Actual source code: ex39f90.F
1: !
2: ! Description: Solves a nonlinear system in parallel with SNES.
3: ! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
4: ! domain, using distributed arrays (DMDAs) to partition the parallel grid.
5: ! The command line options include:
6: ! -par <parameter>, where <parameter> indicates the nonlinearity of the problem
7: ! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)
8: !
9: ! Modified from ex5f90.F by Mike McCourt <mccomic@iit.edu>
10: ! for testing Fortran interface on
11: ! SNESLineSearchSet(), SNESLineSearchSetPreCheck(), SNESLineSearchSetPostCheck()
12: !
13: ! --------------------------------------------------------------------------
14: !
15: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
16: ! the partial differential equation
17: !
18: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
19: !
20: ! with boundary conditions
21: !
22: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
23: !
24: ! A finite difference approximation with the usual 5-point stencil
25: ! is used to discretize the boundary value problem to obtain a nonlinear
26: ! system of equations.
27: !
28: ! The uniprocessor version of this code is snes/examples/tutorials/ex4f.F
29: !
30: ! --------------------------------------------------------------------------
31: ! The following define must be used before including any PETSc include files
32: ! into a module or interface. This is because they can't handle declarations
33: ! in them
34: !
36: module f90module
37: type userctx
38: #include <finclude/petscsysdef.h>
39: #include <finclude/petscvecdef.h>
40: #include <finclude/petscdmdef.h>
41: DM da
42: integer xs,xe,xm,gxs,gxe,gxm
43: integer ys,ye,ym,gys,gye,gym
44: integer mx,my,rank
45: double precision lambda
46: end type userctx
47: contains
48: ! ---------------------------------------------------------------------
49: !
50: ! FormFunction - Evaluates nonlinear function, F(x).
51: !
52: ! Input Parameters:
53: ! snes - the SNES context
54: ! X - input vector
55: ! dummy - optional user-defined context, as set by SNESSetFunction()
56: ! (not used here)
57: !
58: ! Output Parameter:
59: ! F - function vector
60: !
61: ! Notes:
62: ! This routine serves as a wrapper for the lower-level routine
63: ! "FormFunctionLocal", where the actual computations are
64: ! done using the standard Fortran style of treating the local
65: ! vector data as a multidimensional array over the local mesh.
66: ! This routine merely handles ghost point scatters and accesses
67: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
68: !
69: subroutine FormFunction(snes,X,F,user,ierr)
70: implicit none
72: #include <finclude/petscsys.h>
73: #include <finclude/petscvec.h>
74: #include <finclude/petscdmda.h>
75: #include <finclude/petscis.h>
76: #include <finclude/petscmat.h>
77: #include <finclude/petscksp.h>
78: #include <finclude/petscpc.h>
79: #include <finclude/petscsnes.h>
81: #include <finclude/petscvec.h90>
84: ! Input/output variables:
85: SNES snes
86: Vec X,F
87: integer ierr
88: type (userctx) user
90: ! Declarations for use with local arrays:
91: PetscScalar,pointer :: lx_v(:),lf_v(:)
92: Vec localX
94: write(*,*)"Inside FormFunction, user%xm=",user%xm
96: ! Scatter ghost points to local vector, using the 2-step process
97: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
98: ! By placing code between these two statements, computations can
99: ! be done while messages are in transition.
101: call DMGetLocalVector(user%da,localX,ierr)
102: call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES, &
103: & localX,ierr)
104: call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
106: ! Get a pointer to vector data.
107: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
108: ! the data array. Otherwise, the routine is implementation dependent.
109: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
110: ! the array.
111: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
112: ! and is useable from Fortran-90 Only.
