Actual source code: ex5f90t.F90
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: !/*T
10: ! Concepts: SNES^parallel Bratu example
11: ! Concepts: DMDA^using distributed arrays;
12: ! Processors: n
13: ! TODO: Need to update to latest API
14: !T*/
15: !
16: ! --------------------------------------------------------------------------
17: !
18: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
19: ! the partial differential equation
20: !
21: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
22: !
23: ! with boundary conditions
24: !
25: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
26: !
27: ! A finite difference approximation with the usual 5-point stencil
28: ! is used to discretize the boundary value problem to obtain a nonlinear
29: ! system of equations.
30: !
31: ! The uniprocessor version of this code is snes/tutorials/ex4f.F
32: !
33: ! --------------------------------------------------------------------------
34: ! The following define must be used before including any PETSc include files
35: ! into a module or interface. This is because they can't handle declarations
36: ! in them
37: !
39: module f90modulet
40: #include <petsc/finclude/petscdm.h>
41: use petscdmdef
42: type userctx
43: type(tDM) da
44: PetscInt xs,xe,xm,gxs,gxe,gxm
45: PetscInt ys,ye,ym,gys,gye,gym
46: PetscInt mx,my
47: PetscMPIInt rank
48: PetscReal lambda
49: end type userctx
51: contains
52: ! ---------------------------------------------------------------------
53: !
54: ! FormFunction - Evaluates nonlinear function, F(x).
55: !
56: ! Input Parameters:
57: ! snes - the SNES context
58: ! X - input vector
59: ! dummy - optional user-defined context, as set by SNESSetFunction()
60: ! (not used here)
61: !
62: ! Output Parameter:
63: ! F - function vector
64: !
65: ! Notes:
66: ! This routine serves as a wrapper for the lower-level routine
67: ! "FormFunctionLocal", where the actual computations are
68: ! done using the standard Fortran style of treating the local
69: ! vector data as a multidimensional array over the local mesh.
70: ! This routine merely handles ghost point scatters and accesses
71: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
72: !
73: subroutine FormFunction(snesIn,X,F,user,ierr)
74: #include <petsc/finclude/petscsnes.h>
75: use petscsnes
77: ! Input/output variables:
78: type(tSNES) snesIn
79: type(tVec) X,F
80: PetscErrorCode ierr
81: type (userctx) user
83: ! Declarations for use with local arrays:
84: PetscScalar,pointer :: lx_v(:),lf_v(:)
85: type(tVec) localX
87: ! Scatter ghost points to local vector, using the 2-step process
88: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
89: ! By placing code between these two statements, computations can
90: ! be done while messages are in transition.
91: call DMGetLocalVector(user%da,localX,ierr);CHKERRQ(ierr)
92: call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
93: call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
95: ! Get a pointer to vector data.
96: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
97: ! the data array. Otherwise, the routine is implementation dependent.
98: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
99: ! the array.
100: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
101: ! and is useable from Fortran-90 Only.
103: call VecGetArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
104: call VecGetArrayF90(F,lf_v,ierr);CHKERRQ(ierr)
106: ! Compute function over the locally owned part of the grid
107: call FormFunctionLocal(lx_v,lf_v,user,ierr);CHKERRQ(ierr)
109: ! Restore vectors
110: call VecRestoreArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
111: call VecRestoreArrayF90(F,lf_v,ierr);CHKERRQ(ierr)
113: ! Insert values into global vector
115: call DMRestoreLocalVector(user%da,localX,ierr);CHKERRQ(ierr)
116: call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)
118: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
119: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
120: return
121: end subroutine formfunction
122: end module f90modulet
124: module f90moduleinterfacest
125: use f90modulet
127: Interface SNESSetApplicationContext
128: Subroutine SNESSetApplicationContext(snesIn,ctx,ierr)
129: #include <petsc/finclude/petscsnes.h>
130: use petscsnes
131: use f90modulet
132: type(tSNES) snesIn
133: type(userctx) ctx
134: PetscErrorCode ierr
135: End Subroutine
136: End Interface SNESSetApplicationContext
138: Interface SNESGetApplicationContext
139: Subroutine SNESGetApplicationContext(snesIn,ctx,ierr)
140: #include <petsc/finclude/petscsnes.h>
141: use petscsnes
142: use f90modulet
143: type(tSNES) snesIn
144: type(userctx), pointer :: ctx
145: PetscErrorCode ierr
146: End Subroutine
147: End Interface SNESGetApplicationContext
148: end module f90moduleinterfacest
150: program main
151: #include <petsc/finclude/petscdm.h>
152: #include <petsc/finclude/petscsnes.h>
153: use petscdmda
154: use petscdm
155: use petscsnes
156: use f90modulet
157: use f90moduleinterfacest
158: implicit none
159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: ! Variable declarations
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: !
