1*u1 + u2*u2
733:                   det = njac11*njac22-njac21*njac12
734:                   u1 = u1-(njac22*nf1-njac12*nf2)/det
735:                   u2 = u2-(njac11*nf2-njac21*nf1)/det
736:                else
737:                   exitloop = .true.
738:                endif
739:                k=k+1
740:             enddo

742:             boundary_v(1+i) = u1*u1-u2*u2
743:             if ((j .eq. 0) .or. (j .eq. 1)) then
744:                xt = xt + hx
745:             else
746:                yt = yt + hy
747:             endif

749:          enddo

751:          if (j.eq.0) then
752:             PetscCall(VecRestoreArrayF90(Bottom,boundary_v,ierr))
753:          elseif (j.eq.1) then
754:             PetscCall(VecRestoreArrayF90(Top,boundary_v,ierr))
755:          elseif (j.eq.2) then
756:             PetscCall(VecRestoreArrayF90(Left,boundary_v,ierr))
757:          elseif (j.eq.3) then
758:             PetscCall(VecRestoreArrayF90(Right,boundary_v,ierr))
759:          endif

761:       enddo

763: ! Scale the boundary if desired
764:       PetscCall(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-bottom',scl,flg,ierr))
765:       if (flg .eqv. PETSC_TRUE) then
766:          PetscCall(VecScale(Bottom,scl,ierr))
767:       endif

769:       PetscCall(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-top',scl,flg,ierr))
770:       if (flg .eqv. PETSC_TRUE) then
771:          PetscCall(VecScale(Top,scl,ierr))
772:       endif

774:       PetscCall(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-right',scl,flg,ierr))
775:       if (flg .eqv. PETSC_TRUE) then
776:          PetscCall(VecScale(Right,scl,ierr))
777:       endif

779:       PetscCall(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-left',scl,flg,ierr))
780:       if (flg .eqv. PETSC_TRUE) then
781:          PetscCall(VecScale(Left,scl,ierr))
782:       endif

784:       end

786: ! ----------------------------------------------------------------------------
787: !
788: !/*
789: !     MSA_Plate - Calculates an obstacle for surface to stretch over
790: !
791: !     Output Parameter:
792: !.    xl - lower bound vector
793: !.    xu - upper bound vector
794: !
795: !*/

797:       subroutine MSA_Plate(tao,xl,xu,dummy,ierr)
798:       use plate2fmodule
799:       implicit none

801:       Tao        tao
802:       Vec              xl,xu
803:       PetscErrorCode   ierr
804:       PetscInt         i,j,row
805:       PetscInt         xs, xm, ys, ym
806:       PetscReal      lb,ub
807:       PetscInt         dummy
808:       PetscReal, pointer :: xl_v(:)

810:       lb = PETSC_NINFINITY
811:       ub = PETSC_INFINITY

813:       if (bmy .lt. 0) bmy = 0
814:       if (bmy .gt. my) bmy = my
815:       if (bmx .lt. 0) bmx = 0
816:       if (bmx .gt. mx) bmx = mx

818:       PetscCall(DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr))

820:       PetscCall(VecSet(xl,lb,ierr))
821:       PetscCall(VecSet(xu,ub,ierr))

823:       PetscCall(VecGetArrayF90(xl,xl_v,ierr))

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

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

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

831:             if (i.ge.((mx-bmx)/2) .and. i.lt.(mx-(mx-bmx)/2) .and.           &
832:      &          j.ge.((my-bmy)/2) .and. j.lt.(my-(my-bmy)/2)) then
833:                xl_v(1+row) = bheight

835:             endif

837:          enddo
838:       enddo

840:       PetscCall(VecRestoreArrayF90(xl,xl_v,ierr))

842:       end

844: ! ----------------------------------------------------------------------------
845: !
846: !/*
847: !     MSA_InitialPoint - Calculates an obstacle for surface to stretch over
848: !
849: !     Output Parameter:
850: !.    X - vector for initial guess
851: !
852: !*/

