Actual source code: ex5f.F
petsc-3.4.5 2014-06-29
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*/
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: ! --------------------------------------------------------------------------
33: program main
34: implicit none
35: !
36: ! We place common blocks, variable declarations, and other include files
37: ! needed for this code in the single file ex5f.h. We then need to include
38: ! only this file throughout the various routines in this program. See
39: ! additional comments in the file ex5f.h.
40: !
41: #include "ex5f.h"
43: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
44: ! Variable declarations
45: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
46: !
47: ! Variables:
48: ! snes - nonlinear solver
49: ! x, r - solution, residual vectors
50: ! its - iterations for convergence
51: !
52: ! See additional variable declarations in the file ex5f.h
53: !
54: SNES snes
55: Vec x,r
56: PetscInt its,i1,i4
57: PetscErrorCode ierr
58: PetscReal lambda_max,lambda_min
59: PetscBool flg
62: ! Note: Any user-defined Fortran routines (such as FormJacobianLocal)
63: ! MUST be declared as external.
65: external FormInitialGuess
66: external FormFunctionLocal,FormJacobianLocal
68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
69: ! Initialize program
70: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
72: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
73: call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
74: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
76: ! Initialize problem parameters
78: i1 = 1
79: i4 = -4
80: lambda_max = 6.81
81: lambda_min = 0.0
82: lambda = 6.0
83: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par',lambda, &
84: & flg,ierr)
85: if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
86: if (rank .eq. 0) write(6,*) 'Lambda is out of range'
87: SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
88: endif
90: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
91: ! Create nonlinear solver context
92: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
94: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
96: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: ! Create vector data structures; set function evaluation routine
98: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100: ! Create distributed array (DMDA) to manage parallel grid and vectors
102: ! This really needs only the star-type stencil, but we use the box
103: ! stencil temporarily.
104: call DMDACreate2d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE, &
105: & DMDA_BOUNDARY_NONE, &
106: & DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE,i1,i1, &
107: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
109: ! Extract global and local vectors from DMDA; then duplicate for remaining
110: ! vectors that are the same types
112: call DMCreateGlobalVector(da,x,ierr)
113: call VecDuplicate(x,r,ierr)
115: ! Get local grid boundaries (for 2-dimensional DMDA)
117: call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER, &
118: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
119: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
120: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
121: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
122: & PETSC_NULL_INTEGER,ierr)
123: call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym, &
124: & PETSC_NULL_INTEGER,ierr)
125: call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym, &
126: & PETSC_NULL_INTEGER,ierr)
128: ! Here we shift the starting indices up by one so that we can easily
129: ! use the Fortran convention of 1-based indices (rather 0-based indices).
131: xs = xs+1
132: ys = ys+1
133: gxs = gxs+1
134: gys = gys+1
136: ye = ys+ym-1
137: xe = xs+xm-1
138: gye = gys+gym-1
139: gxe = gxs+gxm-1
141: ! Set function evaluation routine and vector
143: call DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal, &
144: & PETSC_NULL_OBJECT,ierr)
145: call DMDASNESSetJacobianLocal(da,FormJacobianLocal, &
146: & PETSC_NULL_OBJECT,ierr)
147: call SNESSetDM(snes,da,ierr)
149: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: ! Customize nonlinear solver; set runtime options
151: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
155: call SNESSetFromOptions(snes,ierr)
156: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: ! Evaluate initial guess; then solve nonlinear system.
158: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: ! Note: The user should initialize the vector, x, with the initial guess
161: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
162: ! to employ an initial guess of zero, the user should explicitly set
163: ! this vector to zero by calling VecSet().
165: call FormInitialGuess(x,ierr)
166: call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
167: call SNESGetIterationNumber(snes,its,ierr)
168: if (rank .eq. 0) then
169: write(6,100) its
170: endif
171: 100 format('Number of SNES iterations = ',i5)
174: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: ! Free work space. All PETSc objects should be destroyed when they
176: ! are no longer needed.
177: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: call VecDestroy(x,ierr)
180: call VecDestroy(r,ierr)
181: call SNESDestroy(snes,ierr)
182: call DMDestroy(da,ierr)
183: call PetscFinalize(ierr)
184: end
186: ! ---------------------------------------------------------------------
187: !
188: ! FormInitialGuess - Forms initial approximation.
189: !
190: ! Input Parameters:
191: ! X - vector
192: !
193: ! Output Parameter:
194: ! X - vector
195: !
196: ! Notes:
197: ! This routine serves as a wrapper for the lower-level routine
198: ! "ApplicationInitialGuess", where the actual computations are
199: ! done using the standard Fortran style of treating the local
200: ! vector data as a multidimensional array over the local mesh.
