Actual source code: ex22f.F

petsc-3.7.3 2016-07-24
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  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 <petsc/finclude/petscsys.h>
 20: #include <petsc/finclude/petscvec.h>
 21: #include <petsc/finclude/petscmat.h>
 22: #include <petsc/finclude/petscsnes.h>
 23: #include <petsc/finclude/petscts.h>
 24: #include <petsc/finclude/petscdm.h>
 25: #include <petsc/finclude/petscdmda.h>
 26: !
 27: !  Create an application context to contain data needed by the
 28: !  application-provided call-back routines, FormJacobian() and
 29: !  FormFunction(). We use a double precision array with six
 30: !  entries, two for each problem parameter a, k, s.
 31: !
 32:       PetscReal user(6)
 33:       integer user_a,user_k,user_s
 34:       parameter (user_a = 0,user_k = 2,user_s = 4)

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

 39:       TS             ts
 40:       SNES           snes
 41:       SNESLineSearch linesearch
 42:       Vec            X
 43:       Mat            J
 44:       PetscInt       maxsteps,mx
 45:       PetscErrorCode ierr
 46:       DM             da
 47:       PetscReal      ftime,dt
 48:       PetscReal      zero,one,pone
 49:       PetscInt       im11,i2
 50:       PetscBool      flg

 52:       im11 = -11
 53:       i2   = 2
 54:       zero = 0.0
 55:       one = 1.0
 56:       pone = one / 10

 58:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)

 60: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 61: !  Create distributed array (DMDA) to manage parallel grid and vectors
 62: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 63:       call DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,im11,i2,i2,   &
 64:      &     PETSC_NULL_INTEGER,da,ierr)

 66: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 67: !    Extract global vectors from DMDA;
 68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 69:       call DMCreateGlobalVector(da,X,ierr)

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

 92: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93: !    Create timestepping solver context
 94: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 95:       call TSCreate(PETSC_COMM_WORLD,ts,ierr)
 96:       call TSSetDM(ts,da,ierr)
 97:       call TSSetType(ts,TSARKIMEX,ierr)
 98:       call TSSetRHSFunction(ts,PETSC_NULL_OBJECT,FormRHSFunction,       &
 99:      &     user,ierr)
100:       call TSSetIFunction(ts,PETSC_NULL_OBJECT,FormIFunction,user,ierr)
101:       call DMSetMatType(da,MATAIJ,ierr)
102:       call DMCreateMatrix(da,J,ierr)
103:       call TSSetIJacobian(ts,J,J,FormIJacobian,user,ierr)

105:       call TSGetSNES(ts,snes,ierr)
106:       call SNESGetLineSearch(snes,linesearch,ierr)
107:       call SNESLineSearchSetType(linesearch,SNESLINESEARCHBASIC,ierr)

109:       ftime = 1.0
110:       maxsteps = 10000
111:       call TSSetDuration(ts,maxsteps,ftime,ierr)
112:       call TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER,ierr)
113: 
114: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
115: !  Set initial conditions
116: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117:       call FormInitialSolution(ts,X,user,ierr)
118:       call TSSetSolution(ts,X,ierr)
119:       call VecGetSize(X,mx,ierr)
120: !  Advective CFL, I don't know why it needs so much safety factor.
121:       dt = pone * max(user(user_a+1),user(user_a+2)) / mx;
122:       call TSSetInitialTimeStep(ts,zero,dt,ierr)

124: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: !   Set runtime options
126: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:       call TSSetFromOptions(ts,ierr)

129: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: !  Solve nonlinear system
131: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132:       call TSSolve(ts,X,ierr)

134: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135: !  Free work space.
136: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137:       call MatDestroy(J,ierr)
138:       call VecDestroy(X,ierr)
139:       call TSDestroy(ts,ierr)
140:       call DMDestroy(da,ierr)
141:       call PetscFinalize(ierr)
142:       end program

