Actual source code: ex3.c


  2: static char help[] = "Model Equations for Advection-Diffusion\n";

  4: /*
  5:     Page 9, Section 1.2 Model Equations for Advection-Diffusion

  7:           u_t = a u_x + d u_xx

  9:    The initial conditions used here different then in the book.

 11: */

 13: /*
 14:      Helpful runtime linear solver options:
 15:            -pc_type mg -da_refine 2 -snes_monitor -ksp_monitor -ts_view   (geometric multigrid with three levels)

 17: */

 19: /*
 20:    Include "petscts.h" so that we can use TS solvers.  Note that this file
 21:    automatically includes:
 22:      petscsys.h       - base PETSc routines   petscvec.h  - vectors
 23:      petscmat.h  - matrices
 24:      petscis.h     - index sets            petscksp.h  - Krylov subspace methods
 25:      petscviewer.h - viewers               petscpc.h   - preconditioners
 26:      petscksp.h   - linear solvers        petscsnes.h - nonlinear solvers
 27: */

 29: #include <petscts.h>
 30: #include <petscdm.h>
 31: #include <petscdmda.h>

 33: /*
 34:    User-defined application context - contains data needed by the
 35:    application-provided call-back routines.
 36: */
 37: typedef struct {
 38:   PetscScalar a, d; /* advection and diffusion strength */
 39:   PetscBool   upwind;
 40: } AppCtx;

 42: /*
 43:    User-defined routines
 44: */
 45: extern PetscErrorCode InitialConditions(TS, Vec, AppCtx *);
 46: extern PetscErrorCode RHSMatrixHeat(TS, PetscReal, Vec, Mat, Mat, void *);
 47: extern PetscErrorCode Solution(TS, PetscReal, Vec, AppCtx *);

 49: int main(int argc, char **argv)
 50: {
 51:   AppCtx    appctx; /* user-defined application context */
 52:   TS        ts;     /* timestepping context */
 53:   Vec       U;      /* approximate solution vector */
 54:   PetscReal dt;
 55:   DM        da;
 56:   PetscInt  M;

 58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59:      Initialize program and set problem parameters
 60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 63:   PetscInitialize(&argc, &argv, (char *)0, help);
 64:   appctx.a = 1.0;
 65:   appctx.d = 0.0;
 66:   PetscOptionsGetScalar(NULL, NULL, "-a", &appctx.a, NULL);
 67:   PetscOptionsGetScalar(NULL, NULL, "-d", &appctx.d, NULL);
 68:   appctx.upwind = PETSC_TRUE;
 69:   PetscOptionsGetBool(NULL, NULL, "-upwind", &appctx.upwind, NULL);

 71:   DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 60, 1, 1, NULL, &da);
 72:   DMSetFromOptions(da);
 73:   DMSetUp(da);
 74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 75:      Create vector data structures
 76:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 78:   /*
 79:      Create vector data structures for approximate and exact solutions
 80:   */
 81:   DMCreateGlobalVector(da, &U);

 83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 84:      Create timestepping solver context
 85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 87:   TSCreate(PETSC_COMM_WORLD, &ts);
 88:   TSSetDM(ts, da);

 90:   /*
 91:       For linear problems with a time-dependent f(U,t) in the equation
 92:      u_t = f(u,t), the user provides the discretized right-hand-side
 93:       as a time-dependent matrix.
 94:   */
 95:   TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx);
 96:   TSSetRHSJacobian(ts, NULL, NULL, RHSMatrixHeat, &appctx);
 97:   TSSetSolutionFunction(ts, (PetscErrorCode(*)(TS, PetscReal, Vec, void *))Solution, &appctx);

 99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100:      Customize timestepping solver:
101:        - Set timestepping duration info
102:      Then set runtime options, which can override these defaults.
103:      For example,
104:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
105:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

108:   DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
109:   dt = .48 / (M * M);
110:   TSSetTimeStep(ts, dt);
111:   TSSetMaxSteps(ts, 1000);
112:   TSSetMaxTime(ts, 100.0);
113:   TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER);
114:   TSSetType(ts, TSARKIMEX);
115:   TSSetFromOptions(ts);

117:   /*
118:      Evaluate initial conditions
119:   */
120:   InitialConditions(ts, U, &appctx);

122:   /*
123:      Run the timestepping solver
124:   */
125:   TSSolve(ts, U);

127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128:      Free work space.  All PETSc objects should be destroyed when they
129:      are no longer needed.
130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

132:   TSDestroy(&ts);
133:   VecDestroy(&U);
134:   DMDestroy(&da);

136:   /*
137:      Always call PetscFinalize() before exiting a program.  This routine
138:        - finalizes the PETSc libraries as well as MPI
139:        - provides summary and diagnostic information if certain runtime
140:          options are chosen (e.g., -log_view).
141:   */
142:   PetscFinalize();
143:   return 0;
144: }
145: /* --------------------------------------------------------------------- */
146: /*
147:    InitialConditions - Computes the solution at the initial time.