114: call VecGetArrayF90(localX,lx_v,ierr)
115: call VecGetArrayF90(F,lf_v,ierr)
117: ! Compute function over the locally owned part of the grid
119: call FormFunctionLocal(lx_v,lf_v,user,ierr)
121: ! Restore vectors
123: call VecRestoreArrayF90(localX,lx_v,ierr)
124: call VecRestoreArrayF90(F,lf_v,ierr)
126: ! Insert values into global vector
128: call DMRestoreLocalVector(user%da,localX,ierr)
129: call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)
131: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
132: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
134: return
135: end subroutine formfunction
136: end module f90module
140: program main
141: use f90module
142: implicit none
143: !
144: !
145: #include <finclude/petscsys.h>
146: #include <finclude/petscvec.h>
147: #include <finclude/petscdmda.h>
148: #include <finclude/petscis.h>
149: #include <finclude/petscmat.h>
150: #include <finclude/petscksp.h>
151: #include <finclude/petscpc.h>
152: #include <finclude/petscsnes.h>
153: #include <finclude/petscvec.h90>
154: #include <finclude/petscdmda.h90>
156: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: ! Variable declarations
158: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
159: !
160: ! Variables:
161: ! snes - nonlinear solver
162: ! x, r - solution, residual vectors
163: ! J - Jacobian matrix
164: ! its - iterations for convergence
165: ! Nx, Ny - number of preocessors in x- and y- directions
166: ! matrix_free - flag - 1 indicates matrix-free version
167: !
168: !
169: SNES snes
170: Vec x,r
171: Mat J
172: integer its,matrix_free,flg,ierr
173: double precision lambda_max,lambda_min
174: type (userctx) user
175: PetscBool test_linesearch,test_check
177: ! Note: Any user-defined Fortran routines (such as FormJacobian)
178: ! MUST be declared as external.
180: external FormInitialGuess,FormJacobian,FormLineSearch
181: external FormPostCheck,FormPreCheck
183: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184: ! Initialize program
185: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
188: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
190: ! Initialize problem parameters
192: lambda_max = 6.81
193: lambda_min = 0.0
194: user%lambda = 6.0
195: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par', &
196: & user%lambda,flg,ierr)
197: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
198: & then
199: if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
200: SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
201: endif
204: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: ! Create nonlinear solver context
206: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
210: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211: ! Create vector data structures; set function evaluation routine
212: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: ! Create distributed array (DMDA) to manage parallel grid and vectors
216: ! This really needs only the star-type stencil, but we use the box
217: ! stencil temporarily.
218: call DMDACreate2d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE, &
219: & DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX, &
220: & -4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1, &
221: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr)
222: call DMDAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my, &
223: & PETSC_NULL_INTEGER, &
224: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
225: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
226: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
227: & PETSC_NULL_INTEGER,ierr)
228:
229: !
230: ! Visualize the distribution of the array across the processors
231: !
232: ! call DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)
234: ! Extract global and local vectors from DMDA; then duplicate for remaining
235: ! vectors that are the same types
237: call DMCreateGlobalVector(user%da,x,ierr)
238: call VecDuplicate(x,r,ierr)
240: ! Get local grid boundaries (for 2-dimensional DMDA)
242: call DMDAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER, &
243: & user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
244: call DMDAGetGhostCorners(user%da,user%gxs,user%gys, &
245: & PETSC_NULL_INTEGER,user%gxm,user%gym, &
246: & PETSC_NULL_INTEGER,ierr)
248: ! Here we shift the starting indices up by one so that we can easily
249: ! use the Fortran convention of 1-based indices (rather 0-based indices).
251: user%xs = user%xs+1
252: user%ys = user%ys+1
253: user%gxs = user%gxs+1
254: user%gys = user%gys+1
256: user%ye = user%ys+user%ym-1
257: user%xe = user%xs+user%xm-1
258: user%gye = user%gys+user%gym-1
259: user%gxe = user%gxs+user%gxm-1
261: ! Set function evaluation routine and vector
263: call SNESSetFunction(snes,r,FormFunction,user,ierr)
265: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
266: ! Create matrix data structure; set Jacobian evaluation routine
267: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269: ! Set Jacobian matrix data structure and default Jacobian evaluation
270: ! routine. User can override with:
271: ! -snes_fd : default finite differencing approximation of Jacobian
272: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
273: ! (unless user explicitly sets preconditioner)
274: ! -snes_mf_operator : form preconditioning matrix as set by the user,
275: ! but use matrix-free approx for Jacobian-vector
276: ! products within Newton-Krylov method
277: !
