Actual source code: ex5f.F90
petsc-3.9.0 2018-04-07
1: !
2: ! Description: This example 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 <param>, where <param> indicates the nonlinearity of the problem
7: ! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)
8: !
9: !
10: !!/*T
11: ! Concepts: SNES^parallel Bratu example
12: ! Concepts: DMDA^using distributed arrays;
13: ! Processors: n
14: !T*/
17: !
18: ! --------------------------------------------------------------------------
19: !
20: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
21: ! the partial differential equation
22: !
23: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
24: !
25: ! with boundary conditions
26: !
27: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
28: !
29: ! A finite difference approximation with the usual 5-point stencil
30: ! is used to discretize the boundary value problem to obtain a nonlinear
31: ! system of equations.
32: !
33: ! --------------------------------------------------------------------------
35: program main
36: #include <petsc/finclude/petscsnes.h>
37: use petscdmda
38: use petscsnes
39: implicit none
40: !
41: ! We place common blocks, variable declarations, and other include files
42: ! needed for this code in the single file ex5f.h. We then need to include
43: ! only this file throughout the various routines in this program. See
44: ! additional comments in the file ex5f.h.
45: !
46: #include "ex5f.h"
48: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49: ! Variable declarations
50: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: !
52: ! Variables:
53: ! snes - nonlinear solver
54: ! x, r - solution, residual vectors
55: ! its - iterations for convergence
56: !
57: ! See additional variable declarations in the file ex5f.h
58: !
59: SNES snes
60: Vec x,r
61: PetscInt its,i1,i4
62: PetscErrorCode ierr
63: PetscReal lambda_max,lambda_min
64: PetscBool flg
65: DM da
67: ! Note: Any user-defined Fortran routines (such as FormJacobianLocal)
68: ! MUST be declared as external.
70: external FormInitialGuess
71: external FormFunctionLocal,FormJacobianLocal
72: external MySNESConverged
74: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
75: ! Initialize program
76: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
78: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
79: if (ierr .ne. 0) then
80: print*,'Unable to initialize PETSc'
81: stop
82: endif
83: call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
84: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
86: ! Initialize problem parameters
88: i1 = 1
89: i4 = 4
90: lambda_max = 6.81
91: lambda_min = 0.0
92: lambda = 6.0
93: call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,flg,ierr)
94: if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then; SETERRA(PETSC_COMM_WORLD,1,'Lambda out of range'); endif
96: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: ! Create nonlinear solver context
98: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
102: ! Set convergence test routine if desired
104: call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)
105: if (flg) then
106: call SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,ierr)
107: endif
109: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110: ! Create vector data structures; set function evaluation routine
111: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113: ! Create distributed array (DMDA) to manage parallel grid and vectors
115: ! This really needs only the star-type stencil, but we use the box
116: ! stencil temporarily.
117: call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE, &
118: & DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE,i1,i1, &
119: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
120: call DMSetFromOptions(da,ierr)
121: call DMSetUp(da,ierr)
123: ! Extract global and local vectors from DMDA; then duplicate for remaining
124: ! vectors that are the same types
126: call DMCreateGlobalVector(da,x,ierr)
127: call VecDuplicate(x,r,ierr)
129: ! Get local grid boundaries (for 2-dimensional DMDA)
131: call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER, &
132: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
133: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
134: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
135: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
136: & PETSC_NULL_INTEGER,ierr)
137: call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)
138: call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)
140: ! Here we shift the starting indices up by one so that we can easily
141: ! use the Fortran convention of 1-based indices (rather 0-based indices).
143: xs = xs+1
144: ys = ys+1
145: gxs = gxs+1
146: gys = gys+1
148: ye = ys+ym-1
149: xe = xs+xm-1
150: gye = gys+gym-1
151: gxe = gxs+gxm-1
153: ! Set function evaluation routine and vector
155: call DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)
156: call DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)
157: call SNESSetDM(snes,da,ierr)
159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: ! Customize nonlinear solver; set runtime options
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
165: call SNESSetFromOptions(snes,ierr)
166: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: ! Evaluate initial guess; then solve nonlinear system.
168: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: ! Note: The user should initialize the vector, x, with the initial guess
171: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
172: ! to employ an initial guess of zero, the user should explicitly set
173: ! this vector to zero by calling VecSet().
175: call FormInitialGuess(x,ierr)
176: call SNESSolve(snes,PETSC_NULL_VEC,x,ierr)
177: call SNESGetIterationNumber(snes,its,ierr)
178: if (rank .eq. 0) then
179: write(6,100) its
180: endif
181: 100 format('Number of SNES iterations = ',i5)
184: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: ! Free work space. All PETSc objects should be destroyed when they
186: ! are no longer needed.
187: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189: call VecDestroy(x,ierr)
190: call VecDestroy(r,ierr)
191: call SNESDestroy(snes,ierr)
192: call DMDestroy(da,ierr)
193: call PetscFinalize(ierr)
194: end
196: ! ---------------------------------------------------------------------
197: !
198: ! FormInitialGuess - Forms initial approximation.
