Actual source code: ex2f.F

  1: !
  2: !/*T
  3: !   Concepts: TS^time-dependent nonlinear problems
  4: !   Processors: n
  5: !T*/
  6: !
  7: !  ------------------------------------------------------------------------
  8: !
  9: !   This program solves a simple time-dependent nonlinear PDE using implicit
 10: !   timestepping:
 11: !                                    u * u_xx
 12: !                              u_t = ---------
 13: !                                    2*(t+1)^2
 14: !
 15: !             u(0,x) = 1 + x*x; u(t,0) = t + 1; u(t,1) = 2*t + 2
 16: !
 17: !   The exact solution is u(t,x) = (1 + x*x) * (1 + t).
 18: !
 19: !   Note that since the solution is linear in time and quadratic in x,
 20: !   the finite difference scheme actually computes the "exact" solution.
 21: !
 22: !   We use the backward Euler method.
 23: !
 24: !  --------------------------------------------------------------------------

 26:       program main
 27:       implicit none

 29: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 30: !                    Include files
 31: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 32: !
 33: !  Each routine within this program uses the include file 'ex2f.h',
 34: !  which itself includes the various PETSc include files as well as
 35: !  problem-specific data in several common blocks.
 36: !
 37: !  This program uses CPP for preprocessing, as indicated by the use of
 38: !  PETSc include files in the directory petsc/include/finclude.  This
 39: !  convention enables use of the CPP preprocessor, which allows the use
 40: !  of the #include statements that define PETSc objects and variables.
 41: !
 42: !  Use of the conventional Fortran include statements is also supported
 43: !  In this case, the PETsc include files are located in the directory
 44: !  petsc/include/foldinclude.
 45: !
 46: !  Since one must be very careful to include each file no more than once
 47: !  in a Fortran routine, application programmers must exlicitly list
 48: !  each file needed for the various PETSc components within their
 49: !  program (unlike the C/C++ interface).
 50: !
 51: !  See the Fortran section of the PETSc users manual for details.

 53: #include "ex2f.h"

 55: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 56: !                   Variable declarations
 57: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 58: !
 59: !  Variables:
 60: !     ts             - timestepping solver
 61: !     A              - Jacobian matrix context
 62: !     u_local        - local vector
 63: !     u              - approximate solution vector
 64: !     ftime          - final time
 65: !     time_total_max - default total max time
 66: !     time_steps_max - default max timesteps
 67: !
 68: !  Note that vectors are declared as PETSc "Vec" objects.  These vectors
 69: !  are mathematical objects that contain more than just an array of
 70: !  double precision numbers. I.e., vectors in PETSc are not just
 71: !        double precision x(*).
 72: !  However, local vector data can be easily accessed via VecGetArray().
 73: !  See the Fortran section of the PETSc users manual for details.

 75:       TS               ts
 76:       Vec              u
 77:       Mat              A
 78:       PetscTruth       flg,monitor
 79:       PetscErrorCode ierr
 80:       PetscInt  time_steps_max,steps,i1
 81:       PetscReal dt,ftime,time_total_max

 83: !  Note: Any user-defined Fortran routines (such as RHSFunction)
 84: !  MUST be declared as external.

 86:       external MyMonitor,RHSFunction
 87:       external InitialConditions,RHSJacobian

 89: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90: !                 Beginning of program
 91: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 93:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 94:       comm = PETSC_COMM_WORLD
 95:       call MPI_Comm_size(comm,size,ierr)
 96:       call MPI_Comm_rank(comm,rank,ierr)

 98: !  Initialize problem parameters

100:       time_steps_max = 1000
101:       time_total_max = 100.0
102:       m              = 60
103:       debug          = 0
104:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-m',M,flg,ierr)
105:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-debug',debug,ierr)
106:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-monitor',monitor,       &
107:      &                         ierr)
108:       one_d0  = 1.0d0
109:       two_d0  = 2.0d0
110:       four_d0 = 4.0d0
111:       h       = one_d0/(m-one_d0)

113: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: !  Create vector data structures
115: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

117: !  Create distributed array (DA) to manage parallel grid and vectors
118: !  Set up the ghost point communication pattern.  There are m total
119: !  grid values spread equally among all the processors.
120:       i1 = 1
121:       call DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,m,i1,i1,                &
122:      &     PETSC_NULL_INTEGER,da,ierr)

124: !  Extract global and local vectors from DA; then duplicate for remaining
125: !  vectors that are the same types.