278: ! Note: For the parallel case, vectors and matrices MUST be partitioned
279: ! accordingly. When using distributed arrays (DMDAs) to create vectors,
280: ! the DMDAs determine the problem partitioning. We must explicitly
281: ! specify the local matrix dimensions upon its creation for compatibility
282: ! with the vector distribution. Thus, the generic MatCreate() routine
283: ! is NOT sufficient when working with distributed arrays.
284: !
285: ! Note: Here we only approximately preallocate storage space for the
286: ! Jacobian. See the users manual for a discussion of better techniques
287: ! for preallocating matrix memory.
289: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf', &
290: & matrix_free,ierr)
291: if (matrix_free .eq. 0) then
292: call DMGetMatrix(user%da,MATAIJ,J,ierr)
293: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
294: endif
296: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
297: ! Customize nonlinear solver; set runtime options
298: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
300: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
302: call SNESSetFromOptions(snes,ierr)
303: test_linesearch = 0
304: test_check = 0
305: call PetscOptionsGetBool(PETSC_NULL_CHARACTER,'-test_check',
306: & test_check,PETSC_NULL_INTEGER,ierr)
307: if (test_check.eq.1) then
308: call SNESLineSearchSetPreCheck(snes,FormPreCheck,user,ierr)
309: call SNESLineSearchSetPostCheck(snes,FormPostCheck,user,ierr)
310: else
311: call PetscOptionsGetBool(PETSC_NULL_CHARACTER,
312: & '-test_linesearch',test_linesearch,PETSC_NULL_INTEGER,ierr)
313: if (test_linesearch.eq.1) then
314: call SNESLineSearchSet(snes,FormLineSearch,user,ierr)
315: end if
316: end if
317:
318: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
319: ! Evaluate initial guess; then solve nonlinear system.
320: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
322: ! Note: The user should initialize the vector, x, with the initial guess
323: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
324: ! to employ an initial guess of zero, the user should explicitly set
325: ! this vector to zero by calling VecSet().
327: call FormInitialGuess(user,x,ierr)
328: write(*,*)"Before SNESSolve"
329: write(*,*)"user%xm=",user%xm
330: call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
331: call SNESGetIterationNumber(snes,its,ierr);
332: if (user%rank .eq. 0) then
333: write(6,100) its
334: endif
335: 100 format('Number of Newton iterations = ',i5)
337: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
338: ! Free work space. All PETSc objects should be destroyed when they
339: ! are no longer needed.
340: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
342: if (matrix_free .eq. 0) call MatDestroy(J,ierr)
343: call VecDestroy(x,ierr)
344: call VecDestroy(r,ierr)
345: call SNESDestroy(snes,ierr)
346: call DMDestroy(user%da,ierr)
347: call PetscFinalize(ierr)
348: end
350: ! ---------------------------------------------------------------------
351: !
352: ! FormLineSearch - Applies the line search to the step size
353: !
354: subroutine FormLineSearch(snes,user,x,f,g,y,w,fnorm,ynorm,gnorm,
355: & flag,ierr)
357: use f90module
359: #include <finclude/petscsys.h>
360: #include <finclude/petscvec.h>
361: #include <finclude/petscvec.h90>
362: #include <finclude/petscmat.h>
363: #include <finclude/petscmat.h90>
364: #include <finclude/petscksp.h>
365: #include <finclude/petscpc.h>
366: #include <finclude/petscsnes.h>
368: SNES snes
369: type (userctx) user
370: Vec x,f,g,y,w
371: PetscReal fnorm,ynorm,gnorm
372: PetscBool flag
373: PetscErrorCode ierr
375: PetscScalar mone
377: write(*,*)"Inside FormLineSearch, user%xm=",user%xm
378: mone = -1.0d0
379: flag = 0
380: call VecNorm(y,NORM_2,ynorm,ierr)
381: call VecAYPX(y,mone,x,ierr)
382: call SNESComputeFunction(snes,y,g,ierr)
383: call VecNorm(g,NORM_2,gnorm,ierr)
384: return
385: end
387: ! ---------------------------------------------------------------------
388: !