163: ! Variables:
164: ! mysnes - nonlinear solver
165: ! x, r - solution, residual vectors
166: ! J - Jacobian matrix
167: ! its - iterations for convergence
168: ! Nx, Ny - number of preocessors in x- and y- directions
169: ! matrix_free - flag - 1 indicates matrix-free version
170: !
171: type(tSNES) mysnes
172: type(tVec) x,r
173: type(tMat) J
174: PetscErrorCode ierr
175: PetscInt its
176: PetscBool flg,matrix_free,set
177: PetscInt ione,nfour
178: PetscReal lambda_max,lambda_min
179: type(userctx) user
180: type(userctx), pointer:: puser
181: type(tPetscOptions) :: options
183: ! Note: Any user-defined Fortran routines (such as FormJacobian)
184: ! MUST be declared as external.
185: external FormInitialGuess,FormJacobian
187: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: ! Initialize program
189: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
191: if (ierr .ne. 0) then
192: print*,'Unable to initialize PETSc'
193: stop
194: endif
195: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
197: ! Initialize problem parameters
198: options%v = 0
199: lambda_max = 6.81
200: lambda_min = 0.0
201: user%lambda = 6.0
202: ione = 1
203: nfour = 4
204: call PetscOptionsGetReal(options,PETSC_NULL_CHARACTER,'-par',user%lambda,flg,ierr);CHKERRA(ierr)
205: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) then; SETERRA(PETSC_COMM_SELF,PETSC_ERR_USER,'Lambda provided with -par is out of range '); endif
207: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: ! Create nonlinear solver context
209: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
210: call SNESCreate(PETSC_COMM_WORLD,mysnes,ierr);CHKERRA(ierr)
212: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
213: ! Create vector data structures; set function evaluation routine
214: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
216: ! Create distributed array (DMDA) to manage parallel grid and vectors
218: ! This really needs only the star-type stencil, but we use the box
219: ! stencil temporarily.
220: call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,ione,ione, &
221: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr);CHKERRA(ierr)
222: call DMSetFromOptions(user%da,ierr);CHKERRA(ierr)
223: call DMSetUp(user%da,ierr);CHKERRA(ierr)
224: call DMDAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
225: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
227: !
228: ! Visualize the distribution of the array across the processors
229: !
230: ! call DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)
232: ! Extract global and local vectors from DMDA; then duplicate for remaining
233: ! vectors that are the same types
234: call DMCreateGlobalVector(user%da,x,ierr);CHKERRA(ierr)
235: call VecDuplicate(x,r,ierr);CHKERRA(ierr)
237: ! Get local grid boundaries (for 2-dimensional DMDA)
238: call DMDAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER,user%xm,user%ym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
239: call DMDAGetGhostCorners(user%da,user%gxs,user%gys,PETSC_NULL_INTEGER,user%gxm,user%gym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
241: ! Here we shift the starting indices up by one so that we can easily
242: ! use the Fortran convention of 1-based indices (rather 0-based indices).