127:       call DACreateGlobalVector(da,u,ierr)
128:       call DACreateLocalVector(da,u_local,ierr)

130: !  Make local work vector for evaluating right-hand-side function
131:       call VecDuplicate(u_local,localwork,ierr)

133: !  Make global work vector for storing exact solution
134:       call VecDuplicate(u,solution,ierr)

136: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: !  Create timestepping solver context; set callback routine for
138: !  right-hand-side function evaluation.
139: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

141:       call TSCreate(comm,ts,ierr)
142:       call TSSetProblemType(ts,TS_NONLINEAR,ierr)
143:       call TSSetRHSFunction(ts,RHSFunction,PETSC_NULL_OBJECT,ierr)

145: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146: !  Set optional user-defined monitoring routine
147: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -


150:       if (monitor .eq. 1) then
151:         call TSMonitorSet(ts,MyMonitor,PETSC_NULL_OBJECT,               &
152:      &                    PETSC_NULL_FUNCTION,ierr)
153:       endif

155: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: !  For nonlinear problems, the user can provide a Jacobian evaluation
157: !  routine (or use a finite differencing approximation).
158: !
159: !  Create matrix data structure; set Jacobian evaluation routine.
160: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

162:       call MatCreate(comm,A,ierr)
163:       call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,m,ierr)
164:       call MatSetFromOptions(A,ierr)
165:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-fdjac',flg,ierr)
166:       if (flg .eq. 1) then
167:          call SetCRoutineFromFortran(ts,A,A,ierr)
168:       else
169:          call TSSetRHSJacobian(ts,A,A,RHSJacobian,PETSC_NULL_OBJECT,    &
170:      &        ierr)
171:       endif

173: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174: !  Set solution vector and initial timestep
175: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

177:       dt = h/two_d0
178:       call TSSetInitialTimeStep(ts,0.d0,dt,ierr)
179:       call TSSetSolution(ts,u,ierr)

181: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182: !  Customize timestepping solver:
183: !     - Set the solution method to be the Backward Euler method.
184: !     - Set timestepping duration info
185: !  Then set runtime options, which can override these defaults.
186: !  For example,
187: !     -ts_max_steps <maxsteps> -ts_max_time <maxtime>
188: !  to override the defaults set by TSSetDuration().
189: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

191:       call TSSetType(ts,TS_BEULER,ierr)
192:       call TSSetDuration(ts,time_steps_max,time_total_max,ierr)
193:       call TSSetFromOptions(ts,ierr)

195: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: !  Solve the problem
197: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

199: !  Evaluate initial conditions

201:       call InitialConditions(u)

203: !  Run the timestepping solver

205:       call TSStep(ts,steps,ftime,ierr)

207: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: !  Free work space.  All PETSc objects should be destroyed when they
209: !  are no longer needed.
210: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

212:       call TSDestroy(ts,ierr)
213:       call VecDestroy(localwork,ierr)
214:       call VecDestroy(solution,ierr)
215:       call VecDestroy(u_local,ierr)
216:       call VecDestroy(u,ierr)
217:       call DADestroy(da,ierr)
218:       call MatDestroy(A,ierr)

220: !  Always call PetscFinalize() before exiting a program.  This routine
221: !    - finalizes the PETSc libraries as well as MPI
222: !    - provides summary and diagnostic information if certain runtime
223: !      options are chosen (e.g., -log_summary).