149:    Input Parameter:
150:    u - uninitialized solution vector (global)
151:    appctx - user-defined application context

153:    Output Parameter:
154:    u - vector with solution at initial time (global)
155: */
156: PetscErrorCode InitialConditions(TS ts, Vec U, AppCtx *appctx)
157: {
158:   PetscScalar *u, h;
159:   PetscInt     i, mstart, mend, xm, M;
160:   DM           da;

162:   TSGetDM(ts, &da);
163:   DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0);
164:   DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
165:   h    = 1.0 / M;
166:   mend = mstart + xm;
167:   /*
168:     Get a pointer to vector data.
169:     - For default PETSc vectors, VecGetArray() returns a pointer to
170:       the data array.  Otherwise, the routine is implementation dependent.
171:     - You MUST call VecRestoreArray() when you no longer need access to
172:       the array.
173:     - Note that the Fortran interface to VecGetArray() differs from the
174:       C version.  See the users manual for details.
175:   */
176:   DMDAVecGetArray(da, U, &u);

178:   /*
179:      We initialize the solution array by simply writing the solution
180:      directly into the array locations.  Alternatively, we could use
181:      VecSetValues() or VecSetValuesLocal().
182:   */
183:   for (i = mstart; i < mend; i++) u[i] = PetscSinScalar(PETSC_PI * i * 6. * h) + 3. * PetscSinScalar(PETSC_PI * i * 2. * h);

185:   /*
186:      Restore vector
187:   */
188:   DMDAVecRestoreArray(da, U, &u);
189:   return 0;
190: }
191: /* --------------------------------------------------------------------- */
192: /*
193:    Solution - Computes the exact solution at a given time.

195:    Input Parameters:
196:    t - current time
197:    solution - vector in which exact solution will be computed
198:    appctx - user-defined application context

200:    Output Parameter:
201:    solution - vector with the newly computed exact solution
202: */
203: PetscErrorCode Solution(TS ts, PetscReal t, Vec U, AppCtx *appctx)
204: {
205:   PetscScalar *u, ex1, ex2, sc1, sc2, h;
206:   PetscInt     i, mstart, mend, xm, M;
207:   DM           da;

209:   TSGetDM(ts, &da);
210:   DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0);
211:   DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
212:   h    = 1.0 / M;
213:   mend = mstart + xm;
214:   /*
215:      Get a pointer to vector data.
216:   */
217:   DMDAVecGetArray(da, U, &u);

219:   /*
220:      Simply write the solution directly into the array locations.
221:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
222:   */
223:   ex1 = PetscExpScalar(-36. * PETSC_PI * PETSC_PI * appctx->d * t);
224:   ex2 = PetscExpScalar(-4. * PETSC_PI * PETSC_PI * appctx->d * t);
225:   sc1 = PETSC_PI * 6. * h;
226:   sc2 = PETSC_PI * 2. * h;
227:   for (i = mstart; i < mend; i++) u[i] = PetscSinScalar(sc1 * (PetscReal)i + appctx->a * PETSC_PI * 6. * t) * ex1 + 3. * PetscSinScalar(sc2 * (PetscReal)i + appctx->a * PETSC_PI * 2. * t) * ex2;

229:   /*
230:      Restore vector
231:   */
232:   DMDAVecRestoreArray(da, U, &u);
233:   return 0;
234: }

236: /* --------------------------------------------------------------------- */
237: /*
238:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
239:    matrix for the heat equation.