243: user%xs = user%xs+1
244: user%ys = user%ys+1
245: user%gxs = user%gxs+1
246: user%gys = user%gys+1
248: user%ye = user%ys+user%ym-1
249: user%xe = user%xs+user%xm-1
250: user%gye = user%gys+user%gym-1
251: user%gxe = user%gxs+user%gxm-1
253: call SNESSetApplicationContext(mysnes,user,ierr);CHKERRA(ierr)
255: ! Set function evaluation routine and vector
256: call SNESSetFunction(mysnes,r,FormFunction,user,ierr);CHKERRA(ierr)
258: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
259: ! Create matrix data structure; set Jacobian evaluation routine
260: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
262: ! Set Jacobian matrix data structure and default Jacobian evaluation
263: ! routine. User can override with:
264: ! -snes_fd : default finite differencing approximation of Jacobian
265: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
266: ! (unless user explicitly sets preconditioner)
267: ! -snes_mf_operator : form preconditioning matrix as set by the user,
268: ! but use matrix-free approx for Jacobian-vector
269: ! products within Newton-Krylov method
270: !
271: ! Note: For the parallel case, vectors and matrices MUST be partitioned
272: ! accordingly. When using distributed arrays (DMDAs) to create vectors,
273: ! the DMDAs determine the problem partitioning. We must explicitly
274: ! specify the local matrix dimensions upon its creation for compatibility
275: ! with the vector distribution. Thus, the generic MatCreate() routine
276: ! is NOT sufficient when working with distributed arrays.
277: !
278: ! Note: Here we only approximately preallocate storage space for the
279: ! Jacobian. See the users manual for a discussion of better techniques
280: ! for preallocating matrix memory.
282: call PetscOptionsHasName(options,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr);CHKERRA(ierr)
283: if (.not. matrix_free) then
284: call DMSetMatType(user%da,MATAIJ,ierr);CHKERRA(ierr)
285: call DMCreateMatrix(user%da,J,ierr);CHKERRA(ierr)
286: call SNESSetJacobian(mysnes,J,J,FormJacobian,user,ierr);CHKERRA(ierr)
287: endif
289: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
290: ! Customize nonlinear solver; set runtime options
291: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
292: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
293: call SNESSetFromOptions(mysnes,ierr);CHKERRA(ierr)
295: ! Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
296: call PetscOptionsGetBool(options,PETSC_NULL_CHARACTER,'-test_appctx',flg,set,ierr);CHKERRA(ierr)
297: if (flg) then
298: call SNESGetApplicationContext(mysnes,puser,ierr);CHKERRA(ierr)
299: endif
301: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
302: ! Evaluate initial guess; then solve nonlinear system.
303: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
304: ! Note: The user should initialize the vector, x, with the initial guess
305: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
306: ! to employ an initial guess of zero, the user should explicitly set
307: ! this vector to zero by calling VecSet().
309: call FormInitialGuess(mysnes,x,ierr);CHKERRA(ierr)
310: call SNESSolve(mysnes,PETSC_NULL_VEC,x,ierr);CHKERRA(ierr)
311: call SNESGetIterationNumber(mysnes,its,ierr);CHKERRA(ierr)
312: if (user%rank .eq. 0) then
313: write(6,100) its
314: endif
315: 100 format('Number of SNES iterations = ',i5)
317: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
318: ! Free work space. All PETSc objects should be destroyed when they
319: ! are no longer needed.
320: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
321: if (.not. matrix_free) call MatDestroy(J,ierr);CHKERRA(ierr)
322: call VecDestroy(x,ierr);CHKERRA(ierr)
323: call VecDestroy(r,ierr);CHKERRA(ierr)
324: call SNESDestroy(mysnes,ierr);CHKERRA(ierr)
325: call DMDestroy(user%da,ierr);CHKERRA(ierr)
327: call PetscFinalize(ierr)
328: end
330: ! ---------------------------------------------------------------------
331: !
332: ! FormInitialGuess - Forms initial approximation.
333: !
334: ! Input Parameters:
335: ! X - vector
336: !