225:       call PetscFinalize(ierr)
226:       end

228: !  ------------------------------------------------------------------------
229: !
230: !  InitialConditions - Computes the solution at the initial time.
231: !
232: !  Input Parameters:
233: !     u - uninitialized solution vector (global)
234: !     appctx - user-defined application context
235: !
236: !  Output Parameter:
237: !     u - vector with solution at initial time (global)
238: !
239:       subroutine InitialConditions(u)
240:       implicit none
241: #include "ex2f.h"

243: !  Input/output parameters:
244:       Vec     u

246: !  Local variables:
247:       PetscScalar localptr(1),x
248:       PetscInt    i,mybase,myend
249:       PetscErrorCode ierr
250:       PetscOffset idx

252: !  Determine starting and ending point of each processor's range of
253: !  grid values.  Note that we shift by 1 to convert from the 0-based
254: !  C convention of starting indices to the 1-based Fortran convention.

256:       call VecGetOwnershipRange(u,mybase,myend,ierr)
257:       mybase = mybase + 1

259: !  Get a pointer to vector data.
260: !    - For default PETSc vectors, VecGetArray() returns a pointer to
261: !      the data array.  Otherwise, the routine is implementation dependent.
262: !    - You MUST call VecRestoreArray() when you no longer need access to
263: !      the array.
264: !    - Note that the Fortran interface to VecGetArray() differs from the
265: !      C version.  See the users manual for details.

267:       call VecGetArray(u,localptr,idx,ierr)

269: !     We initialize the solution array by simply writing the solution
270: !     directly into the array locations.  Alternatively, we could use
271: !     VecSetValues() or VecSetValuesLocal().

273:       do 10, i=mybase,myend
274: !       x - current location in global grid
275:         x = h*(i-1)
276:         localptr(i-mybase+idx+1) = one_d0 + x*x
277:  10   continue

279: !  Restore vector

281:       call VecRestoreArray(u,localptr,idx,ierr)

283: !  Print debugging information if desired
284:       if (debug .eq. 1) then
285:         if (rank .eq. 0) write(6,*) 'initial guess vector'
286:         call VecView(u,PETSC_VIEWER_STDOUT_WORLD,ierr)
287:       endif

289:       return
290:       end

292: !  ------------------------------------------------------------------------
293: !
294: !  ExactSolution - Computes the exact solution at a given time.
295: !
296: !  Input Parameters:
297: !    t - current time
298: !    appctx - user-defined application context
299: !
300: !  Output Parameter:
301: !    ierr - error code
302: !
303: !  Note: The solution vector is stored in the common block!
304: !
305:       subroutine ExactSolution(t,ierr)
306:       implicit none
307: #include "ex2f.h"

309: !  Input/output parameters:
310:       PetscReal  t
311:       PetscScalar  x
312:       PetscErrorCode          ierr

314: !  Local variables:
315:       PetscScalar localptr(1)
316:       PetscInt    i,mybase,myend
317:       PetscOffset idx

319: !  Determine starting and ending point of each processors range of
320: !  grid values.  Note that we shift by 1 to convert from the 0-based
321: !  C convention of starting indices to the 1-based Fortran convention.

323:       call VecGetOwnershipRange(solution,mybase,myend,ierr)
324:       mybase = mybase + 1

326: !  Get a pointer to vector data
327:       call VecGetArray(solution,localptr,idx,ierr)

329: !  Simply write the solution directly into the array locations
330: !  Alternatively, we could use VecSetValues() or VecSetValuesLocal().

332:       do 10, i=mybase,myend
333: !       x - current location in global grid
334:         x = h*(i-1)
335:         localptr(i-mybase+idx+1) = (t + one_d0)*(one_d0 + x*x)
336:  10   continue

338: !  Restore vector

340:       call VecRestoreArray(solution,localptr,idx,ierr)

342:       return
343:       end

345: !  ------------------------------------------------------------------------
346: !
347: !   MyMonitor - A user-provided routine to monitor the solution computed at
348: !   each time-step.  This example plots the solution and computes the
349: !   error in two different norms.
350: !
351: !   Input Parameters:
352: !   ts     - the time-step context
353: !   step   - the count of the current step (with 0 meaning the
354: !            initial condition)
355: !   time   - the current time
356: !   u      - the solution at this timestep
357: !   dummy  - optional user-provided context for this monitoring
358: !            routine (not used here)
359: !
360:       subroutine MyMonitor(ts,step,time,u,dummy,ierr)
361:       implicit none
362: #include "ex2f.h"