389: ! FormInitialGuess - Forms initial approximation.
390: !
391: ! Input Parameters:
392: ! X - vector
393: !
394: ! Output Parameter:
395: ! X - vector
396: !
397: ! Notes:
398: ! This routine serves as a wrapper for the lower-level routine
399: ! "InitialGuessLocal", where the actual computations are
400: ! done using the standard Fortran style of treating the local
401: ! vector data as a multidimensional array over the local mesh.
402: ! This routine merely handles ghost point scatters and accesses
403: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
404: !
405: subroutine FormInitialGuess(user,X,ierr)
406: use f90module
407: implicit none
409: #include <finclude/petscvec.h90>
410: #include <finclude/petscsys.h>
411: #include <finclude/petscvec.h>
412: #include <finclude/petscdmda.h>
413: #include <finclude/petscis.h>
414: #include <finclude/petscmat.h>
415: #include <finclude/petscksp.h>
416: #include <finclude/petscpc.h>
417: #include <finclude/petscsnes.h>
419: ! Input/output variables:
420: type (userctx) user
421: Vec X
422: integer ierr
423:
424: ! Declarations for use with local arrays:
425: PetscScalar,pointer :: lx_v(:)
426: Vec localX
428: 0
430: ! Get a pointer to vector data.
431: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
432: ! the data array. Otherwise, the routine is implementation dependent.
433: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
434: ! the array.
435: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
436: ! and is useable from Fortran-90 Only.
438: call DMGetLocalVector(user%da,localX,ierr)
439: call VecGetArrayF90(localX,lx_v,ierr)
441: ! Compute initial guess over the locally owned part of the grid
443: call InitialGuessLocal(user,lx_v,ierr)
445: ! Restore vector
447: call VecRestoreArrayF90(localX,lx_v,ierr)
449: ! Insert values into global vector
451: call DMLocalToGlobalBegin(user%da,localX,INSERT_VALUES,X,ierr)
452: call DMLocalToGlobalEnd(user%da,localX,INSERT_VALUES,X,ierr)
453: call DMRestoreLocalVector(user%da,localX,ierr)
455: return
456: end
458: ! ---------------------------------------------------------------------
459: !
460: ! InitialGuessLocal - Computes initial approximation, called by
461: ! the higher level routine FormInitialGuess().
462: !
463: ! Input Parameter:
464: ! x - local vector data
465: !
466: ! Output Parameters:
467: ! x - local vector data
468: ! ierr - error code
469: !
470: ! Notes:
471: ! This routine uses standard Fortran-style computations over a 2-dim array.
472: !
473: subroutine InitialGuessLocal(user,x,ierr)
474: use f90module
475: implicit none
477: #include <finclude/petscsys.h>
478: #include <finclude/petscvec.h>
479: #include <finclude/petscdmda.h>
480: #include <finclude/petscis.h>
481: #include <finclude/petscmat.h>
482: #include <finclude/petscksp.h>
483: #include <finclude/petscpc.h>
484: #include <finclude/petscsnes.h>
486: ! Input/output variables:
487: type (userctx) user
488: PetscScalar x(user%gxs:user%gxe, &
489: & user%gys:user%gye)
490: integer ierr
492: ! Local variables:
493: integer i,j
494: PetscScalar temp1,temp,hx,hy
495: PetscScalar one
497: ! Set parameters
499: 0
500: one = 1.0
501: hx = one/(dble(user%mx-1))
502: hy = one/(dble(user%my-1))
503: temp1 = user%lambda/(user%lambda + one)
505: do 20 j=user%ys,user%ye
506: temp = dble(min(j-1,user%my-j))*hy
507: do 10 i=user%xs,user%xe
508: if (i .eq. 1 .or. j .eq. 1 &
509: & .or. i .eq. user%mx .or. j .eq. user%my) then
510: x(i,j) = 0.0
511: else
512: x(i,j) = temp1 * &
513: & sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
514: endif
515: 10 continue
516: 20 continue
518: return
519: end
521: ! ---------------------------------------------------------------------
522: !
