Actual source code: ex1f.F

  1: !
  2: ! "$Id: ex1f.F,v 1.29 2001/08/10 15:44:18 balay Exp $"
  3: !
  4: !   Solves the time dependent Bratu problem using pseudo-timestepping
  5: !
  6: !   Concepts: TS^pseudo-timestepping
  7: !   Concepts: pseudo-timestepping
  8: !   Concepts: nonlinear problems
  9: !   Processors: 1
 10: !
 11: !   This code demonstrates how one may solve a nonlinear problem
 12: !   with pseudo-timestepping. In this simple example, the pseudo-timestep
 13: !   is the same for all grid points, i.e., this is equivalent to using
 14: !   the backward Euler method with a variable timestep.
 15: !
 16: !   Note: This example does not require pseudo-timestepping since it
 17: !   is an easy nonlinear problem, but it is included to demonstrate how
 18: !   the pseudo-timestepping may be done.
 19: !
 20: !   See snes/examples/tutorials/ex4.c[ex4f.F] and
 21: !   snes/examples/tutorials/ex5.c[ex5f.F] where the problem is described
 22: !   and solved using the method of Newton alone.
 23: !
 24: !   Include "petscts.h"    to use the PETSc timestepping routines,
 25: !           "petsc.h" for basic PETSc operation,
 26: !           "petscmat.h"   for matrix operations,
 27: !           "petscpc.h"    for preconditions, and
 28: !           "petscvec.h"   for vector operations.
 29: !
 30: !23456789012345678901234567890123456789012345678901234567890123456789012
 31:       program main
 32:       implicit none
 33:  #include finclude/petsc.h
 34:  #include finclude/petscvec.h
 35:  #include finclude/petscmat.h
 36:  #include finclude/petscpc.h
 37:  #include finclude/petscts.h
 38: !
 39: !  Create an application context to contain data needed by the
 40: !  application-provided call-back routines, FormJacobian() and
 41: !  FormFunction(). We use a double precision array with three
 42: !  entries indexed by param, lmx, lmy.
 43: !
 44:       double precision user(3)
 45:       integer          param,lmx,lmy
 46:       parameter (param = 1,lmx = 2,lmy = 3)
 47: !
 48: !   User-defined routines
 49: !
 50:       external FormJacobian,FormFunction
 51: !
 52: !   Data for problem
 53: !
 54:       TS                ts
 55:       Vec               x,r
 56:       Mat               J
 57:       integer           its
 58:       integer           ierr,N,flg
 59:       double precision  param_max,param_min,dt,tmax,zero
 60:       double precision  ftime

 62:       param_max = 6.81
 63:       param_min = 0

 65:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 66:       user(lmx)        = 4
 67:       user(lmy)        = 4
 68:       user(param)      = 6.0
 69: 
 70: !
 71: !     Allow user to set the grid dimensions and nonlinearity parameter at run-time
 72: !
 73:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-mx',user(lmx),    &
 74:      &     flg,ierr)
 75:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-my',user(lmy),     &
 76:      &     flg,ierr)
 77:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-param',           &
 78:      &     user(param),flg,ierr)
 79:       if (user(param) .ge. param_max .or.                               &
 80:      &                                user(param) .le. param_min) then
 81:         print*,'Parameter is out of range'
 82:       endif
 83:       if (user(lmx) .gt. user(lmy)) then
 84:         dt = .5/user(lmx)
 85:       else
 86:         dt = .5/user(lmy)
 87:       endif
 88:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-dt',dt,flg,ierr)
 89:       N          = user(lmx)*user(lmy)
 90: 
 91: !
 92: !      Create vectors to hold the solution and function value
 93: !
 94:       call VecCreateSeq(PETSC_COMM_SELF,N,x,ierr)
 95:       call VecDuplicate(x,r,ierr)

 97: !
 98: !    Create matrix to hold Jacobian. Preallocate 5 nonzeros per row
 99: !    in the sparse matrix. Note that this is not the optimal strategy see
100: !    the Performance chapter of the users manual for information on
101: !    preallocating memory in sparse matrices.
102: !

104:       call MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,5,PETSC_NULL_INTEGER,    &
105:      &     J,ierr)

107: !
108: !     Create timestepper context
109: !

111:       call TSCreate(PETSC_COMM_WORLD,ts,ierr)
112:       call TSSetProblemType(ts,TS_NONLINEAR,ierr)

114: !
115: !     Tell the timestepper context where to compute solutions
116: !

118:       call TSSetSolution(ts,x,ierr)

120: !
121: !    Provide the call-back for the nonlinear function we are
122: !    evaluating. Thus whenever the timestepping routines need the
123: !    function they will call this routine. Note the final argument
124: !    is the application context used by the call-back functions.
125: !

127:       call TSSetRHSFunction(ts,FormFunction,user,ierr)

129: !
130: !     Set the Jacobian matrix and the function used to compute
131: !     Jacobians.
132: !

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

136: !
137: !       For the initial guess for the problem
138: !

140:       call FormInitialGuess(x,user,ierr)

142: !
143: !       This indicates that we are using pseudo timestepping to
144: !     find a steady state solution to the nonlinear problem.
145: !

147:       call TSSetType(ts,TS_PSEUDO,ierr)

149: !
150: !       Set the initial time to start at (this is arbitrary for
151: !     steady state problems and the initial timestep given above
152: !