364: !  Input/output parameters:
365:       TS       ts
366:       PetscInt step
367:       PetscObject dummy
368:       PetscReal time
369:       Vec      u
370:       PetscErrorCode ierr

372: !  Local variables:
373:       PetscScalar en2,en2s,enmax
374:       PetscScalar mone
375:       PetscDraw   draw

377:       mone = -1.0d0

379: !  We use the default X windows viewer
380: !       PETSC_VIEWER_DRAW_WORLD
381: !  that is associated with the PETSC_COMM_WORLD communicator. This
382: !  saves the effort of calling PetscViewerDrawOpen() to create the window.
383: !  Note that if we wished to plot several items in separate windows we
384: !  would create each viewer with PetscViewerDrawOpen() and store them in
385: !  the application context, appctx.
386: !
387: !  Double buffering makes graphics look better.

389:       call PetscViewerDrawGetDraw(PETSC_VIEWER_DRAW_WORLD,0,draw,ierr)
390:       call PetscDrawSetDoubleBuffer(draw,ierr)
391:       call VecView(u,PETSC_VIEWER_DRAW_WORLD,ierr)

393: !  Compute the exact solution at this time-step.  Note that the
394: !  solution vector is passed via the user-defined common block.
395:       call ExactSolution(time,ierr)

397: !  Print debugging information if desired
398:       if (debug .eq. 1) then
399:         if (rank .eq. 0) write(6,*) 'Computed solution vector'
400:         call VecView(u,PETSC_VIEWER_STDOUT_WORLD,ierr)
401:         if (rank .eq. 0) write(6,*) 'Exact solution vector'
402:         call VecView(solution,PETSC_VIEWER_STDOUT_WORLD,ierr)
403:       endif

405: !  Compute the 2-norm and max-norm of the error
406:       call VecAXPY(solution,mone,u,ierr)
407:       call VecNorm(solution,NORM_2,en2,ierr)

409: !  Scale the 2-norm by the grid spacing
410:       en2s = dsqrt(h)*en2
411:       call VecNorm(solution,NORM_MAX,enmax,ierr)

413: !  Print only from processor 0
414:       if (rank .eq. 0) write(6,100) step,time,en2s,enmax
415:  100  format('Timestep = ',i5,',time = ',f8.3,                          &
416:      &       ' sec, error [2-norm] = ',e9.3,                            &
417:      &       ', error [max-norm] = ',e9.3)

419: !  Print debugging information if desired
420:       if (debug .eq. 1) then
421:         if (rank .eq. 0) write(6,*) 'Error vector'
422:         call VecView(solution,PETSC_VIEWER_STDOUT_WORLD,ierr)
423:       endif

425:       return
426:       end

428: !  ------------------------------------------------------------------------
429: !
430: !   RHSFunction - User-provided routine that evalues the RHS function
431: !   in the ODE.  This routine is set in the main program by calling
432: !   TSSetRHSFunction().  We compute:
433: !         global_out = F(global_in)
434: !
435: !   Input Parameters:
436: !      ts         - timestep context
437: !      t          - current time
438: !      global_in  - input vector to function
439: !      dummy      - (optional) user-provided context for function evaluation
440: !                   (not used here because we use a common block instead)
441: !
442: !   Output Parameter:
443: !      global_out - value of function
444: !
445:       subroutine RHSFunction(ts,t,global_in,global_out,dummy)
446:       implicit none
447: #include "ex2f.h"

449: !  Input/output parameters:
450:       TS        ts
451:       PetscReal t
452:       Vec       global_in,global_out
453:       integer   dummy

455: !  Local variables:
456:       PetscScalar localptr(1),copyptr(1),sc
457:       PetscErrorCode ierr
458:       PetscInt    i,localsize
459:       PetscOffset idx_c,idx_l,il

461: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
462: !  Get ready for local function computations
463: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

465: !  Scatter ghost points to local vector, using the 2-step process
466: !     DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
467: !  By placing code between these two statements, computations can be
468: !  done while messages are in transition.