523: ! FormFunctionLocal - Computes nonlinear function, called by
524: ! the higher level routine FormFunction().
525: !
526: ! Input Parameter:
527: ! x - local vector data
528: !
529: ! Output Parameters:
530: ! f - local vector data, f(x)
531: ! ierr - error code
532: !
533: ! Notes:
534: ! This routine uses standard Fortran-style computations over a 2-dim array.
535: !
536: subroutine FormFunctionLocal(x,f,user,ierr)
537: use f90module
539: implicit none
541: ! Input/output variables:
542: type (userctx) user
543: PetscScalar x(user%gxs:user%gxe, &
544: & user%gys:user%gye)
545: PetscScalar f(user%xs:user%xe, &
546: & user%ys:user%ye)
547: integer ierr
549: ! Local variables:
550: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
551: PetscScalar u,uxx,uyy
552: integer i,j
554: one = 1.0
555: two = 2.0
556: hx = one/dble(user%mx-1)
557: hy = one/dble(user%my-1)
558: sc = hx*hy*user%lambda
559: hxdhy = hx/hy
560: hydhx = hy/hx
562: ! Compute function over the locally owned part of the grid
564: do 20 j=user%ys,user%ye
565: do 10 i=user%xs,user%xe
566: if (i .eq. 1 .or. j .eq. 1 &
567: & .or. i .eq. user%mx .or. j .eq. user%my) then
568: f(i,j) = x(i,j)
569: else
570: u = x(i,j)
571: uxx = hydhx * (two*u &
572: & - x(i-1,j) - x(i+1,j))
573: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
574: f(i,j) = uxx + uyy - sc*exp(u)
575: endif
576: 10 continue
577: 20 continue
579: return
580: end
582: ! ---------------------------------------------------------------------
583: !
584: ! FormJacobian - Evaluates Jacobian matrix.
585: !
586: ! Input Parameters:
587: ! snes - the SNES context
588: ! x - input vector
589: ! dummy - optional user-defined context, as set by SNESSetJacobian()
590: ! (not used here)
591: !
592: ! Output Parameters:
593: ! jac - Jacobian matrix
594: ! jac_prec - optionally different preconditioning matrix (not used here)
595: ! flag - flag indicating matrix structure
596: !
597: ! Notes:
598: ! This routine serves as a wrapper for the lower-level routine
599: ! "FormJacobianLocal", where the actual computations are
600: ! done using the standard Fortran style of treating the local
601: ! vector data as a multidimensional array over the local mesh.
602: ! This routine merely accesses the local vector data via
603: ! VecGetArrayF90() and VecRestoreArrayF90().
604: !
605: ! Notes:
606: ! Due to grid point reordering with DMDAs, we must always work
607: ! with the local grid points, and then transform them to the new
608: ! global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
609: ! We cannot work directly with the global numbers for the original
610: ! uniprocessor grid!
611: !
612: ! Two methods are available for imposing this transformation
613: ! when setting matrix entries:
614: ! (A) MatSetValuesLocal(), using the local ordering (including
615: ! ghost points!)
