Actual source code: ex22f.F

  1: ! Time-dependent advection-reaction PDE in 1d. Demonstrates IMEX methods
  2: !
  3: !   u_t + a1*u_x = -k1*u + k2*v + s1
  4: !   v_t + a2*v_x = k1*u - k2*v + s2
  5: !   0 < x < 1;
  6: !   a1 = 1, k1 = 10^6, s1 = 0,
  7: !   a2 = 0, k2 = 2*k1, s2 = 1
  8: !
  9: !   Initial conditions:
 10: !   u(x,0) = 1 * s2*x
 11: !   v(x,0) = k0/k1*u(x,0) + s1/k1
 12: !
 13: !   Upstream boundary conditions:
 14: !   u(0,t) = 1-sin(12*t)^4
 15: !

 17:       program main
 18:       implicit none
 19: #include <finclude/petscsys.h>
 20: #include <finclude/petscvec.h>
 21: #include <finclude/petscmat.h>
 22: #include <finclude/petscsnes.h>
 23: #include <finclude/petscts.h>
 24: #include <finclude/petscdmda.h>
 25: !
 26: !  Create an application context to contain data needed by the
 27: !  application-provided call-back routines, FormJacobian() and
 28: !  FormFunction(). We use a double precision array with six
 29: !  entries, two for each problem parameter a, k, s.
 30: !
 31:       PetscReal user(6)
 32:       integer user_a,user_k,user_s
 33:       parameter (user_a = 0,user_k = 2,user_s = 4)

 35:       external FormRHSFunction,FormIFunction,FormIJacobian
 36:       external FormInitialSolution

 38:       TS             ts
 39:       Vec            X
 40:       Mat            J
 41:       PetscInt       steps,maxsteps,mx
 42:       PetscErrorCode ierr
 43:       DM             da
 44:       PetscReal      ftime,dt
 45:       PetscReal      zero,one,pone
 46:       PetscInt       im11,i2
 47:       PetscBool      flg

 49:       im11 = -11
 50:       i2   = 2
 51:       zero = 0.0
 52:       one = 1.0
 53:       pone = one / 10

 55:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)

 57: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 58: !  Create distributed array (DMDA) to manage parallel grid and vectors
 59: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 60:       call DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,im11,i2,i2, &
 61:      &     PETSC_NULL_INTEGER,da,ierr)

 63: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 64: !    Extract global vectors from DMDA;
 65: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 66:       call DMCreateGlobalVector(da,X,ierr)

 68: ! Initialize user application context
 69: ! Use zero-based indexing for command line parameters to match ex22.c
 70:       user(user_a+1) = 1.0
 71:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-a0',              &
 72:      &     user(user_a+1),flg,ierr)
 73:       user(user_a+2) = 0.0
 74:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-a1',              &
 75:      &     user(user_a+2),flg,ierr)
 76:       user(user_k+1) = 1000000.0
 77:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-k0',              &
 78:      &     user(user_k+1),flg,ierr)
 79:       user(user_k+2) = 2*user(user_k+1)
 80:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-k1',              &
 81:      &     user(user_k+2),flg,ierr)
 82:       user(user_s+1) = 0.0
 83:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-s0',              &
 84:      &     user(user_s+1),flg,ierr)
 85:       user(user_s+2) = 1.0
 86:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-s1',              &
 87:      &     user(user_s+2),flg,ierr)

 89: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90: !    Create timestepping solver context
 91: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 92:       call TSCreate(PETSC_COMM_WORLD,ts,ierr)
 93:       call TSSetDM(ts,da,ierr)
 94:       call TSSetType(ts,TSARKIMEX,ierr)
 95:       call TSSetRHSFunction(ts,PETSC_NULL_OBJECT,FormRHSFunction,       &
 96:      &     user,ierr)
 97:       call TSSetIFunction(ts,PETSC_NULL_OBJECT,FormIFunction,user,ierr)
 98:       call DMGetMatrix(da,MATAIJ,J,ierr)
 99:       call TSSetIJacobian(ts,J,J,FormIJacobian,user,ierr)

101:       ftime = 1.0
102:       maxsteps = 10000
103:       call TSSetDuration(ts,maxsteps,ftime,ierr)