470:       call DAGlobalToLocalBegin(da,global_in,INSERT_VALUES,u_local,ierr)
471:       call DAGlobalToLocalEnd(da,global_in,INSERT_VALUES,u_local,ierr)

473: !  Access directly the values in our local INPUT work vector
474:       call VecGetArray(u_local,localptr,idx_l,ierr)

476: !  Access directly the values in our local OUTPUT work vector
477:       call VecGetArray(localwork,copyptr,idx_c,ierr)

479:       sc = one_d0/(h*h*two_d0*(one_d0+t)*(one_d0+t))

481: !  Evaluate our function on the nodes owned by this processor
482:       call VecGetLocalSize(u_local,localsize,ierr)

484: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
485: !  Compute entries for the locally owned part
486: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

488: !  Handle boundary conditions: This is done by using the boundary condition
489: !        u(t,boundary) = g(t,boundary)
490: !  for some function g. Now take the derivative with respect to t to obtain
491: !        u_{t}(t,boundary) = g_{t}(t,boundary)
492: !
493: !  In our case, u(t,0) = t + 1, so that u_{t}(t,0) = 1
494: !          and  u(t,1) = 2t+ 1, so that u_{t}(t,1) = 2

496:        if (rank .eq. 0)      copyptr(1+idx_c) = one_d0
497:        if (rank .eq. size-1) copyptr(localsize+idx_c) = two_d0

499: !  Handle the interior nodes where the PDE is replace by finite
500: !  difference operators.

502:       do 10, i=2,localsize-1
503:          il = i + idx_l
504:          copyptr(i+idx_c) =  localptr(il) * sc *                        &
505:      &     (localptr(il+1) + localptr(il-1) - two_d0*localptr(il))
506:  10   continue

508:       call VecRestoreArray(u_local,localptr,idx_l,ierr)
509:       call VecRestoreArray(localwork,copyptr,idx_c,ierr)

511: !  Return the values from our local OUTPUT vector into our global
512: !  output vector.

514:       call DALocalToGlobal(da,localwork,INSERT_VALUES,global_out,ierr)

516: !  Print debugging information if desired
517:       if (debug .eq. 1) then
518:         if (rank .eq. 0) write(6,*) 'RHS function vector'
519:         call VecView(global_out,PETSC_VIEWER_STDOUT_WORLD,ierr)
520:       endif

522:       return
523:       end

525: !  ------------------------------------------------------------------------
526: !
527: !  RHSJacobian - User-provided routine to compute the Jacobian of the
528: !                right-hand-side function.
529: !
530: !  Input Parameters:
531: !     ts - the TS context
532: !     t - current time
533: !     global_in - global input vector
534: !     dummy - optional user-defined context, as set by TSetRHSJacobian()
535: !
536: !  Output Parameters:
537: !     A - Jacobian matrix
538: !     B - optionally different preconditioning matrix
539: !     str - flag indicating matrix structure
540: !
541: !  Notes:
542: !  RHSJacobian computes entries for the locally owned part of the Jacobian.
543: !   - Currently, all PETSc parallel matrix formats are partitioned by
544: !     contiguous chunks of rows across the processors. The "grow"
545: !     parameter computed below specifies the global row number
546: !     corresponding to each local grid point.
547: !   - Each processor needs to insert only elements that it owns
548: !     locally (but any non-local elements will be sent to the
549: !     appropriate processor during matrix assembly).
550: !   - Always specify global row and columns of matrix entries.
551: !   - Here, we set all entries for a particular row at once.
552: !   - Note that MatSetValues() uses 0-based row and column numbers
553: !     in Fortran as well as in C.

555:       subroutine RHSJacobian(ts,t,global_in,A,B,str,dummy)
556:       implicit none
557: #include "ex2f.h"

559: !  Input/output parameters:
560:       TS               ts
561:       PetscReal t
562:       Vec              global_in
563:       Mat              A,B
564:       MatStructure     str
565:       integer          dummy

567: !  Local variables:
568:       PetscScalar localptr(1),sc,v(3)
569:       PetscInt    i,col(3),i1,i3
570:       PetscErrorCode ierr
571:       PetscInt    mstart(1),mend(1)
572:       PetscInt    mstarts,mends
573:       PetscOffset idx,is

575: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
576: !  Get ready for local Jacobian computations
577: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

579: !  Scatter ghost points to local vector, using the 2-step process
580: !     DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
581: !  By placing code between these two statements, computations can be
582: !  done while messages are in transition.