854:       subroutine MSA_InitialPoint(X, ierr)
855:       use plate2fmodule
856:       implicit none

858:       Vec               X
859:       PetscErrorCode    ierr
860:       PetscInt          start,i,j
861:       PetscInt          row
862:       PetscInt          xs,xm,gxs,gxm
863:       PetscInt          ys,ym,gys,gym
864:       PetscReal       zero, np5

866:       PetscReal,pointer :: left_v(:),right_v(:)
867:       PetscReal,pointer :: bottom_v(:),top_v(:)
868:       PetscReal,pointer :: x_v(:)
869:       PetscBool     flg
870:       PetscRandom   rctx

872:       zero = 0.0
873:       np5 = -0.5

875:       PetscCall(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-start', start,flg,ierr))

877:       if ((flg .eqv. PETSC_TRUE) .and. (start .eq. 0)) then  ! the zero vector is reasonable
878:          PetscCall(VecSet(X,zero,ierr))

880:       elseif ((flg .eqv. PETSC_TRUE) .and. (start .gt. 0)) then  ! random start -0.5 < xi < 0.5
881:          PetscCall(PetscRandomCreate(PETSC_COMM_WORLD,rctx,ierr))
882:          do i=0,start-1
883:             PetscCall(VecSetRandom(X,rctx,ierr))
884:          enddo

886:          PetscCall(PetscRandomDestroy(rctx,ierr))
887:          PetscCall(VecShift(X,np5,ierr))

889:       else   ! average of boundary conditions

891: !        Get Local mesh boundaries
892:          PetscCall(DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr))
893:          PetscCall(DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr))

895: !        Get pointers to vector data
896:          PetscCall(VecGetArrayF90(Top,top_v,ierr))
897:          PetscCall(VecGetArrayF90(Bottom,bottom_v,ierr))
898:          PetscCall(VecGetArrayF90(Left,left_v,ierr))
899:          PetscCall(VecGetArrayF90(Right,right_v,ierr))

901:          PetscCall(VecGetArrayF90(localX,x_v,ierr))

903: !        Perform local computations
904:          do  j=ys,ys+ym-1
905:             do i=xs,xs+xm-1
906:                row = (j-gys)*gxm  + (i-gxs)
907:                x_v(1+row) = ((j+1)*bottom_v(1+i-xs+1)/my + (my-j+1)*top_v(1+i-xs+1)/(my+2) +                  &
908:      &                          (i+1)*left_v(1+j-ys+1)/mx + (mx-i+1)*right_v(1+j-ys+1)/(mx+2))*0.5
909:             enddo
910:          enddo

912: !        Restore vectors
913:          PetscCall(VecRestoreArrayF90(localX,x_v,ierr))

915:          PetscCall(VecRestoreArrayF90(Left,left_v,ierr))
916:          PetscCall(VecRestoreArrayF90(Top,top_v,ierr))
917:          PetscCall(VecRestoreArrayF90(Bottom,bottom_v,ierr))
918:          PetscCall(VecRestoreArrayF90(Right,right_v,ierr))

920:          PetscCall(DMLocalToGlobalBegin(dm,localX,INSERT_VALUES,X,ierr))
921:          PetscCall(DMLocalToGlobalEnd(dm,localX,INSERT_VALUES,X,ierr))

923:       endif

925:       end

927: !
928: !/*TEST
929: !
930: !   build:
931: !      requires: !complex
932: !
933: !   test:
934: !      args: -tao_monitor_short -mx 8 -my 6 -bmx 3 -bmy 3 -bheight 0.2 -tao_type bqnls -tao_gatol 1.e-4
935: !      filter: sort -b
936: !      filter_output: sort -b
937: !      requires: !single
938: !
939: !   test:
940: !      suffix: 2
941: !      nsize: 2
942: !      args: -tao_monitor_short -mx 8 -my 6 -bmx 3 -bmy 3 -bheight 0.2 -tao_type bqnls -tao_gatol 1.e-4
943: !      filter: sort -b
944: !      filter_output: sort -b
945: !      requires: !single
946: !
947: !TEST*/