105: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106: !  Set initial conditions
107: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
108:       call FormInitialSolution(ts,X,user,ierr)
109:       call TSSetSolution(ts,X,ierr)
110:       call VecGetSize(X,mx,ierr)
111: !  Advective CFL, I don't know why it needs so much safety factor.
112:       dt = pone * max(user(user_a+1),user(user_a+2)) / mx;
113:       call TSSetInitialTimeStep(ts,zero,dt,ierr)

115: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116: !   Set runtime options
117: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
118:       call TSSetFromOptions(ts,ierr)

120: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121: !  Solve nonlinear system
122: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
123:       call TSSolve(ts,X,ftime,ierr)
124:       call TSGetTimeStepNumber(ts,steps,ierr)

126: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127: !  Free work space.
128: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129:       call MatDestroy(J,ierr)
130:       call VecDestroy(X,ierr)
131:       call TSDestroy(ts,ierr)
132:       call DMDestroy(da,ierr)
133:       call PetscFinalize(ierr)
134:       end program

136: ! Small helper to extract the layout, result uses 1-based indexing.
137:       subroutine GetLayout(da,mx,xs,xe,gxs,gxe,ierr)
138:       implicit none
139: #include <finclude/petscsys.h>
140: #include <finclude/petscdmda.h>
141:       DM da
142:       PetscInt mx,xs,xe,gxs,gxe
143:       PetscErrorCode ierr
144:       PetscInt xm,gxm
145:             call DMDAGetInfo(da,PETSC_NULL_INTEGER,                     &
146:      &     mx,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                    &
147:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,    &
148:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                       &
149:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,    &
150:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
151:       call DMDAGetCorners(da,xs,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,  &
152:      &     xm,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
153:       call DMDAGetGhostCorners(da,                                      &
154:      &     gxs,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,
155:      &     gxm,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
156:       xs = xs + 1
157:       gxs = gxs + 1
158:       xe = xs + xm - 1
159:       gxe = gxs + gxm - 1
160:       end subroutine

162:       subroutine FormIFunctionLocal(mx,xs,xe,gxs,gxe,x,xdot,f,          &
163:      &     a,k,s,ierr)
164:       implicit none
165:       PetscInt mx,xs,xe,gxs,gxe
166:       PetscScalar x(2,xs:xe)
167:       PetscScalar xdot(2,xs:xe)
168:       PetscScalar f(2,xs:xe)
169:       PetscReal a(2),k(2),s(2)
170:       PetscErrorCode ierr
171:       PetscInt i
172:       do 10 i = xs,xe
173:          f(1,i) = xdot(1,i) + k(1)*x(1,i) - k(2)*x(2,i) - s(1)
174:          f(2,i) = xdot(2,i) - k(1)*x(1,i) + k(2)*x(2,i) - s(2)
175:  10   continue
176:       end subroutine

178:       subroutine FormIFunction(ts,t,X,Xdot,F,user,ierr)
179:       implicit none
180: #include <finclude/petscsys.h>
181: #include <finclude/petscvec.h>
182: #include <finclude/petscmat.h>
183: #include <finclude/petscsnes.h>
184: #include <finclude/petscts.h>
185: #include <finclude/petscdmda.h>
186:       TS ts
187:       PetscReal t
188:       Vec X,Xdot,F
189:       PetscReal user(6)
190:       PetscErrorCode ierr
191:       integer user_a,user_k,user_s
192:       parameter (user_a = 1,user_k = 3,user_s = 5)

194:       DM             da
195:       PetscInt       mx,xs,xe,gxs,gxe
196:       Vec            Xloc
197:       PetscOffset    ixx,ixxdot,iff
198:       PetscScalar    xx(0:1),xxdot(0:1),ff(0:1)

200:       call TSGetDM(ts,da,ierr)
201:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

203: ! Get access to vector data
204:       call VecGetArray(X,xx,ixx,ierr)
205:       call VecGetArray(Xdot,xxdot,ixxdot,ierr)
206:       call VecGetArray(F,ff,iff,ierr)

208:       call FormIFunctionLocal(mx,xs,xe,gxs,gxe,                         &
209:      &     xx(ixx),xxdot(ixxdot),ff(iff),                               &
210:      &     user(user_a),user(user_k),user(user_s),ierr)