241:    Input Parameters:
242:    ts - the TS context
243:    t - current time
244:    global_in - global input vector
245:    dummy - optional user-defined context, as set by TSetRHSJacobian()

247:    Output Parameters:
248:    AA - Jacobian matrix
249:    BB - optionally different preconditioning matrix
250:    str - flag indicating matrix structure

252:    Notes:
253:    Recall that MatSetValues() uses 0-based row and column numbers
254:    in Fortran as well as in C.
255: */
256: PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec U, Mat AA, Mat BB, void *ctx)
257: {
258:   Mat         A      = AA;            /* Jacobian matrix */
259:   AppCtx     *appctx = (AppCtx *)ctx; /* user-defined application context */
260:   PetscInt    mstart, mend;
261:   PetscInt    i, idx[3], M, xm;
262:   PetscScalar v[3], h;
263:   DM          da;

265:   TSGetDM(ts, &da);
266:   DMDAGetInfo(da, 0, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
267:   DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0);
268:   h    = 1.0 / M;
269:   mend = mstart + xm;
270:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
271:      Compute entries for the locally owned part of the matrix
272:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
273:   /*
274:      Set matrix rows corresponding to boundary data
275:   */

277:   /* diffusion */
278:   v[0] = appctx->d / (h * h);
279:   v[1] = -2.0 * appctx->d / (h * h);
280:   v[2] = appctx->d / (h * h);
281:   if (!mstart) {
282:     idx[0] = M - 1;
283:     idx[1] = 0;
284:     idx[2] = 1;
285:     MatSetValues(A, 1, &mstart, 3, idx, v, INSERT_VALUES);
286:     mstart++;
287:   }

289:   if (mend == M) {
290:     mend--;
291:     idx[0] = M - 2;
292:     idx[1] = M - 1;
293:     idx[2] = 0;
294:     MatSetValues(A, 1, &mend, 3, idx, v, INSERT_VALUES);
295:   }

297:   /*
298:      Set matrix rows corresponding to interior data.  We construct the
299:      matrix one row at a time.
300:   */
301:   for (i = mstart; i < mend; i++) {
302:     idx[0] = i - 1;
303:     idx[1] = i;
304:     idx[2] = i + 1;
305:     MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES);
306:   }
307:   MatAssemblyBegin(A, MAT_FLUSH_ASSEMBLY);
308:   MatAssemblyEnd(A, MAT_FLUSH_ASSEMBLY);

310:   DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0);
311:   mend = mstart + xm;
312:   if (!appctx->upwind) {
313:     /* advection -- centered differencing */
314:     v[0] = -.5 * appctx->a / (h);
315:     v[1] = .5 * appctx->a / (h);
316:     if (!mstart) {
317:       idx[0] = M - 1;
318:       idx[1] = 1;
319:       MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES);
320:       mstart++;
321:     }

323:     if (mend == M) {
324:       mend--;
325:       idx[0] = M - 2;
326:       idx[1] = 0;
327:       MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES);
328:     }

330:     for (i = mstart; i < mend; i++) {
331:       idx[0] = i - 1;
332:       idx[1] = i + 1;
333:       MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES);
334:     }
335:   } else {
336:     /* advection -- upwinding */
337:     v[0] = -appctx->a / (h);
338:     v[1] = appctx->a / (h);
339:     if (!mstart) {
340:       idx[0] = 0;
341:       idx[1] = 1;
342:       MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES);
343:       mstart++;
344:     }

346:     if (mend == M) {
347:       mend--;
348:       idx[0] = M - 1;
349:       idx[1] = 0;
350:       MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES);
351:     }

353:     for (i = mstart; i < mend; i++) {
354:       idx[0] = i;
355:       idx[1] = i + 1;
356:       MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES);
357:     }
358:   }

360:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
361:      Complete the matrix assembly process and set some options
362:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
363:   /*
364:      Assemble matrix, using the 2-step process:
365:        MatAssemblyBegin(), MatAssemblyEnd()
366:      Computations can be done while messages are in transition
367:      by placing code between these two statements.
368:   */
369:   MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
370:   MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);

372:   /*
373:      Set and option to indicate that we will never add a new nonzero location
374:      to the matrix. If we do, it will generate an error.
375:   */
376:   MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE);
377:   return 0;
378: }

380: /*TEST

382:    test:
383:       args: -pc_type mg -da_refine 2  -ts_view  -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
384:       requires: double
385:       filter: grep -v "total number of"

387:    test:
388:       suffix: 2
389:       args:  -pc_type mg -da_refine 2  -ts_view  -ts_monitor_draw_solution -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
390:       requires: x
391:       output_file: output/ex3_1.out
392:       requires: double
393:       filter: grep -v "total number of"

395: TEST*/