154:       zero = 0.0
155:       call TSSetInitialTimeStep(ts,zero,dt,ierr)

157: !
158: !      Set a large number of timesteps and final duration time
159: !     to insure convergence to steady state.
160: !
161:       tmax = 1.e12
162:       call TSSetDuration(ts,1000,tmax,ierr)

164: !
165: !      Set any additional options from the options database. This
166: !     includes all options for the nonlinear and linear solvers used
167: !     internally the the timestepping routines.
168: !

170:       call TSSetFromOptions(ts,ierr)

172:       call TSSetUp(ts,ierr)

174: !
175: !      Perform the solve. This is where the timestepping takes place.
176: !
177: 
178:       call TSStep(ts,its,ftime,ierr)
179: 
180:       write(6,100) its,ftime
181:  100  format('Number of pseudo time-steps ',i5,' final time ',1pe8.2)

183: !
184: !     Free the data structures constructed above
185: !

187:       call VecDestroy(x,ierr)
188:       call VecDestroy(r,ierr)
189:       call MatDestroy(J,ierr)
190:       call TSDestroy(ts,ierr)
191:       call PetscFinalize(ierr)
192:       end

194: !
195: !  --------------------  Form initial approximation -----------------
196: !
197:       subroutine FormInitialGuess(X,user,ierr)
198:       implicit none
199:  #include finclude/petsc.h
200:  #include finclude/petscvec.h
201:  #include finclude/petscmat.h
202:  #include finclude/petscpc.h
203:  #include finclude/petscts.h
204:       Vec              X
205:       double precision user(3)
206:       integer          i,j,row,mx,my,ierr
207:       PetscOffset      xidx
208:       double precision two,one,lambda
209:       double precision temp1,temp,hx,hy,hxdhy,hydhx
210:       double precision sc
211:       PetscScalar      xx(1)
212:       integer          param,lmx,lmy
213:       parameter (param = 1,lmx = 2,lmy = 3)

215:       two = 2.0
216:       one = 1.0

218:       mx     = user(lmx)
219:       my     = user(lmy)
220:       lambda = user(param)

222:       hy    = one / (my-1)
223:       hx    = one / (mx-1)
224:       sc    = hx*hy
225:       hxdhy = hx/hy
226:       hydhx = hy/hx

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

269:       two = 2.0
270:       one = 1.0

272:       mx     = user(lmx)
273:       my     = user(lmy)
274:       lambda = user(param)

276:       hx    = 1.0 / dble(mx-1)
277:       hy    = 1.0 / dble(my-1)
278:       sc    = hx*hy
279:       hxdhy = hx/hy
280:       hydhx = hy/hx

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

304:       call VecRestoreArray(X,xx,xidx,ierr)
305:       call VecRestoreArray(F,ff,fidx,ierr)
306:       return
307:       end
308: !
309: !  --------------------  Evaluate Jacobian of F(x) --------------------
310: !
311:       subroutine FormJacobian(ts,ctime,X,JJ,B,flag,user,ierr)
312:       implicit none
313:  #include finclude/petsc.h
314:  #include finclude/petscvec.h
315:  #include finclude/petscmat.h
316:  #include finclude/petscpc.h
317:  #include finclude/petscts.h
318:       TS               ts
319:       Vec              X
320:       Mat              JJ,B
321:       MatStructure     flag
322:       double precision user(3),ctime
323:       Mat              jac
324:       integer          i,j,row,mx,my,col(5),ierr
325:       PetscOffset      xidx
326:       PetscScalar      two,one,lambda,v(5),sc,xx(1)
327:       double precision hx,hy,hxdhy,hydhx

329:       integer   param,lmx,lmy
330:       parameter (param = 1,lmx = 2,lmy = 3)

332:       jac = B
333:       two = 2.0
334:       one = 1.0

336:       mx     = user(lmx)
337:       my     = user(lmy)
338:       lambda = user(param)

340:       hx    = 1.0 / dble(mx-1)
341:       hy    = 1.0 / dble(my-1)
342:       sc    = hx*hy
343:       hxdhy = hx/hy
344:       hydhx = hy/hx

346:       call VecGetArray(X,xx,xidx,ierr)
347:       do 10 j=1,my
348:         do 20 i=1,mx
349: !
350: !      When inserting into PETSc matrices, indices start at 0
351: !
352: !       call PetscTrValid(ierr)
353:           row = i - 1 + (j-1)*mx
354:           if (i .eq. 1 .or. j .eq. 1 .or.                               &
355:      &        i .eq. mx .or. j .eq. my) then
356:             call MatSetValues(jac,1,row,1,row,one,INSERT_VALUES,ierr)
357:           else
358:             v(1)   = hxdhy
359:             col(1) = row - mx
360:             v(2)   = hydhx
361:             col(2) = row - 1
362:             v(3)   = -two*(hydhx+hxdhy)+sc*lambda*exp(xx(row+1+xidx))
363:             col(3) = row
364:             v(4)   = hydhx
365:             col(4) = row + 1
366:             v(5)   = hxdhy
367:             col(5) = row + mx
368:             call MatSetValues(jac,1,row,5,col,v,INSERT_VALUES,ierr)
369:           endif
370:  20     continue
371:  10   continue
372:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
373:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
374:       call VecRestoreArray(X,xx,xidx,ierr)
375:       flag = SAME_NONZERO_PATTERN
376: !       call PetscTrValid(ierr)
377:       return
378:       end