584:       call DAGlobalToLocalBegin(da,global_in,INSERT_VALUES,u_local,ierr)
585:       call DAGlobalToLocalEnd(da,global_in,INSERT_VALUES,u_local,ierr)

587: !  Get pointer to vector data
588:       call VecGetArray(u_local,localptr,idx,ierr)

590: !  Get starting and ending locally owned rows of the matrix
591:       call MatGetOwnershipRange(A,mstarts,mends,ierr)
592:       mstart(1) = mstarts
593:       mend(1)   = mends

595: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
596: !  Compute entries for the locally owned part of the Jacobian.
597: !   - Currently, all PETSc parallel matrix formats are partitioned by
598: !     contiguous chunks of rows across the processors.
599: !   - Each processor needs to insert only elements that it owns
600: !     locally (but any non-local elements will be sent to the
601: !     appropriate processor during matrix assembly).
602: !   - Here, we set all entries for a particular row at once.
603: !   - We can set matrix entries either using either
604: !     MatSetValuesLocal() or MatSetValues().
605: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

607: !  Set matrix rows corresponding to boundary data
608:       i1 = 1
609:       i3 = 3
610:       if (mstart(1) .eq. 0) then
611:         v(1) = zero_d0
612:         call MatSetValues(A,i1,mstart,i1,mstart,v,INSERT_VALUES,ierr)
613:         mstart(1) = mstart(1) + 1
614:       endif
615:       if (mend(1) .eq. m) then
616:         mend(1) = mend(1) - 1
617:         v(1) = zero_d0
618:         call MatSetValues(A,i1,mend,i1,mend,v,INSERT_VALUES,ierr)
619:       endif

621: !  Set matrix rows corresponding to interior data.
622: !  We construct the matrix one row at a time.

624:       sc = one_d0/(h*h*two_d0*(one_d0+t)*(one_d0+t))
625:       do 10, i=mstart(1),mend(1)-1
626:          col(1) = i-1
627:          col(2) = i
628:          col(3) = i+1
629:          is     = i - mstart(1) + 1 +idx + 1
630:          v(1)   = sc*localptr(is)
631:          v(2)   = sc*(localptr(is+1) + localptr(is-1) -                 &
632:      &                four_d0*localptr(is))
633:          v(3)   = sc*localptr(is)
634:         call MatSetValues(A,i1,i,i3,col,v,INSERT_VALUES,ierr)
635:  10   continue

637: !  Restore vector
638:       call VecRestoreArray(u_local,localptr,idx,ierr)

640: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
641: !  Complete the matrix assembly process and set some options
642: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

644: !  Assemble matrix, using the 2-step process:
645: !       MatAssemblyBegin(), MatAssemblyEnd()
646: !  Computations can be done while messages are in transition,
647: !  by placing code between these two statements.

649:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
650:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

652: !  Set flag to indicate that the Jacobian matrix retains an identical
653: !  nonzero structure throughout all timestepping iterations (although the
654: !  values of the entries change). Thus, we can save some work in setting
655: !  up the preconditioner (e.g., no need to redo symbolic factorization for
656: !  ILU/ICC preconditioners).
657: !   - If the nonzero structure of the matrix is different during
658: !     successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
659: !     must be used instead.  If you are unsure whether the matrix
660: !     structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
661: !   - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
662: !     believes your assertion and does not check the structure
663: !     of the matrix.  If you erroneously claim that the structure
664: !     is the same when it actually is not, the new preconditioner
665: !     will not function correctly.  Thus, use this optimization
666: !     feature with caution!

668:       str = SAME_NONZERO_PATTERN

670: !  Set and option to indicate that we will never add a new nonzero location
671: !  to the matrix. If we do, it will generate an error.

673:       call MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,ierr)

675:       return
676:       end