337: ! Output Parameter:
338: ! X - vector
339: !
340: ! Notes:
341: ! This routine serves as a wrapper for the lower-level routine
342: ! "InitialGuessLocal", where the actual computations are
343: ! done using the standard Fortran style of treating the local
344: ! vector data as a multidimensional array over the local mesh.
345: ! This routine merely handles ghost point scatters and accesses
346: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
347: !
348: subroutine FormInitialGuess(mysnes,X,ierr)
349: #include <petsc/finclude/petscsnes.h>
350: use petscsnes
351: use f90modulet
352: use f90moduleinterfacest
353: ! Input/output variables:
354: type(tSNES) mysnes
355: type(userctx), pointer:: puser
356: type(tVec) X
357: PetscErrorCode ierr
359: ! Declarations for use with local arrays:
360: PetscScalar,pointer :: lx_v(:)
362: 0
363: call SNESGetApplicationContext(mysnes,puser,ierr)
364: ! Get a pointer to vector data.
365: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
366: ! the data array. Otherwise, the routine is implementation dependent.
367: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
368: ! the array.
369: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
370: ! and is useable from Fortran-90 Only.
372: call VecGetArrayF90(X,lx_v,ierr)
374: ! Compute initial guess over the locally owned part of the grid
375: call InitialGuessLocal(puser,lx_v,ierr)
377: ! Restore vector
378: call VecRestoreArrayF90(X,lx_v,ierr)
380: ! Insert values into global vector
382: return
383: end
385: ! ---------------------------------------------------------------------
386: !
387: ! InitialGuessLocal - Computes initial approximation, called by
388: ! the higher level routine FormInitialGuess().
389: !
390: ! Input Parameter:
391: ! x - local vector data
392: !
393: ! Output Parameters:
394: ! x - local vector data
395: ! ierr - error code
396: !
397: ! Notes:
398: ! This routine uses standard Fortran-style computations over a 2-dim array.
399: !
400: subroutine InitialGuessLocal(user,x,ierr)
401: #include <petsc/finclude/petscsys.h>
402: use petscsys
403: use f90modulet
404: ! Input/output variables:
405: type (userctx) user
406: PetscScalar x(user%xs:user%xe,user%ys:user%ye)
407: PetscErrorCode ierr
409: ! Local variables:
410: PetscInt i,j
411: PetscScalar temp1,temp,hx,hy
412: PetscScalar one
414: ! Set parameters
416: 0
417: one = 1.0
418: hx = one/(PetscIntToReal(user%mx-1))
419: hy = one/(PetscIntToReal(user%my-1))
420: temp1 = user%lambda/(user%lambda + one)
422: do 20 j=user%ys,user%ye
423: temp = PetscIntToReal(min(j-1,user%my-j))*hy
424: do 10 i=user%xs,user%xe
425: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
426: x(i,j) = 0.0
427: else
428: x(i,j) = temp1 * sqrt(min(PetscIntToReal(min(i-1,user%mx-i)*hx),PetscIntToReal(temp)))
429: endif
430: 10 continue
431: 20 continue
433: return
434: end
436: ! ---------------------------------------------------------------------
437: !
438: ! FormFunctionLocal - Computes nonlinear function, called by
439: ! the higher level routine FormFunction().
440: !
441: ! Input Parameter:
442: ! x - local vector data
443: !
444: ! Output Parameters:
445: ! f - local vector data, f(x)
446: ! ierr - error code
447: !
448: ! Notes:
449: ! This routine uses standard Fortran-style computations over a 2-dim array.
450: !
