Actual source code: ex1f.F

petsc-3.5.4 2015-05-23
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```  1: !
2: !   Solves the time dependent Bratu problem using pseudo-timestepping
3: !
4: !   Concepts: TS^pseudo-timestepping
5: !   Concepts: pseudo-timestepping
6: !   Concepts: TS^nonlinear problems
7: !   Processors: 1
8: !
9: !   This code demonstrates how one may solve a nonlinear problem
10: !   with pseudo-timestepping. In this simple example, the pseudo-timestep
11: !   is the same for all grid points, i.e., this is equivalent to using
12: !   the backward Euler method with a variable timestep.
13: !
14: !   Note: This example does not require pseudo-timestepping since it
15: !   is an easy nonlinear problem, but it is included to demonstrate how
16: !   the pseudo-timestepping may be done.
17: !
18: !   See snes/examples/tutorials/ex4.c[ex4f.F] and
19: !   snes/examples/tutorials/ex5.c[ex5f.F] where the problem is described
20: !   and solved using the method of Newton alone.
21: !
22: !   Include "petscts.h"    to use the PETSc timestepping routines,
23: !           "petscsys.h" for basic PETSc operation,
24: !           "petscmat.h"   for matrix operations,
25: !           "petscpc.h"    for preconditions, and
26: !           "petscvec.h"   for vector operations.
27: !
28: !23456789012345678901234567890123456789012345678901234567890123456789012
29:       program main
30:       implicit none
31: #include <finclude/petscsys.h>
32: #include <finclude/petscvec.h>
33: #include <finclude/petscmat.h>
34: #include <finclude/petscpc.h>
35: #include <finclude/petscts.h>
36: !
37: !  Create an application context to contain data needed by the
38: !  application-provided call-back routines, FormJacobian() and
39: !  FormFunction(). We use a double precision array with three
40: !  entries indexed by param, lmx, lmy.
41: !
42:       PetscReal user(3)
43:       PetscInt          param,lmx,lmy,i5
44:       parameter (param = 1,lmx = 2,lmy = 3)
45: !
46: !   User-defined routines
47: !
48:       external FormJacobian,FormFunction
49: !
50: !   Data for problem
51: !
52:       TS                ts
53:       Vec               x,r
54:       Mat               J
55:       PetscInt           its,N,i1000
56:       PetscBool  flg
57:       PetscErrorCode      ierr
58:       PetscReal  param_max,param_min,dt
59:       PetscReal  tmax,zero
60:       PetscReal  ftime
61:       TSConvergedReason reason

63:       i5 = 5
64:       param_max = 6.81
65:       param_min = 0

67:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
68:       user(lmx)        = 4
69:       user(lmy)        = 4
70:       user(param)      = 6.0

72: !
73: !     Allow user to set the grid dimensions and nonlinearity parameter at run-time
74: !
75:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-mx',user(lmx),    &
76:      &     flg,ierr)
77:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-my',user(lmy),     &
78:      &     flg,ierr)
79:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-param',           &
80:      &     user(param),flg,ierr)
81:       if (user(param) .ge. param_max .or.                               &
82:      &                                user(param) .le. param_min) then
83:         print*,'Parameter is out of range'
84:       endif
85:       if (user(lmx) .gt. user(lmy)) then
86:         dt = .5/user(lmx)
87:       else
88:         dt = .5/user(lmy)
89:       endif
90:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-dt',dt,flg,ierr)
91:       N          = int(user(lmx)*user(lmy))

93: !
94: !      Create vectors to hold the solution and function value
95: !
96:       call VecCreateSeq(PETSC_COMM_SELF,N,x,ierr)
97:       call VecDuplicate(x,r,ierr)

99: !
100: !    Create matrix to hold Jacobian. Preallocate 5 nonzeros per row
101: !    in the sparse matrix. Note that this is not the optimal strategy see
102: !    the Performance chapter of the users manual for information on
103: !    preallocating memory in sparse matrices.
104: !
105:       i5 = 5
106:       call MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,i5,PETSC_NULL_INTEGER,    &
107:      &     J,ierr)

109: !
110: !     Create timestepper context
111: !

113:       call TSCreate(PETSC_COMM_WORLD,ts,ierr)
114:       call TSSetProblemType(ts,TS_NONLINEAR,ierr)

116: !
117: !     Tell the timestepper context where to compute solutions
118: !

120:       call TSSetSolution(ts,x,ierr)

122: !
123: !    Provide the call-back for the nonlinear function we are
124: !    evaluating. Thus whenever the timestepping routines need the
125: !    function they will call this routine. Note the final argument
126: !    is the application context used by the call-back functions.
127: !