201: ! This routine merely handles ghost point scatters and accesses
202: ! the local vector data via VecGetArray() and VecRestoreArray().
203: !
204: subroutine FormInitialGuess(X,ierr)
205: implicit none
207: #include "ex5f.h"
209: ! Input/output variables:
210: Vec X
211: PetscErrorCode ierr
213: ! Declarations for use with local arrays:
214: PetscScalar lx_v(0:1)
215: PetscOffset lx_i
216: Vec localX
218: 0
220: ! Get a pointer to vector data.
221: ! - For default PETSc vectors, VecGetArray() returns a pointer to
222: ! the data array. Otherwise, the routine is implementation dependent.
223: ! - You MUST call VecRestoreArray() when you no longer need access to
224: ! the array.
225: ! - Note that the Fortran interface to VecGetArray() differs from the
226: ! C version. See the users manual for details.
228: call DMGetLocalVector(da,localX,ierr)
229: call VecGetArray(localX,lx_v,lx_i,ierr)
231: ! Compute initial guess over the locally owned part of the grid
233: call InitialGuessLocal(lx_v(lx_i),ierr)
235: ! Restore vector
237: call VecRestoreArray(localX,lx_v,lx_i,ierr)
239: ! Insert values into global vector
241: call DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X,ierr)
242: call DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X,ierr)
243: call DMRestoreLocalVector(da,localX,ierr)
244: return
245: end
247: ! ---------------------------------------------------------------------
248: !
249: ! InitialGuessLocal - Computes initial approximation, called by
250: ! the higher level routine FormInitialGuess().
251: !
252: ! Input Parameter:
253: ! x - local vector data
254: !
255: ! Output Parameters:
256: ! x - local vector data
257: ! ierr - error code
258: !
259: ! Notes:
260: ! This routine uses standard Fortran-style computations over a 2-dim array.
261: !
262: subroutine InitialGuessLocal(x,ierr)
263: implicit none
265: #include "ex5f.h"
267: ! Input/output variables:
268: PetscScalar x(gxs:gxe,gys:gye)
269: PetscErrorCode ierr
271: ! Local variables:
272: PetscInt i,j
273: PetscReal temp1,temp,one,hx,hy
275: ! Set parameters
277: 0
278: one = 1.0
279: hx = one/((mx-1))
280: hy = one/((my-1))
281: temp1 = lambda/(lambda + one)
283: do 20 j=ys,ye
284: temp = (min(j-1,my-j))*hy
285: do 10 i=xs,xe
286: if (i .eq. 1 .or. j .eq. 1 &
287: & .or. i .eq. mx .or. j .eq. my) then
288: x(i,j) = 0.0
289: else
290: x(i,j) = temp1 * &
291: & sqrt(min(min(i-1,mx-i)*hx,(temp)))
292: endif
293: 10 continue
294: 20 continue
296: return
297: end
299: ! ---------------------------------------------------------------------
300: !
301: ! FormFunctionLocal - Computes nonlinear function, called by
302: ! the higher level routine FormFunction().
303: !
304: ! Input Parameter:
305: ! x - local vector data
306: !
307: ! Output Parameters:
308: ! f - local vector data, f(x)
309: ! ierr - error code
310: !
311: ! Notes:
312: ! This routine uses standard Fortran-style computations over a 2-dim array.
313: !
314: !
315: subroutine FormFunctionLocal(info,x,f,dummy,ierr)
317: implicit none
319: #include "ex5f.h"
321: ! Input/output variables:
322: DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
323: PetscScalar x(gxs:gxe,gys:gye)
324: PetscScalar f(xs:xe,ys:ye)
325: PetscErrorCode ierr
326: PetscObject dummy
328: ! Local variables:
329: PetscScalar two,one,hx,hy
330: PetscScalar hxdhy,hydhx,sc
331: PetscScalar u,uxx,uyy
332: PetscInt i,j
334: xs = info(DMDA_LOCAL_INFO_XS)+1
335: xe = xs+info(DMDA_LOCAL_INFO_XM)-1
336: ys = info(DMDA_LOCAL_INFO_YS)+1
337: ye = ys+info(DMDA_LOCAL_INFO_YM)-1
338: mx = info(DMDA_LOCAL_INFO_MX)
339: my = info(DMDA_LOCAL_INFO_MY)
341: one = 1.0
342: two = 2.0
343: hx = one/(mx-1)
344: hy = one/(my-1)
345: sc = hx*hy*lambda
346: hxdhy = hx/hy
347: hydhx = hy/hx
349: ! Compute function over the locally owned part of the grid
351: do 20 j=ys,ye
352: do 10 i=xs,xe
353: if (i .eq. 1 .or. j .eq. 1 &
354: & .or. i .eq. mx .or. j .eq. my) then
355: f(i,j) = x(i,j)
356: else
357: u = x(i,j)
358: uxx = hydhx * (two*u &
359: & - x(i-1,j) - x(i+1,j))
360: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
361: f(i,j) = uxx + uyy - sc*exp(u)
362: endif
363: 10 continue
364: 20 continue
366: call PetscLogFlops(11.0d0*ym*xm,ierr)
368: return
369: end
371: ! ---------------------------------------------------------------------
372: !