451: subroutine FormFunctionLocal(x,f,user,ierr)
452: #include <petsc/finclude/petscsys.h>
453: use petscsys
454: use f90modulet
455: ! Input/output variables:
456: type (userctx) user
457: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
458: PetscScalar f(user%xs:user%xe,user%ys:user%ye)
459: PetscErrorCode ierr
461: ! Local variables:
462: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
463: PetscScalar u,uxx,uyy
464: PetscInt i,j
466: one = 1.0
467: two = 2.0
468: hx = one/PetscIntToReal(user%mx-1)
469: hy = one/PetscIntToReal(user%my-1)
470: sc = hx*hy*user%lambda
471: hxdhy = hx/hy
472: hydhx = hy/hx
474: ! Compute function over the locally owned part of the grid
476: do 20 j=user%ys,user%ye
477: do 10 i=user%xs,user%xe
478: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
479: f(i,j) = x(i,j)
480: else
481: u = x(i,j)
482: uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
483: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
484: f(i,j) = uxx + uyy - sc*exp(u)
485: endif
486: 10 continue
487: 20 continue
488: 0
489: return
490: end
492: ! ---------------------------------------------------------------------
493: !
494: ! FormJacobian - Evaluates Jacobian matrix.
495: !
496: ! Input Parameters:
497: ! snes - the SNES context
498: ! x - input vector
499: ! dummy - optional user-defined context, as set by SNESSetJacobian()
500: ! (not used here)
501: !
502: ! Output Parameters:
503: ! jac - Jacobian matrix
504: ! jac_prec - optionally different preconditioning matrix (not used here)
505: ! flag - flag indicating matrix structure
506: !
507: ! Notes:
508: ! This routine serves as a wrapper for the lower-level routine
509: ! "FormJacobianLocal", where the actual computations are
510: ! done using the standard Fortran style of treating the local
511: ! vector data as a multidimensional array over the local mesh.
512: ! This routine merely accesses the local vector data via
513: ! VecGetArrayF90() and VecRestoreArrayF90().
514: !
515: ! Notes:
516: ! Due to grid point reordering with DMDAs, we must always work
517: ! with the local grid points, and then transform them to the new
518: ! global numbering with the "ltog" mapping
519: ! We cannot work directly with the global numbers for the original
520: ! uniprocessor grid!
521: !
522: ! Two methods are available for imposing this transformation
523: ! when setting matrix entries:
524: ! (A) MatSetValuesLocal(), using the local ordering (including
525: ! ghost points!)
526: ! - Set matrix entries using the local ordering
527: ! by calling MatSetValuesLocal()
528: ! (B) MatSetValues(), using the global ordering
529: ! - Use DMGetLocalToGlobalMapping() then
530: ! ISLocalToGlobalMappingGetIndicesF90() to extract the local-to-global map
531: ! - Then apply this map explicitly yourself
532: ! - Set matrix entries using the global ordering by calling
533: ! MatSetValues()
534: ! Option (A) seems cleaner/easier in many cases, and is the procedure
535: ! used in this example.
536: !
537: subroutine FormJacobian(mysnes,X,jac,jac_prec,user,ierr)
538: #include <petsc/finclude/petscsnes.h>
539: use petscsnes
540: use f90modulet
541: ! Input/output variables:
542: type(tSNES) mysnes
543: type(tVec) X
544: type(tMat) jac,jac_prec
545: type(userctx) user
546: PetscErrorCode ierr
548: ! Declarations for use with local arrays:
549: PetscScalar,pointer :: lx_v(:)
550: type(tVec) localX
552: ! Scatter ghost points to local vector, using the 2-step process
553: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
554: ! Computations can be done while messages are in transition,
555: ! by placing code between these two statements.
557: call DMGetLocalVector(user%da,localX,ierr)
558: call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr)
559: call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
561: ! Get a pointer to vector data
562: call VecGetArrayF90(localX,lx_v,ierr)
564: ! Compute entries for the locally owned part of the Jacobian preconditioner.
565: call FormJacobianLocal(lx_v,jac_prec,user,ierr)
567: ! Assemble matrix, using the 2-step process:
568: ! MatAssemblyBegin(), MatAssemblyEnd()
569: ! Computations can be done while messages are in transition,
570: ! by placing code between these two statements.