129:       call TSSetRHSFunction(ts,PETSC_NULL_OBJECT,FormFunction,user,ierr)

131: !
132: !     Set the Jacobian matrix and the function used to compute
133: !     Jacobians.
134: !

136:       call TSSetRHSJacobian(ts,J,J,FormJacobian,user,ierr)

138: !
139: !       For the initial guess for the problem
140: !

142:       call FormInitialGuess(x,user,ierr)

144: !
145: !       This indicates that we are using pseudo timestepping to
146: !     find a steady state solution to the nonlinear problem.
147: !

149:       call TSSetType(ts,TSPSEUDO,ierr)

151: !
152: !       Set the initial time to start at (this is arbitrary for
153: !     steady state problems and the initial timestep given above
154: !

156:       zero = 0.0
157:       call TSSetInitialTimeStep(ts,zero,dt,ierr)

159: !
160: !      Set a large number of timesteps and final duration time
161: !     to insure convergence to steady state.
162: !
163:       i1000 = 1000
164:       tmax  = 1.e12
165:       call TSSetDuration(ts,i1000,tmax,ierr)

167: !
168: !      Set any additional options from the options database. This
169: !     includes all options for the nonlinear and linear solvers used
170: !     internally the timestepping routines.
171: !

173:       call TSSetFromOptions(ts,ierr)

175:       call TSSetUp(ts,ierr)

177: !
178: !      Perform the solve. This is where the timestepping takes place.
179: !
180:       call TSSolve(ts,x,ierr)
181:       call TSGetSolveTime(ts,ftime,ierr)
182:       call TSGetTimeStepNumber(ts,its,ierr)
183:       call TSGetConvergedReason(ts,reason,ierr)

185:       write(6,100) its,ftime,reason
186:  100  format('Number of pseudo time-steps ',i5,' final time ',1pe8.2    &
187:      &     ,' reason ',i3)

189: !
190: !     Free the data structures constructed above
191: !

193:       call VecDestroy(x,ierr)
194:       call VecDestroy(r,ierr)
195:       call MatDestroy(J,ierr)
196:       call TSDestroy(ts,ierr)
197:       call PetscFinalize(ierr)
198:       end

200: !
201: !  --------------------  Form initial approximation -----------------
202: !
203:       subroutine FormInitialGuess(X,user,ierr)
204:       implicit none
205: #include <finclude/petscsys.h>
206: #include <finclude/petscvec.h>
207: #include <finclude/petscmat.h>
208: #include <finclude/petscpc.h>
209: #include <finclude/petscts.h>
210:       Vec              X
211:       PetscReal user(3)
212:       PetscInt  i,j,row,mx,my
213:       PetscErrorCode ierr
214:       PetscOffset      xidx
215:       PetscReal one,lambda
216:       PetscReal temp1,temp,hx,hy
217:       PetscScalar      xx(1)
218:       PetscInt          param,lmx,lmy
219:       parameter (param = 1,lmx = 2,lmy = 3)

221:       one = 1.0

223:       mx     = int(user(lmx))
224:       my     = int(user(lmy))
225:       lambda = user(param)

227:       hy    = one / (my-1)
228:       hx    = one / (mx-1)

230:       call VecGetArray(X,xx,xidx,ierr)
231:       temp1 = lambda/(lambda + one)
232:       do 10, j=1,my
233:         temp = min(j-1,my-j)*hy
234:         do 20 i=1,mx
235:           row = i + (j-1)*mx
236:           if (i .eq. 1 .or. j .eq. 1 .or.                               &
237:      &        i .eq. mx .or. j .eq. my) then
238:             xx(row+xidx) = 0.0
239:           else
240:             xx(row+xidx) =                                              &
241:      &        temp1*sqrt(min(min(i-1,mx-i)*hx,temp))
242:           endif
243:  20     continue
244:  10   continue
245:       call VecRestoreArray(X,xx,xidx,ierr)
246:       return
247:       end
248: !
249: !  --------------------  Evaluate Function F(x) ---------------------
250: !
251:       subroutine FormFunction(ts,t,X,F,user,ierr)
252:       implicit none
253: #include <finclude/petscsys.h>
254: #include <finclude/petscvec.h>
255: #include <finclude/petscmat.h>
256: #include <finclude/petscpc.h>
257: #include <finclude/petscts.h>
258:       TS       ts
259:       PetscReal  t
260:       Vec               X,F
261:       PetscReal  user(3)
262:       PetscErrorCode     ierr
263:       PetscInt         i,j,row,mx,my
264:       PetscOffset       xidx,fidx
265:       PetscReal  two,lambda
266:       PetscReal  hx,hy,hxdhy,hydhx
267:       PetscScalar  ut,ub,ul,ur,u
268:       PetscScalar  uxx,uyy,sc
269:       PetscScalar  xx(1),ff(1)
270:       PetscInt     param,lmx,lmy
271:       parameter (param = 1,lmx = 2,lmy = 3)

