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:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

 77:   /*
 78:      Create vector data structures for approximate and exact solutions
 79:   */
 80:   DMCreateGlobalVector(da,&U);

 82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 83:      Create timestepping solver context
 84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 89:   /*
 90:       For linear problems with a time-dependent f(U,t) in the equation
 91:      u_t = f(u,t), the user provides the discretized right-hand-side
 92:       as a time-dependent matrix.
 93:   */
 94:   TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);
 95:   TSSetRHSJacobian(ts,NULL,NULL,RHSMatrixHeat,&appctx);
 96:   TSSetSolutionFunction(ts,(PetscErrorCode (*)(TS,PetscReal,Vec,void*))Solution,&appctx);

 98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 99:      Customize timestepping solver:
100:        - Set timestepping duration info
101:      Then set runtime options, which can override these defaults.
102:      For example,
103:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
104:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
105:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

116:   /*
117:      Evaluate initial conditions
118:   */
119:   InitialConditions(ts,U,&appctx);

121:   /*
122:      Run the timestepping solver
123:   */
124:   TSSolve(ts,U);

126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:      Free work space.  All PETSc objects should be destroyed when they
128:      are no longer needed.
129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

135:   /*
136:      Always call PetscFinalize() before exiting a program.  This routine
137:        - finalizes the PETSc libraries as well as MPI
138:        - provides summary and diagnostic information if certain runtime
139:          options are chosen (e.g., -log_view).
140:   */
141:   PetscFinalize();
142:   return 0;
143: }
144: /* --------------------------------------------------------------------- */
145: /*
146:    InitialConditions - Computes the solution at the initial time.

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

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

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

177:   /*
178:      We initialize the solution array by simply writing the solution
179:      directly into the array locations.  Alternatively, we could use
180:      VecSetValues() or VecSetValuesLocal().
181:   */
182:   for (i=mstart; i<mend; i++) u[i] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h);

184:   /*
185:      Restore vector
186:   */
187:   DMDAVecRestoreArray(da,U,&u);
188:   return 0;
189: }
190: /* --------------------------------------------------------------------- */
191: /*
192:    Solution - Computes the exact solution at a given time.

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

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

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

218:   /*
219:      Simply write the solution directly into the array locations.
220:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
221:   */
222:   ex1 = PetscExpScalar(-36.*PETSC_PI*PETSC_PI*appctx->d*t);
223:   ex2 = PetscExpScalar(-4.*PETSC_PI*PETSC_PI*appctx->d*t);
224:   sc1 = PETSC_PI*6.*h;                 sc2 = PETSC_PI*2.*h;
225:   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;

227:   /*
228:      Restore vector
229:   */
230:   DMDAVecRestoreArray(da,U,&u);
231:   return 0;
232: }

234: /* --------------------------------------------------------------------- */
235: /*
236:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
237:    matrix for the heat equation.

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

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

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

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

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

285:   if (mend == M) {
286:     mend--;
287:     idx[0] = M-2; idx[1] = M-1; idx[2] = 0;
288:     MatSetValues(A,1,&mend,3,idx,v,INSERT_VALUES);
289:   }

291:   /*
292:      Set matrix rows corresponding to interior data.  We construct the
293:      matrix one row at a time.
294:   */
295:   for (i=mstart; i<mend; i++) {
296:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
297:     MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
298:   }
299:   MatAssemblyBegin(A,MAT_FLUSH_ASSEMBLY);
300:   MatAssemblyEnd(A,MAT_FLUSH_ASSEMBLY);

302:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
303:   mend = mstart + xm;
304:   if (!appctx->upwind) {
305:     /* advection -- centered differencing */
306:     v[0] = -.5*appctx->a/(h);
307:     v[1] = .5*appctx->a/(h);
308:     if (!mstart) {
309:       idx[0] = M-1; idx[1] = 1;
310:       MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES);
311:       mstart++;
312:     }

314:     if (mend == M) {
315:       mend--;
316:       idx[0] = M-2; idx[1] = 0;
317:       MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);
318:     }

320:     for (i=mstart; i<mend; i++) {
321:       idx[0] = i-1; idx[1] = i+1;
322:       MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);
323:     }
324:   } else {
325:     /* advection -- upwinding */
326:     v[0] = -appctx->a/(h);
327:     v[1] = appctx->a/(h);
328:     if (!mstart) {
329:       idx[0] = 0; idx[1] = 1;
330:       MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES);
331:       mstart++;
332:     }

334:     if (mend == M) {
335:       mend--;
336:       idx[0] = M-1; idx[1] = 0;
337:       MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);
338:     }

340:     for (i=mstart; i<mend; i++) {
341:       idx[0] = i; idx[1] = i+1;
342:       MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);
343:     }
344:   }

346:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
347:      Complete the matrix assembly process and set some options
348:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
349:   /*
350:      Assemble matrix, using the 2-step process:
351:        MatAssemblyBegin(), MatAssemblyEnd()
352:      Computations can be done while messages are in transition
353:      by placing code between these two statements.
354:   */
355:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
356:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

358:   /*
359:      Set and option to indicate that we will never add a new nonzero location
360:      to the matrix. If we do, it will generate an error.
361:   */
362:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
363:   return 0;
364: }

366: /*TEST

368:    test:
369:       args: -pc_type mg -da_refine 2  -ts_view  -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
370:       requires: double
371:       filter: grep -v "total number of"

373:    test:
374:       suffix: 2
375:       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
376:       requires: x
377:       output_file: output/ex3_1.out
378:       requires: double
379:       filter: grep -v "total number of"

381: TEST*/