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: !T*/
16: !
17: ! --------------------------------------------------------------------------
18: !
19: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
20: ! the partial differential equation
21: !
22: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
23: !
24: ! with boundary conditions
25: !
26: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
27: !
28: ! A finite difference approximation with the usual 5-point stencil
29: ! is used to discretize the boundary value problem to obtain a nonlinear
30: ! system of equations.
31: !
32: ! The uniprocessor version of this code is snes/examples/tutorials/ex4f.F
33: !
34: ! --------------------------------------------------------------------------
35: ! The following define must be used before including any PETSc include files
36: ! into a module or interface. This is because they can't handle declarations
37: ! in them
38: !
40: module f90module
41: use petscsys
42: use petscis
43: use petscvec
44: use petscdm
45: use petscdmda
46: use petscmat
47: use petscpc
48: use petscksp
49: use petscsnes
50: #include <petsc/finclude/petscsnes.h> 51: type userctx
52: PetscInt xs,xe,xm,gxs,gxe,gxm
53: PetscInt ys,ye,ym,gys,gye,gym
54: PetscInt mx,my
55: PetscMPIInt rank
56: PetscReal lambda
57: end type userctx
59: contains
60: ! ---------------------------------------------------------------------
61: !
62: ! FormFunction - Evaluates nonlinear function, F(x).
63: !
64: ! Input Parameters:
65: ! snes - the SNES context
66: ! X - input vector
67: ! dummy - optional user-defined context, as set by SNESSetFunction()
68: ! (not used here)
69: !
70: ! Output Parameter:
71: ! F - function vector
72: !
73: ! Notes:
74: ! This routine serves as a wrapper for the lower-level routine
75: ! "FormFunctionLocal", where the actual computations are
76: ! done using the standard Fortran style of treating the local
77: ! vector data as a multidimensional array over the local mesh.
78: ! This routine merely handles ghost point scatters and accesses
79: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
80: !
81: subroutine FormFunction(snes,X,F,user,ierr)
82: implicit none
84: ! Input/output variables:
85: SNES snes
86: Vec X,F
87: PetscErrorCode ierr
88: type (userctx) user
89: DM da
91: ! Declarations for use with local arrays:
92: PetscScalar,pointer :: lx_v(:),lf_v(:)
93: Vec localX
95: ! Scatter ghost points to local vector, using the 2-step process
96: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
97: ! By placing code between these two statements, computations can
98: ! be done while messages are in transition.
99: call SNESGetDM(snes,da,ierr);CHKERRQ(ierr)
100: call DMGetLocalVector(da,localX,ierr);CHKERRQ(ierr)
101: call DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
102: call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
104: ! Get a pointer to vector data.
105: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
106: ! the data array. Otherwise, the routine is implementation dependent.
107: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
108: ! the array.
109: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
110: ! and is useable from Fortran-90 Only.
112: call VecGetArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
113: call VecGetArrayF90(F,lf_v,ierr);CHKERRQ(ierr)
115: ! Compute function over the locally owned part of the grid
116: call FormFunctionLocal(lx_v,lf_v,user,ierr);CHKERRQ(ierr)
118: ! Restore vectors
119: call VecRestoreArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
120: call VecRestoreArrayF90(F,lf_v,ierr);CHKERRQ(ierr)
122: ! Insert values into global vector
124: call DMRestoreLocalVector(da,localX,ierr);CHKERRQ(ierr)
125: call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)
127: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
128: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
129: return
130: end subroutine formfunction
131: end module f90module
133: module f90moduleinterfaces
134: use f90module
136: Interface SNESSetApplicationContext137: Subroutine SNESSetApplicationContext(snes,ctx,ierr)
138: use f90module
139: SNES snes
140: type(userctx) ctx
141: PetscErrorCode ierr
142: End Subroutine
143: End Interface SNESSetApplicationContext145: Interface SNESGetApplicationContext146: Subroutine SNESGetApplicationContext(snes,ctx,ierr)
147: use f90module
148: SNES snes
149: type(userctx), pointer :: ctx
150: PetscErrorCode ierr
151: End Subroutine
152: End Interface SNESGetApplicationContext153: end module f90moduleinterfaces
155: program main
156: use f90module
157: use f90moduleinterfaces
158: implicit none
159: !
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: ! Variable declarations
163: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
164: !
165: ! Variables:
166: ! snes - nonlinear solver
167: ! x, r - solution, residual vectors
168: ! J - Jacobian matrix
169: ! its - iterations for convergence
170: ! Nx, Ny - number of preocessors in x- and y- directions
171: ! matrix_free - flag - 1 indicates matrix-free version
172: !