144: ! Small helper to extract the layout, result uses 1-based indexing.
145:       subroutine GetLayout(da,mx,xs,xe,gxs,gxe,ierr)
146:       implicit none
147: #include <petsc/finclude/petscsys.h>
148: #include <petsc/finclude/petscdm.h>
149: #include <petsc/finclude/petscdmda.h>
150:       DM da
151:       PetscInt mx,xs,xe,gxs,gxe
152:       PetscErrorCode ierr
153:       PetscInt xm,gxm
154:             call DMDAGetInfo(da,PETSC_NULL_INTEGER,                     &
155:      &     mx,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                    &
156:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,    &
157:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                       &
158:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,    &
159:      &     PETSC_NULL_INTEGER,ierr)
160:       call DMDAGetCorners(da,xs,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,  &
161:      &     xm,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
162:       call DMDAGetGhostCorners(da,                                      &
163:      &     gxs,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                   &
164:      &     gxm,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
165:       xs = xs + 1
166:       gxs = gxs + 1
167:       xe = xs + xm - 1
168:       gxe = gxs + gxm - 1
169:       end subroutine

171:       subroutine FormIFunctionLocal(mx,xs,xe,gxs,gxe,x,xdot,f,          &
172:      &     a,k,s,ierr)
173:       implicit none
174:       PetscInt mx,xs,xe,gxs,gxe
175:       PetscScalar x(2,xs:xe)
176:       PetscScalar xdot(2,xs:xe)
177:       PetscScalar f(2,xs:xe)
178:       PetscReal a(2),k(2),s(2)
179:       PetscErrorCode ierr
180:       PetscInt i
181:       do 10 i = xs,xe
182:          f(1,i) = xdot(1,i) + k(1)*x(1,i) - k(2)*x(2,i) - s(1)
183:          f(2,i) = xdot(2,i) - k(1)*x(1,i) + k(2)*x(2,i) - s(2)
184:  10   continue
185:       end subroutine

187:       subroutine FormIFunction(ts,t,X,Xdot,F,user,ierr)
188:       implicit none
189: #include <petsc/finclude/petscsys.h>
190: #include <petsc/finclude/petscvec.h>
191: #include <petsc/finclude/petscmat.h>
192: #include <petsc/finclude/petscsnes.h>
193: #include <petsc/finclude/petscts.h>
194: #include <petsc/finclude/petscdm.h>
195: #include <petsc/finclude/petscdmda.h>
196:       TS ts
197:       PetscReal t
198:       Vec X,Xdot,F
199:       PetscReal user(6)
200:       PetscErrorCode ierr
201:       integer user_a,user_k,user_s
202:       parameter (user_a = 1,user_k = 3,user_s = 5)

204:       DM             da
205:       PetscInt       mx,xs,xe,gxs,gxe
206:       PetscOffset    ixx,ixxdot,iff
207:       PetscScalar    xx(0:1),xxdot(0:1),ff(0:1)

209:       call TSGetDM(ts,da,ierr)
210:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

212: ! Get access to vector data
213:       call VecGetArrayRead(X,xx,ixx,ierr)
214:       call VecGetArrayRead(Xdot,xxdot,ixxdot,ierr)
215:       call VecGetArray(F,ff,iff,ierr)

217:       call FormIFunctionLocal(mx,xs,xe,gxs,gxe,                         &
218:      &     xx(ixx),xxdot(ixxdot),ff(iff),                               &
219:      &     user(user_a),user(user_k),user(user_s),ierr)

221:       call VecRestoreArrayRead(X,xx,ixx,ierr)
222:       call VecRestoreArrayRead(Xdot,xxdot,ixxdot,ierr)
223:       call VecRestoreArray(F,ff,iff,ierr)
224:       end subroutine