572: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
573: ! if (jac .ne. jac_prec) then
574: call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
575: ! endif
576: call VecRestoreArrayF90(localX,lx_v,ierr)
577: call DMRestoreLocalVector(user%da,localX,ierr)
578: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
579: ! if (jac .ne. jac_prec) then
580: call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
581: ! endif
583: ! Tell the matrix we will never add a new nonzero location to the
584: ! matrix. If we do it will generate an error.
586: call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr)
588: return
589: end
591: ! ---------------------------------------------------------------------
592: !
593: ! FormJacobianLocal - Computes Jacobian preconditioner matrix,
594: ! called by the higher level routine FormJacobian().
595: !
596: ! Input Parameters:
597: ! x - local vector data
598: !
599: ! Output Parameters:
600: ! jac_prec - Jacobian preconditioner matrix
601: ! ierr - error code
602: !
603: ! Notes:
604: ! This routine uses standard Fortran-style computations over a 2-dim array.
605: !
606: ! Notes:
607: ! Due to grid point reordering with DMDAs, we must always work
608: ! with the local grid points, and then transform them to the new
609: ! global numbering with the "ltog" mapping
610: ! We cannot work directly with the global numbers for the original
611: ! uniprocessor grid!
612: !
613: ! Two methods are available for imposing this transformation
614: ! when setting matrix entries:
615: ! (A) MatSetValuesLocal(), using the local ordering (including
616: ! ghost points!)
617: ! - Set matrix entries using the local ordering
618: ! by calling MatSetValuesLocal()
619: ! (B) MatSetValues(), using the global ordering
620: ! - Set matrix entries using the global ordering by calling
621: ! MatSetValues()
622: ! Option (A) seems cleaner/easier in many cases, and is the procedure
623: ! used in this example.
624: !
625: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
626: #include <petsc/finclude/petscmat.h>
627: use petscmat
628: use f90modulet
629: ! Input/output variables:
630: type (userctx) user
631: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
632: type(tMat) jac_prec
633: PetscErrorCode ierr
635: ! Local variables:
636: PetscInt row,col(5),i,j
637: PetscInt ione,ifive
638: PetscScalar two,one,hx,hy,hxdhy
639: PetscScalar hydhx,sc,v(5)
641: ! Set parameters
642: ione = 1
643: ifive = 5
644: one = 1.0
645: two = 2.0
646: hx = one/PetscIntToReal(user%mx-1)
647: hy = one/PetscIntToReal(user%my-1)
648: sc = hx*hy
649: hxdhy = hx/hy
650: hydhx = hy/hx
652: ! Compute entries for the locally owned part of the Jacobian.
653: ! - Currently, all PETSc parallel matrix formats are partitioned by
654: ! contiguous chunks of rows across the processors.
655: ! - Each processor needs to insert only elements that it owns
656: ! locally (but any non-local elements will be sent to the
657: ! appropriate processor during matrix assembly).
658: ! - Here, we set all entries for a particular row at once.
659: ! - We can set matrix entries either using either
660: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
661: ! - Note that MatSetValues() uses 0-based row and column numbers
662: ! in Fortran as well as in C.
664: do 20 j=user%ys,user%ye
665: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
666: do 10 i=user%xs,user%xe
667: row = row + 1
668: ! boundary points
669: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
670: col(1) = row
671: v(1) = one
672: call MatSetValuesLocal(jac_prec,ione,row,ione,col,v,INSERT_VALUES,ierr)
673: ! interior grid points
674: else
675: v(1) = -hxdhy
676: v(2) = -hydhx
677: v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j))
678: v(4) = -hydhx
679: v(5) = -hxdhy
680: col(1) = row - user%gxm
681: col(2) = row - 1
682: col(3) = row
683: col(4) = row + 1
684: col(5) = row + user%gxm
685: call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,INSERT_VALUES,ierr)
686: endif
687: 10 continue
688: 20 continue
689: return
690: end
692: !/*TEST
693: !
694: ! test:
695: ! nsize: 4
696: ! args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
697: !
698: !TEST*/