616: ! - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
617: ! - Associate this map with the matrix by calling
618: ! MatSetLocalToGlobalMapping() once
619: ! - Set matrix entries using the local ordering
620: ! by calling MatSetValuesLocal()
621: ! (B) MatSetValues(), using the global ordering
622: ! - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
623: ! - Then apply this map explicitly yourself
624: ! - Set matrix entries using the global ordering by calling
625: ! MatSetValues()
626: ! Option (A) seems cleaner/easier in many cases, and is the procedure
627: ! used in this example.
628: !
629: subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
630: use f90module
631: implicit none
633: #include <finclude/petscsys.h>
634: #include <finclude/petscvec.h>
635: #include <finclude/petscdmda.h>
636: #include <finclude/petscis.h>
637: #include <finclude/petscmat.h>
638: #include <finclude/petscksp.h>
639: #include <finclude/petscpc.h>
640: #include <finclude/petscsnes.h>
642: #include <finclude/petscvec.h90>
644: ! Input/output variables:
645: SNES snes
646: Vec X
647: Mat jac,jac_prec
648: MatStructure flag
649: type(userctx) user
650: integer ierr
652: ! Declarations for use with local arrays:
653: PetscScalar,pointer :: lx_v(:)
654: Vec localX
656: ! Scatter ghost points to local vector, using the 2-step process
657: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
658: ! Computations can be done while messages are in transition,
659: ! by placing code between these two statements.
661: call DMGetLocalVector(user%da,localX,ierr)
662: call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX, &
663: & ierr)
664: call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
666: ! Get a pointer to vector data
668: call VecGetArrayF90(localX,lx_v,ierr)
670: ! Compute entries for the locally owned part of the Jacobian.
672: call FormJacobianLocal(lx_v,jac,jac_prec,user,ierr)
674: ! Assemble matrix, using the 2-step process:
675: ! MatAssemblyBegin(), MatAssemblyEnd()
676: ! Computations can be done while messages are in transition,
677: ! by placing code between these two statements.
679: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
680: call VecRestoreArrayF90(localX,lx_v,ierr)
681: call DMRestoreLocalVector(user%da,localX,ierr)
682: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
684: ! Set flag to indicate that the Jacobian matrix retains an identical
685: ! nonzero structure throughout all nonlinear iterations (although the
686: ! values of the entries change). Thus, we can save some work in setting
687: ! up the preconditioner (e.g., no need to redo symbolic factorization for
688: ! ILU/ICC preconditioners).
689: ! - If the nonzero structure of the matrix is different during
690: ! successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
691: ! must be used instead. If you are unsure whether the matrix
692: ! structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
693: ! - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
694: ! believes your assertion and does not check the structure
695: ! of the matrix. If you erroneously claim that the structure
696: ! is the same when it actually is not, the new preconditioner
697: ! will not function correctly. Thus, use this optimization
698: ! feature with caution!
700: flag = SAME_NONZERO_PATTERN
702: ! Tell the matrix we will never add a new nonzero location to the
703: ! matrix. If we do it will generate an error.
705: ! call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,ierr)
707: return
708: end
710: ! ---------------------------------------------------------------------
711: !
712: ! FormJacobianLocal - Computes Jacobian matrix, called by
713: ! the higher level routine FormJacobian().
714: !
715: ! Input Parameters:
716: ! x - local vector data
717: !
718: ! Output Parameters:
719: ! jac - Jacobian matrix
720: ! jac_prec - optionally different preconditioning matrix (not used here)
721: ! ierr - error code
722: !
723: ! Notes:
724: ! This routine uses standard Fortran-style computations over a 2-dim array.
725: !
726: ! Notes:
727: ! Due to grid point reordering with DMDAs, we must always work
728: ! with the local grid points, and then transform them to the new
729: ! global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
730: ! We cannot work directly with the global numbers for the original
731: ! uniprocessor grid!
732: !
733: ! Two methods are available for imposing this transformation
734: ! when setting matrix entries:
735: ! (A) MatSetValuesLocal(), using the local ordering (including
736: ! ghost points!)