226:       subroutine FormRHSFunctionLocal(mx,xs,xe,gxs,gxe,t,x,f,           &
227:      &     a,k,s,ierr)
228:       implicit none
229:       PetscInt mx,xs,xe,gxs,gxe
230:       PetscReal t
231:       PetscScalar x(2,gxs:gxe),f(2,xs:xe)
232:       PetscReal a(2),k(2),s(2)
233:       PetscErrorCode ierr
234:       PetscInt i,j
235:       PetscReal hx,u0t(2)
236:       PetscReal one,two,three,four,six,twelve
237:       PetscReal half,third,twothird,sixth
238:       PetscReal twelfth

240:       one = 1.0
241:       two = 2.0
242:       three = 3.0
243:       four = 4.0
244:       six = 6.0
245:       twelve = 12.0
246:       hx = one / mx
247:       u0t(1) = one - sin(twelve*t)**four
248:       u0t(2) = 0.0
249:       half = one/two
250:       third = one / three
251:       twothird = two / three
252:       sixth = one / six
253:       twelfth = one / twelve
254:       do 20 i = xs,xe
255:          do 10 j = 1,2
256:             if (i .eq. 1) then
257:                f(j,i) = a(j)/hx*(third*u0t(j) + half*x(j,i) - x(j,i+1)  &
258:      &              + sixth*x(j,i+2))
259:             else if (i .eq. 2) then
260:                f(j,i) = a(j)/hx*(-twelfth*u0t(j) + twothird*x(j,i-1)    &
261:      &              - twothird*x(j,i+1) + twelfth*x(j,i+2))
262:             else if (i .eq. mx-1) then
263:                f(j,i) = a(j)/hx*(-sixth*x(j,i-2) + x(j,i-1)             &
264:      &         - half*x(j,i) -third*x(j,i+1))
265:             else if (i .eq. mx) then
266:                f(j,i) = a(j)/hx*(-x(j,i) + x(j,i-1))
267:             else
268:                f(j,i) = a(j)/hx*(-twelfth*x(j,i-2)                      &
269:      &              + twothird*x(j,i-1)                                 &
270:      &              - twothird*x(j,i+1) + twelfth*x(j,i+2))
271:             end if
272:  10      continue
273:  20   continue
274:       end subroutine

276:       subroutine FormRHSFunction(ts,t,X,F,user,ierr)
277:       implicit none
278: #include <petsc/finclude/petscsys.h>
279: #include <petsc/finclude/petscvec.h>
280: #include <petsc/finclude/petscmat.h>
281: #include <petsc/finclude/petscsnes.h>
282: #include <petsc/finclude/petscts.h>
283: #include <petsc/finclude/petscdm.h>
284: #include <petsc/finclude/petscdmda.h>
285:       TS ts
286:       PetscReal t
287:       Vec X,F
288:       PetscReal user(6)
289:       PetscErrorCode ierr
290:       integer user_a,user_k,user_s
291:       parameter (user_a = 1,user_k = 3,user_s = 5)
292:       DM             da
293:       Vec            Xloc
294:       PetscInt       mx,xs,xe,gxs,gxe
295:       PetscOffset    ixx,iff
296:       PetscScalar    xx(0:1),ff(0:1)

298:       call TSGetDM(ts,da,ierr)
299:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

301: !     Scatter ghost points to local vector,using the 2-step process
302: !        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
303: !     By placing code between these two statements, computations can be
304: !     done while messages are in transition.
305:       call DMGetLocalVector(da,Xloc,ierr)
306:       call DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc,ierr)
307:       call DMGlobalToLocalEnd(da,X,INSERT_VALUES,Xloc,ierr)

309: ! Get access to vector data
310:       call VecGetArrayRead(Xloc,xx,ixx,ierr)
311:       call VecGetArray(F,ff,iff,ierr)

313:       call FormRHSFunctionLocal(mx,xs,xe,gxs,gxe,                       &
314:      &     t,xx(ixx),ff(iff),                                           &
315:      &     user(user_a),user(user_k),user(user_s),ierr)

317:       call VecRestoreArrayRead(Xloc,xx,ixx,ierr)
318:       call VecRestoreArray(F,ff,iff,ierr)
319:       call DMRestoreLocalVector(da,Xloc,ierr)
320:       end subroutine