173: SNES snes
174: Vec x,r
175: Mat J
176: PetscErrorCode ierr
177: PetscInt its
178: PetscBool flg,matrix_free
179: PetscInt ione,nfour
180: PetscReal lambda_max,lambda_min
181: type (userctx) user
182: DM da
184: ! Note: Any user-defined Fortran routines (such as FormJacobian)
185: ! MUST be declared as external.
186: external FormInitialGuess,FormJacobian
188: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189: ! Initialize program
190: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
192: if (ierr .ne. 0) then
193: print*,'Unable to initialize PETSc'
194: stop
195: endif
196: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
198: ! Initialize problem parameters
199: lambda_max = 6.81
200: lambda_min = 0.0
201: user%lambda = 6.0
202: ione = 1
203: nfour = 4
204: call PetscOptionsGetReal(PETSC_NULL_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,1,'Lambda provided with -par is out of range '); endif
207: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: ! Create nonlinear solver context
209: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
210: call SNESCreate(PETSC_COMM_WORLD,snes,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,da,ierr);CHKERRA(ierr)
222: call DMSetFromOptions(da,ierr)
223: call DMSetUp(da,ierr)
225: call DMDAGetInfo(da,PETSC_NULL_INTEGER,user%mx,user%my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
226: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
228: !
229: ! Visualize the distribution of the array across the processors
230: !
231: ! call DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr)
233: ! Extract global and local vectors from DMDA; then duplicate for remaining
234: ! vectors that are the same types
235: call DMCreateGlobalVector(da,x,ierr);CHKERRA(ierr)
236: call VecDuplicate(x,r,ierr);CHKERRA(ierr)
238: ! Get local grid boundaries (for 2-dimensional DMDA)
239: call DMDAGetCorners(da,user%xs,user%ys,PETSC_NULL_INTEGER,user%xm,user%ym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
240: call DMDAGetGhostCorners(da,user%gxs,user%gys,PETSC_NULL_INTEGER,user%gxm,user%gym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
242: ! Here we shift the starting indices up by one so that we can easily
243: ! use the Fortran convention of 1-based indices (rather 0-based indices).
244: user%xs = user%xs+1
245: user%ys = user%ys+1
246: user%gxs = user%gxs+1
247: user%gys = user%gys+1
249: user%ye = user%ys+user%ym-1
250: user%xe = user%xs+user%xm-1
251: user%gye = user%gys+user%gym-1
252: user%gxe = user%gxs+user%gxm-1
254: call SNESSetApplicationContext(snes,user,ierr);CHKERRA(ierr)
256: ! Set function evaluation routine and vector
257: call SNESSetFunction(snes,r,FormFunction,user,ierr);CHKERRA(ierr)
259: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
260: ! Create matrix data structure; set Jacobian evaluation routine
261: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
263: ! Set Jacobian matrix data structure and default Jacobian evaluation
264: ! routine. User can override with:
265: ! -snes_fd : default finite differencing approximation of Jacobian
266: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
267: ! (unless user explicitly sets preconditioner)
268: ! -snes_mf_operator : form preconditioning matrix as set by the user,
269: ! but use matrix-free approx for Jacobian-vector
270: ! products within Newton-Krylov method
271: !
272: ! Note: For the parallel case, vectors and matrices MUST be partitioned
273: ! accordingly. When using distributed arrays (DMDAs) to create vectors,
274: ! the DMDAs determine the problem partitioning. We must explicitly
275: ! specify the local matrix dimensions upon its creation for compatibility
276: ! with the vector distribution. Thus, the generic MatCreate() routine
277: ! is NOT sufficient when working with distributed arrays.
278: !
279: ! Note: Here we only approximately preallocate storage space for the
280: ! Jacobian. See the users manual for a discussion of better techniques
281: ! for preallocating matrix memory.
283: call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr);CHKERRA(ierr)
284: if (.not. matrix_free) then
285: call DMSetMatType(da,MATAIJ,ierr);CHKERRA(ierr)
286: call DMCreateMatrix(da,J,ierr);CHKERRA(ierr)
287: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr);CHKERRA(ierr)
288: endif
290: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
291: ! Customize nonlinear solver; set runtime options
292: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
293: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
294: call SNESSetDM(snes,da,ierr);CHKERRA(ierr)
295: call SNESSetFromOptions(snes,ierr);CHKERRA(ierr)
298: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
299: ! Evaluate initial guess; then solve nonlinear system.
300: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
301: ! Note: The user should initialize the vector, x, with the initial guess
302: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
303: ! to employ an initial guess of zero, the user should explicitly set
304: ! this vector to zero by calling VecSet().