737: ! - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
738: ! - Associate this map with the matrix by calling
739: ! MatSetLocalToGlobalMapping() once
740: ! - Set matrix entries using the local ordering
741: ! by calling MatSetValuesLocal()
742: ! (B) MatSetValues(), using the global ordering
743: ! - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
744: ! - Then apply this map explicitly yourself
745: ! - Set matrix entries using the global ordering by calling
746: ! MatSetValues()
747: ! Option (A) seems cleaner/easier in many cases, and is the procedure
748: ! used in this example.
749: !
750: subroutine FormJacobianLocal(x,jac,jac_prec,user,ierr)
751: use f90module
752: implicit none
754: #include <finclude/petscsys.h>
755: #include <finclude/petscvec.h>
756: #include <finclude/petscdmda.h>
757: #include <finclude/petscis.h>
758: #include <finclude/petscmat.h>
759: #include <finclude/petscksp.h>
760: #include <finclude/petscpc.h>
761: #include <finclude/petscsnes.h>
763: ! Input/output variables:
764: type (userctx) user
765: PetscScalar x(user%gxs:user%gxe, &
766: & user%gys:user%gye)
767: Mat jac,jac_prec
768: integer ierr
770: ! Local variables:
771: integer row,col(5),i,j
772: PetscScalar two,one,hx,hy,hxdhy
773: PetscScalar hydhx,sc,v(5)
775: ! Set parameters
777: one = 1.0
778: two = 2.0
779: hx = one/dble(user%mx-1)
780: hy = one/dble(user%my-1)
781: sc = hx*hy
782: hxdhy = hx/hy
783: hydhx = hy/hx
785: ! Compute entries for the locally owned part of the Jacobian.
786: ! - Currently, all PETSc parallel matrix formats are partitioned by
787: ! contiguous chunks of rows across the processors.
788: ! - Each processor needs to insert only elements that it owns
789: ! locally (but any non-local elements will be sent to the
790: ! appropriate processor during matrix assembly).
791: ! - Here, we set all entries for a particular row at once.
792: ! - We can set matrix entries either using either
793: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
794: ! - Note that MatSetValues() uses 0-based row and column numbers
795: ! in Fortran as well as in C.
797: do 20 j=user%ys,user%ye
798: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
799: do 10 i=user%xs,user%xe
800: row = row + 1
801: ! boundary points
802: if (i .eq. 1 .or. j .eq. 1 &
803: & .or. i .eq. user%mx .or. j .eq. user%my) then
804: col(1) = row
805: v(1) = one
806: call MatSetValuesLocal(jac,1,row,1,col,v, &
807: & INSERT_VALUES,ierr)
808: ! interior grid points
809: else
810: v(1) = -hxdhy
811: v(2) = -hydhx
812: v(3) = two*(hydhx + hxdhy) &
813: & - sc*user%lambda*exp(x(i,j))
814: v(4) = -hydhx
815: v(5) = -hxdhy
816: col(1) = row - user%gxm
817: col(2) = row - 1
818: col(3) = row
819: col(4) = row + 1
820: col(5) = row + user%gxm
821: call MatSetValuesLocal(jac,1,row,5,col,v, &
822: & INSERT_VALUES,ierr)
823: endif
824: 10 continue
825: 20 continue
827: return
828: end
830: subroutine FormPreCheck(snes,X,Y,user,changed_Y,ierr)
831: use f90module
833: SNES snes
834: Vec X,Y
835: type (userctx) user
836: PetscBool changed_Y
837: PetscErrorCode ierr
839: write(*,*)"Inside formPreCheck, user%xm=",user%xm
840: end subroutine formPreCheck
842: subroutine FormPostCheck(snes,X,Y,W,user,changed_Y,changed_W,ierr)
843: use f90module
845: SNES snes
846: Vec X,Y,W
847: type (userctx) user
848: PetscBool changed_Y,changed_W
849: PetscErrorCode ierr
851: write(*,*)"Inside formPostCheck, user%xm=",user%xm
852: end subroutine formPostCheck