322: ! ---------------------------------------------------------------------
323: !
324: !  IJacobian - Compute IJacobian = dF/dU + shift*dF/dUdot
325: !
326:       subroutine FormIJacobian(ts,t,X,Xdot,shift,J,Jpre,user,ierr)
327:       implicit none
328: #include <petsc/finclude/petscsys.h>
329: #include <petsc/finclude/petscvec.h>
330: #include <petsc/finclude/petscmat.h>
331: #include <petsc/finclude/petscsnes.h>
332: #include <petsc/finclude/petscts.h>
333: #include <petsc/finclude/petscdm.h>
334: #include <petsc/finclude/petscdmda.h>
335:       TS ts
336:       PetscReal t,shift
337:       Vec X,Xdot
338:       Mat J,Jpre
339:       PetscReal user(6)
340:       PetscErrorCode ierr
341:       integer user_a,user_k,user_s
342:       parameter (user_a = 0,user_k = 2,user_s = 4)

344:       DM             da
345:       PetscInt       mx,xs,xe,gxs,gxe
346:       PetscInt       i,i1,row,col
347:       PetscReal      k1,k2;
348:       PetscScalar    val(4)

350:       call TSGetDM(ts,da,ierr)
351:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

353:       i1 = 1
354:       k1 = user(user_k+1)
355:       k2 = user(user_k+2)
356:       do 10 i = xs,xe
357:          row = i-gxs
358:          col = i-gxs
359:          val(1) = shift + k1
360:          val(2) = -k2
361:          val(3) = -k1
362:          val(4) = shift + k2
363:          call MatSetValuesBlockedLocal(Jpre,i1,row,i1,col,val,          &
364:      &        INSERT_VALUES,ierr)
365:  10   continue
366:       call MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY,ierr)
367:       call MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY,ierr)
368:       if (J /= Jpre) then
369:          call MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY,ierr)
370:          call MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY,ierr)
371:       end if
372:       end subroutine

374:       subroutine FormInitialSolutionLocal(mx,xs,xe,gxs,gxe,x,a,k,s,ierr)
375:       implicit none
376:       PetscInt mx,xs,xe,gxs,gxe
377:       PetscScalar x(2,xs:xe)
378:       PetscReal a(2),k(2),s(2)
379:       PetscErrorCode ierr

381:       PetscInt i
382:       PetscReal one,hx,r,ik
383:       one = 1.0
384:       hx = one / mx
385:       do 10 i=xs,xe
386:          r = i*hx
387:          if (k(2) .ne. 0.0) then
388:             ik = one/k(2)
389:          else
390:             ik = one
391:          end if
392:          x(1,i) = one + s(2)*r
393:          x(2,i) = k(1)*ik*x(1,i) + s(2)*ik
394:  10   continue
395:       end subroutine

397:       subroutine FormInitialSolution(ts,X,user,ierr)
398:       implicit none
399: #include <petsc/finclude/petscsys.h>
400: #include <petsc/finclude/petscvec.h>
401: #include <petsc/finclude/petscmat.h>
402: #include <petsc/finclude/petscsnes.h>
403: #include <petsc/finclude/petscts.h>
404: #include <petsc/finclude/petscdm.h>
405: #include <petsc/finclude/petscdmda.h>
406:       TS ts
407:       Vec X
408:       PetscReal user(6)
409:       PetscErrorCode ierr
410:       integer user_a,user_k,user_s
411:       parameter (user_a = 1,user_k = 3,user_s = 5)

413:       DM             da
414:       PetscInt       mx,xs,xe,gxs,gxe
415:       PetscOffset    ixx
416:       PetscScalar    xx(0:1)

418:       call TSGetDM(ts,da,ierr)
419:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

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

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

427:       call VecRestoreArray(X,xx,ixx,ierr)
428:       end subroutine