373: ! FormJacobianLocal - Computes Jacobian matrix, called by
374: ! the higher level routine FormJacobian().
375: !
376: ! Input Parameters:
377: ! x - local vector data
378: !
379: ! Output Parameters:
380: ! jac - Jacobian matrix
381: ! jac_prec - optionally different preconditioning matrix (not used here)
382: ! ierr - error code
383: !
384: ! Notes:
385: ! This routine uses standard Fortran-style computations over a 2-dim array.
386: !
387: ! Notes:
388: ! Due to grid point reordering with DMDAs, we must always work
389: ! with the local grid points, and then transform them to the new
390: ! global numbering with the "ltog" mapping (via DMDAGetGlobalIndices()).
391: ! We cannot work directly with the global numbers for the original
392: ! uniprocessor grid!
393: !
394: ! Two methods are available for imposing this transformation
395: ! when setting matrix entries:
396: ! (A) MatSetValuesLocal(), using the local ordering (including
397: ! ghost points!)
398: ! - Use DMDAGetGlobalIndices() to extract the local-to-global map
399: ! - Associate this map with the matrix by calling
400: ! MatSetLocalToGlobalMapping() once
401: ! - Set matrix entries using the local ordering
402: ! by calling MatSetValuesLocal()
403: ! (B) MatSetValues(), using the global ordering
404: ! - Use DMDAGetGlobalIndices() to extract the local-to-global map
405: ! - Then apply this map explicitly yourself
406: ! - Set matrix entries using the global ordering by calling
407: ! MatSetValues()
408: ! Option (A) seems cleaner/easier in many cases, and is the procedure
409: ! used in this example.
410: !
411: subroutine FormJacobianLocal(info,x,A,jac,ctx,str,ierr)
412: implicit none
414: #include "ex5f.h"
416: ! Input/output variables:
417: PetscScalar x(gxs:gxe,gys:gye)
418: Mat A,jac
419: MatStructure str
420: PetscErrorCode ierr
421: integer ctx
422: DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
425: ! Local variables:
426: PetscInt row,col(5),i,j,i1,i5
427: PetscScalar two,one,hx,hy,v(5)
428: PetscScalar hxdhy,hydhx,sc
430: ! Set parameters
432: i1 = 1
433: i5 = 5
434: one = 1.0
435: two = 2.0
436: hx = one/(mx-1)
437: hy = one/(my-1)
438: sc = hx*hy
439: hxdhy = hx/hy
440: hydhx = hy/hx
442: ! Compute entries for the locally owned part of the Jacobian.
443: ! - Currently, all PETSc parallel matrix formats are partitioned by
444: ! contiguous chunks of rows across the processors.
445: ! - Each processor needs to insert only elements that it owns
446: ! locally (but any non-local elements will be sent to the
447: ! appropriate processor during matrix assembly).
448: ! - Here, we set all entries for a particular row at once.
449: ! - We can set matrix entries either using either
450: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
451: ! - Note that MatSetValues() uses 0-based row and column numbers
452: ! in Fortran as well as in C.
454: do 20 j=ys,ye
455: row = (j - gys)*gxm + xs - gxs - 1
456: do 10 i=xs,xe
457: row = row + 1
458: ! boundary points
459: if (i .eq. 1 .or. j .eq. 1 &
460: & .or. i .eq. mx .or. j .eq. my) then
461: ! Some f90 compilers need 4th arg to be of same type in both calls
462: col(1) = row
463: v(1) = one
464: call MatSetValuesLocal(jac,i1,row,i1,col,v, &
465: & INSERT_VALUES,ierr)
466: ! interior grid points
467: else
468: v(1) = -hxdhy
469: v(2) = -hydhx
470: v(3) = two*(hydhx + hxdhy) &
471: & - sc*lambda*exp(x(i,j))
472: v(4) = -hydhx
473: v(5) = -hxdhy
474: col(1) = row - gxm
475: col(2) = row - 1
476: col(3) = row
477: col(4) = row + 1
478: col(5) = row + gxm
479: call MatSetValuesLocal(jac,i1,row,i5,col,v, &
480: & INSERT_VALUES,ierr)
481: endif
482: 10 continue
483: 20 continue
484: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
485: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
486: if (A .ne. jac) then
487: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
488: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
489: endif
490: str = SAME_NONZERO_PATTERN
491: return
492: end