212:       call VecRestoreArray(X,xx,ixx,ierr)
213:       call VecRestoreArray(Xdot,xxdot,ixxdot,ierr)
214:       call VecRestoreArray(F,ff,iff,ierr)
215:       end subroutine

217:       subroutine FormRHSFunctionLocal(mx,xs,xe,gxs,gxe,t,x,f,           &
218:      &     a,k,s,ierr)
219:       implicit none
220:       PetscInt mx,xs,xe,gxs,gxe
221:       PetscReal t
222:       PetscScalar x(2,gxs:gxe),f(2,xs:xe)
223:       PetscReal a(2),k(2),s(2)
224:       PetscErrorCode ierr
225:       PetscInt i,j
226:       PetscReal hx,u0t(2)
227:       PetscReal one,two,three,four,six,twelve
228:       PetscReal half,third,twothird,sixth
229:       PetscReal twelfth

231:       one = 1.0
232:       two = 2.0
233:       three = 3.0
234:       four = 4.0
235:       six = 6.0
236:       twelve = 12.0
237:       hx = one / mx
238:       u0t(1) = one - sin(twelve*t)**four
239:       u0t(2) = 0.0
240:       half = one/two
241:       third = one / three
242:       twothird = two / three
243:       sixth = one / six
244:       twelfth = one / twelve
245:       do 20 i = xs,xe
246:          do 10 j = 1,2
247:             if (i .eq. 1) then
248:                f(j,i) = a(j)/hx*(third*u0t(j) + half*x(j,i) - x(j,i+1)  &
249:      &              + sixth*x(j,i+2))
250:             else if (i .eq. 2) then
251:                f(j,i) = a(j)/hx*(-twelfth*u0t(j) + twothird*x(j,i-1)    &
252:      &              - twothird*x(j,i+1) + twelfth*x(j,i+2))
253:             else if (i .eq. mx-1) then
254:                f(j,i) = a(j)/hx*(-sixth*x(j,i-2) + x(j,i-1)             &
255:      &         - half*x(j,i) -third*x(j,i+1))
256:             else if (i .eq. mx) then
257:                f(j,i) = a(j)/hx*(-x(j,i) + x(j,i-1))
258:             else
259:                f(j,i) = a(j)/hx*(-twelfth*x(j,i-2)                      &
260:      &              + twothird*x(j,i-1)                                 &
261:      &              - twothird*x(j,i+1) + twelfth*x(j,i+2))
262:             end if
263:  10      continue
264:  20   continue
265:       end subroutine

267:       subroutine FormRHSFunction(ts,t,X,F,user,ierr)
268:       implicit none
269: #include <finclude/petscsys.h>
270: #include <finclude/petscvec.h>
271: #include <finclude/petscmat.h>
272: #include <finclude/petscsnes.h>
273: #include <finclude/petscts.h>
274: #include <finclude/petscdmda.h>
275:       TS ts
276:       PetscReal t
277:       Vec X,F
278:       PetscReal user(6)
279:       PetscErrorCode ierr
280:       integer user_a,user_k,user_s
281:       parameter (user_a = 1,user_k = 3,user_s = 5)
282:       DM             da
283:       Vec            Xloc
284:       PetscInt       mx,xs,xe,gxs,gxe
285:       PetscOffset    ixx,iff
286:       PetscScalar    xx(0:1),ff(0:1)

288:       call TSGetDM(ts,da,ierr)
289:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

291: !     Scatter ghost points to local vector,using the 2-step process
292: !        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
293: !     By placing code between these two statements, computations can be
294: !     done while messages are in transition.
295:       call DMGetLocalVector(da,Xloc,ierr)
296:       call DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc,ierr)
297:       call DMGlobalToLocalEnd(da,X,INSERT_VALUES,Xloc,ierr)

299: ! Get access to vector data
300:       call VecGetArray(Xloc,xx,ixx,ierr)
301:       call VecGetArray(F,ff,iff,ierr)

303:       call FormRHSFunctionLocal(mx,xs,xe,gxs,gxe,                       &
304:      &     t,xx(ixx),ff(iff),                                           &
305:      &     user(user_a),user(user_k),user(user_s),ierr)