306: call FormInitialGuess(snes,x,ierr);CHKERRA(ierr)
307: call SNESSolve(snes,PETSC_NULL_VEC,x,ierr);CHKERRA(ierr)
308: call SNESGetIterationNumber(snes,its,ierr);;CHKERRA(ierr)
309: if (user%rank .eq. 0) then
310: write(6,100) its
311: endif
312: 100 format('Number of SNES iterations = ',i5)
314: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
315: ! Free work space. All PETSc objects should be destroyed when they
316: ! are no longer needed.
317: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
318: if (.not. matrix_free) call MatDestroy(J,ierr);CHKERRA(ierr)
319: call VecDestroy(x,ierr);CHKERRA(ierr)
320: call VecDestroy(r,ierr);CHKERRA(ierr)
321: call SNESDestroy(snes,ierr);CHKERRA(ierr)
322: call DMDestroy(da,ierr);CHKERRA(ierr)
324: call PetscFinalize(ierr)
325: end
327: ! ---------------------------------------------------------------------
328: !
329: ! FormInitialGuess - Forms initial approximation.
330: !
331: ! Input Parameters:
332: ! X - vector
333: !
334: ! Output Parameter:
335: ! X - vector
336: !
337: ! Notes:
338: ! This routine serves as a wrapper for the lower-level routine
339: ! "InitialGuessLocal", where the actual computations are
340: ! done using the standard Fortran style of treating the local
341: ! vector data as a multidimensional array over the local mesh.
342: ! This routine merely handles ghost point scatters and accesses
343: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
344: !
345: subroutine FormInitialGuess(snes,X,ierr)
346: use f90module
347: use f90moduleinterfaces
348: implicit none
350: ! Input/output variables:
351: SNES snes
352: type(userctx), pointer:: puser
353: Vec X
354: PetscErrorCode ierr
355: DM da
357: ! Declarations for use with local arrays:
358: PetscScalar,pointer :: lx_v(:)
360: 0
361: call SNESGetDM(snes,da,ierr);CHKERRQ(ierr)
362: call SNESGetApplicationContext(snes,puser,ierr);CHKERRQ(ierr)
363: ! Get a pointer to vector data.
364: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
365: ! the data array. Otherwise, the routine is implementation dependent.
366: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
367: ! the array.
368: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
369: ! and is useable from Fortran-90 Only.
371: call VecGetArrayF90(X,lx_v,ierr);CHKERRQ(ierr)
373: ! Compute initial guess over the locally owned part of the grid
374: call InitialGuessLocal(puser,lx_v,ierr);CHKERRQ(ierr)
376: ! Restore vector
377: call VecRestoreArrayF90(X,lx_v,ierr);CHKERRQ(ierr)
379: ! Insert values into global vector
381: return
382: end
384: ! ---------------------------------------------------------------------
385: !
386: ! InitialGuessLocal - Computes initial approximation, called by
387: ! the higher level routine FormInitialGuess().
388: !
389: ! Input Parameter:
390: ! x - local vector data
391: !
392: ! Output Parameters:
393: ! x - local vector data
394: ! ierr - error code
395: !
396: ! Notes:
397: ! This routine uses standard Fortran-style computations over a 2-dim array.
398: !
399: subroutine InitialGuessLocal(user,x,ierr)
400: use f90module
401: implicit none
403: ! Input/output variables:
404: type (userctx) user
405: PetscScalar x(user%xs:user%xe,user%ys:user%ye)
406: PetscErrorCode ierr
408: ! Local variables:
409: PetscInt i,j
410: PetscReal temp1,temp,hx,hy
411: PetscReal one
413: ! Set parameters
415: 0
416: one = 1.0
417: hx = one/(user%mx-1)
418: hy = one/(user%my-1)
419: temp1 = user%lambda/(user%lambda + one)
421: do 20 j=user%ys,user%ye
422: temp = min(j-1,user%my-j)*hy
423: do 10 i=user%xs,user%xe
424: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
425: x(i,j) = 0.0
426: else
427: x(i,j) = temp1 * sqrt(min(hx*min(i-1,user%mx-i),temp))
428: endif
429: 10 continue
430: 20 continue
432: return
433: end
435: ! ---------------------------------------------------------------------
436: !
437: ! FormFunctionLocal - Computes nonlinear function, called by
438: ! the higher level routine FormFunction().
439: !
440: ! Input Parameter:
441: ! x - local vector data
442: !
443: ! Output Parameters:
444: ! f - local vector data, f(x)
445: ! ierr - error code
446: !
447: ! Notes:
448: ! This routine uses standard Fortran-style computations over a 2-dim array.
449: !