199: !
200: ! Input Parameters:
201: ! X - vector
202: !
203: ! Output Parameter:
204: ! X - vector
205: !
206: ! Notes:
207: ! This routine serves as a wrapper for the lower-level routine
208: ! "ApplicationInitialGuess", where the actual computations are
209: ! done using the standard Fortran style of treating the local
210: ! vector data as a multidimensional array over the local mesh.
211: ! This routine merely handles ghost point scatters and accesses
212: ! the local vector data via VecGetArray() and VecRestoreArray().
213: !
214: subroutine FormInitialGuess(X,ierr)
215: use petscsnes
216: implicit none
218: #include "ex5f.h"
220: ! Input/output variables:
221: Vec X
222: PetscErrorCode ierr
224: ! Declarations for use with local arrays:
225: PetscScalar lx_v(0:1)
226: PetscOffset lx_i
228: 0
230: ! Get a pointer to vector data.
231: ! - For default PETSc vectors, VecGetArray() returns a pointer to
232: ! the data array. Otherwise, the routine is implementation dependent.
233: ! - You MUST call VecRestoreArray() when you no longer need access to
234: ! the array.
235: ! - Note that the Fortran interface to VecGetArray() differs from the
236: ! C version. See the users manual for details.
238: call VecGetArray(X,lx_v,lx_i,ierr)
240: ! Compute initial guess over the locally owned part of the grid
242: call InitialGuessLocal(lx_v(lx_i),ierr)
244: ! Restore vector
246: call VecRestoreArray(X,lx_v,lx_i,ierr)
248: return
249: end
251: ! ---------------------------------------------------------------------
252: !
253: ! InitialGuessLocal - Computes initial approximation, called by
254: ! the higher level routine FormInitialGuess().
255: !
256: ! Input Parameter:
257: ! x - local vector data
258: !
259: ! Output Parameters:
260: ! x - local vector data
261: ! ierr - error code
262: !
263: ! Notes:
264: ! This routine uses standard Fortran-style computations over a 2-dim array.
265: !
266: subroutine InitialGuessLocal(x,ierr)
267: use petscsnes
268: implicit none
270: #include "ex5f.h"
272: ! Input/output variables:
273: PetscScalar x(xs:xe,ys:ye)
274: PetscErrorCode ierr
276: ! Local variables:
277: PetscInt i,j
278: PetscReal temp1,temp,one,hx,hy
280: ! Set parameters
282: 0
283: one = 1.0
284: hx = one/((mx-1))
285: hy = one/((my-1))
286: temp1 = lambda/(lambda + one)
288: do 20 j=ys,ye
289: temp = (min(j-1,my-j))*hy
290: do 10 i=xs,xe
291: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
292: x(i,j) = 0.0
293: else
294: x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,(temp)))
295: endif
296: 10 continue
297: 20 continue
299: return
300: end
302: ! ---------------------------------------------------------------------
303: !
304: ! FormFunctionLocal - Computes nonlinear function, called by
305: ! the higher level routine FormFunction().
306: !
307: ! Input Parameter:
308: ! x - local vector data
309: !
310: ! Output Parameters:
311: ! f - local vector data, f(x)
312: ! ierr - error code
313: !
314: ! Notes:
315: ! This routine uses standard Fortran-style computations over a 2-dim array.
316: !
317: !
318: subroutine FormFunctionLocal(info,x,f,da,ierr)
319: #include <petsc/finclude/petscdmda.h>
320: use petscsnes
321: implicit none
323: #include "ex5f.h"
324: DM da
326: ! Input/output variables:
327: DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
328: PetscScalar x(gxs:gxe,gys:gye)
329: PetscScalar f(xs:xe,ys:ye)
330: PetscErrorCode ierr
332: ! Local variables:
333: PetscScalar two,one,hx,hy
334: PetscScalar hxdhy,hydhx,sc
335: PetscScalar u,uxx,uyy
336: PetscInt i,j
338: xs = info(DMDA_LOCAL_INFO_XS)+1
339: xe = xs+info(DMDA_LOCAL_INFO_XM)-1
340: ys = info(DMDA_LOCAL_INFO_YS)+1
341: ye = ys+info(DMDA_LOCAL_INFO_YM)-1
342: mx = info(DMDA_LOCAL_INFO_MX)
343: my = info(DMDA_LOCAL_INFO_MY)
345: one = 1.0
346: two = 2.0
347: hx = one/(mx-1)
348: hy = one/(my-1)
349: sc = hx*hy*lambda
350: hxdhy = hx/hy
351: hydhx = hy/hx
353: ! Compute function over the locally owned part of the grid
355: do 20 j=ys,ye
356: do 10 i=xs,xe
357: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
358: f(i,j) = x(i,j)
359: else
360: u = x(i,j)
361: uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
362: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
363: f(i,j) = uxx + uyy - sc*exp(u)
364: endif
365: 10 continue
366: 20 continue
368: call PetscLogFlops(11.0d0*ym*xm,ierr)
370: return
371: end
373: ! ---------------------------------------------------------------------
374: !