307:       call VecRestoreArray(Xloc,xx,ixx,ierr)
308:       call VecRestoreArray(F,ff,iff,ierr)
309:       call DMRestoreLocalVector(da,Xloc,ierr)
310:       end subroutine

312: ! ---------------------------------------------------------------------
313: !
314: !  IJacobian - Compute IJacobian = dF/dU + shift*dF/dUdot
315: !
316:       subroutine FormIJacobian(ts,t,X,Xdot,shift,J,Jpre,mstr,user,ierr)
317:       implicit none
318: #include <finclude/petscsys.h>
319: #include <finclude/petscvec.h>
320: #include <finclude/petscmat.h>
321: #include <finclude/petscsnes.h>
322: #include <finclude/petscts.h>
323: #include <finclude/petscdmda.h>
324:       TS ts
325:       PetscReal t,shift
326:       Vec X,Xdot
327:       Mat J,Jpre
328:       MatStructure mstr
329:       PetscReal user(6)
330:       PetscErrorCode ierr
331:       integer user_a,user_k,user_s
332:       parameter (user_a = 0,user_k = 2,user_s = 4)

334:       DM             da
335:       PetscInt       mx,xs,xe,gxs,gxe
336:       PetscInt       i,i1,row,col
337:       PetscReal      k1,k2;
338:       PetscScalar    val(4)

340:       call TSGetDM(ts,da,ierr)
341:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

343:       i1 = 1
344:       k1 = user(user_k+1)
345:       k2 = user(user_k+2)
346:       do 10 i = xs,xe
347:          row = i-gxs
348:          col = i-gxs
349:          val(1) = shift + k1
350:          val(2) = -k2
351:          val(3) = -k1
352:          val(4) = shift + k2
353:          call MatSetValuesBlockedLocal(Jpre,i1,row,i1,col,val,          &
354:      &        INSERT_VALUES,ierr)
355:  10   continue
356:       call MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY,ierr)
357:       call MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY,ierr)
358:       if (J /= Jpre) then
359:          call MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY,ierr)
360:          call MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY,ierr)
361:       end if
362:       mstr = SAME_NONZERO_PATTERN
363:       end subroutine

365:       subroutine FormInitialSolutionLocal(mx,xs,xe,gxs,gxe,x,a,k,s,ierr)
366:       implicit none
367:       PetscInt mx,xs,xe,gxs,gxe
368:       PetscScalar x(2,xs:xe)
369:       PetscReal a(2),k(2),s(2)
370:       PetscErrorCode ierr

372:       PetscInt i
373:       PetscReal one,hx,r,ik
374:       one = 1.0
375:       hx = one / mx
376:       do 10 i=xs,xe
377:          r = i*hx
378:          if (k(2) .ne. 0.0) then
379:             ik = one/k(2)
380:          else
381:             ik = one
382:          end if
383:          x(1,i) = one + s(2)*r
384:          x(2,i) = k(1)*ik*x(1,i) + s(2)*ik
385:  10   continue
386:       end subroutine

388:       subroutine FormInitialSolution(ts,X,user,ierr)
389:       implicit none
390: #include <finclude/petscsys.h>
391: #include <finclude/petscvec.h>
392: #include <finclude/petscmat.h>
393: #include <finclude/petscsnes.h>
394: #include <finclude/petscts.h>
395: #include <finclude/petscdmda.h>
396:       TS ts
397:       PetscReal t
398:       Vec X
399:       PetscReal user(6)
400:       PetscErrorCode ierr
401:       integer user_a,user_k,user_s
402:       parameter (user_a = 1,user_k = 3,user_s = 5)

404:       DM             da
405:       PetscInt       mx,xs,xe,gxs,gxe
406:       PetscOffset    ixx
407:       PetscScalar    xx(0:1)

409:       call TSGetDM(ts,da,ierr)
410:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

412: ! Get access to vector data
413:       call VecGetArray(X,xx,ixx,ierr)

415:       call FormInitialSolutionLocal(mx,xs,xe,gxs,gxe,                       &
416:      &     xx(ixx),user(user_a),user(user_k),user(user_s),ierr)

418:       call VecRestoreArray(X,xx,ixx,ierr)
419:       end subroutine