450: subroutine FormFunctionLocal(x,f,user,ierr)
451: use f90module
453: implicit none
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/(user%mx-1)
469: hy = one/(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
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
530: ! - Set matrix entries using the global ordering by calling
531: ! MatSetValues()
532: ! Option (A) seems cleaner/easier in many cases, and is the procedure
533: ! used in this example.
534: !
535: subroutine FormJacobian(snes,X,jac,jac_prec,user,ierr)
536: use f90module
537: implicit none
539: ! Input/output variables:
540: SNES snes
541: Vec X
542: Mat jac,jac_prec
543: type(userctx) user
544: PetscErrorCode ierr
545: DM da
547: ! Declarations for use with local arrays:
548: PetscScalar,pointer :: lx_v(:)
549: Vec localX
551: ! Scatter ghost points to local vector, using the 2-step process
552: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
553: ! Computations can be done while messages are in transition,
554: ! by placing code between these two statements.
556: call SNESGetDM(snes,da,ierr);CHKERRQ(ierr)
557: call DMGetLocalVector(da,localX,ierr);CHKERRQ(ierr)
558: call DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
559: call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
561: ! Get a pointer to vector data
562: call VecGetArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
564: ! Compute entries for the locally owned part of the Jacobian preconditioner.
565: call FormJacobianLocal(lx_v,jac_prec,user,ierr);CHKERRQ(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);CHKERRQ(ierr)
573: if (jac .ne. jac_prec) then
574: call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)
575: endif
576: call VecRestoreArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
577: call DMRestoreLocalVector(da,localX,ierr);CHKERRQ(ierr)
578: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)
579: if (jac .ne. jac_prec) then
580: call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(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);CHKERRQ(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: ! - Then apply this map explicitly yourself
621: ! - Set matrix entries using the global ordering by calling
622: ! MatSetValues()
623: ! Option (A) seems cleaner/easier in many cases, and is the procedure
624: ! used in this example.
625: !
626: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
627: use f90module
628: implicit none
632: ! Input/output variables:
633: type (userctx) user
634: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
635: Mat jac_prec
636: PetscErrorCode ierr
638: ! Local variables:
639: PetscInt row,col(5),i,j
640: PetscInt ione,ifive
641: PetscScalar two,one,hx,hy,hxdhy
642: PetscScalar hydhx,sc,v(5)
644: ! Set parameters
645: ione = 1
646: ifive = 5
647: one = 1.0
648: two = 2.0
649: hx = one/(user%mx-1)
650: hy = one/(user%my-1)
651: sc = hx*hy
652: hxdhy = hx/hy
653: hydhx = hy/hx
655: ! Compute entries for the locally owned part of the Jacobian.
656: ! - Currently, all PETSc parallel matrix formats are partitioned by
657: ! contiguous chunks of rows across the processors.
658: ! - Each processor needs to insert only elements that it owns
659: ! locally (but any non-local elements will be sent to the
660: ! appropriate processor during matrix assembly).
661: ! - Here, we set all entries for a particular row at once.
662: ! - We can set matrix entries either using either
663: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
664: ! - Note that MatSetValues() uses 0-based row and column numbers
665: ! in Fortran as well as in C.
667: do 20 j=user%ys,user%ye
668: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
669: do 10 i=user%xs,user%xe
670: row = row + 1
671: ! boundary points
672: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
673: col(1) = row
674: v(1) = one
675: call MatSetValuesLocal(jac_prec,ione,row,ione,col,v,INSERT_VALUES,ierr);CHKERRQ(ierr)
676: ! interior grid points
677: else
678: v(1) = -hxdhy
679: v(2) = -hydhx
680: v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j))
681: v(4) = -hydhx
682: v(5) = -hxdhy
683: col(1) = row - user%gxm
684: col(2) = row - 1
685: col(3) = row
686: col(4) = row + 1
687: col(5) = row + user%gxm
688: call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,INSERT_VALUES,ierr);CHKERRQ(ierr)
689: endif
690: 10 continue
691: 20 continue
693: return
694: end
699: !
700: !/*TEST
701: !
702: ! test:
703: ! nsize: 4
704: ! args: -snes_mf -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
705: ! requires: !single
706: !
707: ! test:
708: ! suffix: 2
709: ! nsize: 4
710: ! args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
711: ! requires: !single
712: !
713: ! test:
714: ! suffix: 3
715: ! nsize: 3
716: ! args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
717: ! requires: !single
718: !
719: ! test:
720: ! suffix: 4
721: ! nsize: 3
722: ! args: -snes_mf_operator -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
723: ! requires: !single
724: !
725: ! test:
726: ! suffix: 5
727: ! requires: !single
728: !
729: !TEST*/