273:       two = 2.0

275:       mx     = int(user(lmx))
276:       my     = int(user(lmy))
277:       lambda = user(param)

279:       hx    = 1.0 / (mx-1)
280:       hy    = 1.0 / (my-1)
281:       sc    = hx*hy
282:       hxdhy = hx/hy
283:       hydhx = hy/hx

285:       call VecGetArray(X,xx,xidx,ierr)
286:       call VecGetArray(F,ff,fidx,ierr)
287:       do 10 j=1,my
288:         do 20 i=1,mx
289:           row = i + (j-1)*mx
290:           if (i .eq. 1 .or. j .eq. 1 .or.                               &
291:      &        i .eq. mx .or. j .eq. my) then
292:             ff(row+fidx) = xx(row+xidx)
293:           else
294:             u            = xx(row + xidx)
295:             ub           = xx(row - mx + xidx)
296:             ul           = xx(row - 1 + xidx)
297:             ut           = xx(row + mx + xidx)
298:             ur           = xx(row + 1 + xidx)
299:             uxx          = (-ur + two*u - ul)*hydhx
300:             uyy          = (-ut + two*u - ub)*hxdhy
301:             ff(row+fidx) = -uxx - uyy + sc*lambda*exp(u)
302:             u =  -uxx - uyy + sc*lambda*exp(u)
303:          endif
304:  20   continue
305:  10   continue

307:       call VecRestoreArray(X,xx,xidx,ierr)
308:       call VecRestoreArray(F,ff,fidx,ierr)
309:       return
310:       end
311: !
312: !  --------------------  Evaluate Jacobian of F(x) --------------------
313: !
314:       subroutine FormJacobian(ts,ctime,X,JJ,B,user,ierr)
315:       implicit none
316: #include <finclude/petscsys.h>
317: #include <finclude/petscvec.h>
318: #include <finclude/petscmat.h>
319: #include <finclude/petscpc.h>
320: #include <finclude/petscts.h>
321:       TS               ts
322:       Vec              X
323:       Mat              JJ,B
324:       PetscReal user(3),ctime
325:       PetscErrorCode   ierr
326:       Mat              jac
327:       PetscOffset xidx
328:       PetscInt    i,j,row(1),mx,my
329:       PetscInt    col(5),i1,i5
330:       PetscScalar two,one,lambda
331:       PetscScalar v(5),sc,xx(1)
332:       PetscReal hx,hy,hxdhy,hydhx

334:       PetscInt  param,lmx,lmy
335:       parameter (param = 1,lmx = 2,lmy = 3)

337:       i1 = 1
338:       i5 = 5
339:       jac = B
340:       two = 2.0
341:       one = 1.0

343:       mx     = int(user(lmx))
344:       my     = int(user(lmy))
345:       lambda = user(param)

347:       hx    = 1.0 / (mx-1)
348:       hy    = 1.0 / (my-1)
349:       sc    = hx*hy
350:       hxdhy = hx/hy
351:       hydhx = hy/hx

353:       call VecGetArray(X,xx,xidx,ierr)
354:       do 10 j=1,my
355:         do 20 i=1,mx
356: !
357: !      When inserting into PETSc matrices, indices start at 0
358: !
359:           row(1) = i - 1 + (j-1)*mx
360:           if (i .eq. 1 .or. j .eq. 1 .or.                               &
361:      &        i .eq. mx .or. j .eq. my) then
362:             call MatSetValues(jac,i1,row,i1,row,one,INSERT_VALUES,ierr)
363:           else
364:             v(1)   = hxdhy
365:             col(1) = row(1) - mx
366:             v(2)   = hydhx
367:             col(2) = row(1) - 1
368:             v(3)   = -two*(hydhx+hxdhy)+sc*lambda*exp(xx(row(1)+1+xidx))
369:             col(3) = row(1)
370:             v(4)   = hydhx
371:             col(4) = row(1) + 1
372:             v(5)   = hxdhy
373:             col(5) = row(1) + mx
374:             call MatSetValues(jac,i1,row,i5,col,v,INSERT_VALUES,ierr)
375:           endif
376:  20     continue
377:  10   continue
378:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
379:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
380:       call VecRestoreArray(X,xx,xidx,ierr)
381:       return
382:       end

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