375: ! FormJacobianLocal - Computes Jacobian matrix, called by
376: ! the higher level routine FormJacobian().
377: !
378: ! Input Parameters:
379: ! x - local vector data
380: !
381: ! Output Parameters:
382: ! jac - Jacobian matrix
383: ! jac_prec - optionally different preconditioning matrix (not used here)
384: ! ierr - error code
385: !
386: ! Notes:
387: ! This routine uses standard Fortran-style computations over a 2-dim array.
388: !
389: ! Notes:
390: ! Due to grid point reordering with DMDAs, we must always work
391: ! with the local grid points, and then transform them to the new
392: ! global numbering with the "ltog" mapping
393: ! We cannot work directly with the global numbers for the original
394: ! uniprocessor grid!
395: !
396: ! Two methods are available for imposing this transformation
397: ! when setting matrix entries:
398: ! (A) MatSetValuesLocal(), using the local ordering (including
399: ! ghost points!)
400: ! by calling MatSetValuesLocal()
401: ! (B) MatSetValues(), using the global ordering
402: ! - Use DMDAGetGlobalIndices() to extract the local-to-global map
403: ! - Then apply this map explicitly yourself
404: ! - Set matrix entries using the global ordering by calling
405: ! MatSetValues()
406: ! Option (A) seems cleaner/easier in many cases, and is the procedure
407: ! used in this example.
408: !
409: subroutine FormJacobianLocal(info,x,A,jac,da,ierr)
410: use petscsnes
411: implicit none
413: #include "ex5f.h"
414: DM da
415:
416: ! Input/output variables:
417: PetscScalar x(gxs:gxe,gys:gye)
418: Mat A,jac
419: PetscErrorCode ierr
420: DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
423: ! Local variables:
424: PetscInt row,col(5),i,j,i1,i5
425: PetscScalar two,one,hx,hy,v(5)
426: PetscScalar hxdhy,hydhx,sc
428: ! Set parameters
430: i1 = 1
431: i5 = 5
432: one = 1.0
433: two = 2.0
434: hx = one/(mx-1)
435: hy = one/(my-1)
436: sc = hx*hy
437: hxdhy = hx/hy
438: hydhx = hy/hx
440: ! Compute entries for the locally owned part of the Jacobian.
441: ! - Currently, all PETSc parallel matrix formats are partitioned by
442: ! contiguous chunks of rows across the processors.
443: ! - Each processor needs to insert only elements that it owns
444: ! locally (but any non-local elements will be sent to the
445: ! appropriate processor during matrix assembly).
446: ! - Here, we set all entries for a particular row at once.
447: ! - We can set matrix entries either using either
448: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
449: ! - Note that MatSetValues() uses 0-based row and column numbers
450: ! in Fortran as well as in C.
452: do 20 j=ys,ye
453: row = (j - gys)*gxm + xs - gxs - 1
454: do 10 i=xs,xe
455: row = row + 1
456: ! boundary points
457: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
458: ! Some f90 compilers need 4th arg to be of same type in both calls
459: col(1) = row
460: v(1) = one
461: call MatSetValuesLocal(jac,i1,row,i1,col,v,INSERT_VALUES,ierr)
462: ! interior grid points
463: else
464: v(1) = -hxdhy
465: v(2) = -hydhx
466: v(3) = two*(hydhx + hxdhy) - sc*lambda*exp(x(i,j))
467: v(4) = -hydhx
468: v(5) = -hxdhy
469: col(1) = row - gxm
470: col(2) = row - 1
471: col(3) = row
472: col(4) = row + 1
473: col(5) = row + gxm
474: call MatSetValuesLocal(jac,i1,row,i5,col,v, INSERT_VALUES,ierr)
475: endif
476: 10 continue
477: 20 continue
478: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
479: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
480: if (A .ne. jac) then
481: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
482: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
483: endif
484: return
485: end
487: !
488: ! Simple convergence test based on the infinity norm of the residual being small
489: !
490: subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr)
491: use petscsnes
492: implicit none
494: SNES snes
495: PetscInt it,dummy
496: PetscReal xnorm,snorm,fnorm,nrm
497: SNESConvergedReason reason
498: Vec f
499: PetscErrorCode ierr
501: call SNESGetFunction(snes,f,PETSC_NULL_FUNCTION,dummy,ierr)
502: call VecNorm(f,NORM_INFINITY,nrm,ierr)
503: if (nrm .le. 1.e-5) reason = SNES_CONVERGED_FNORM_ABS
505: end
507: !/*TEST
508: !
509: ! build:
510: ! requires: !complex !single
511: !
512: ! test:
513: ! nsize: 4
514: ! args: -snes_mf -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
515: !
516: ! test:
517: ! suffix: 2
518: ! nsize: 4
519: ! args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
520: !
521: ! test:
522: ! suffix: 3
523: ! nsize: 3
524: ! args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
525: !
526: ! test:
527: ! suffix: 6
528: ! nsize: 1
529: ! args: -snes_monitor_short -my_snes_convergence
530: !
531: !TEST*/