Actual source code: ex3.c

petsc-3.12.2 2019-11-22
Report Typos and Errors

  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 */
 55:   PetscReal      dt;
 56:   DM             da;
 57:   PetscInt       M;

 59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 60:      Initialize program and set problem parameters
 61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 63:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 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);


128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129:      Free work space.  All PETSc objects should be destroyed when they
130:      are no longer needed.
131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

164:   TSGetDM(ts,&da);
165:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
166:   DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);
167:   h    = 1.0/M;
168:   mend = mstart + xm;
169:   /*
170:     Get a pointer to vector data.
171:     - For default PETSc vectors, VecGetArray() returns a pointer to
172:       the data array.  Otherwise, the routine is implementation dependent.
173:     - You MUST call VecRestoreArray() when you no longer need access to
174:       the array.
175:     - Note that the Fortran interface to VecGetArray() differs from the
176:       C version.  See the users manual for details.
177:   */
178:   DMDAVecGetArray(da,U,&u);

180:   /*
181:      We initialize the solution array by simply writing the solution
182:      directly into the array locations.  Alternatively, we could use
183:      VecSetValues() or VecSetValuesLocal().
184:   */
185:   for (i=mstart; i<mend; i++) u[i] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h);

187:   /*
188:      Restore vector
189:   */
190:   DMDAVecRestoreArray(da,U,&u);
191:   return 0;
192: }
193: /* --------------------------------------------------------------------- */
194: /*
195:    Solution - Computes the exact solution at a given time.

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

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

212:   TSGetDM(ts,&da);
213:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
214:   DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);
215:   h    = 1.0/M;
216:   mend = mstart + xm;
217:   /*
218:      Get a pointer to vector data.
219:   */
220:   DMDAVecGetArray(da,U,&u);

222:   /*
223:      Simply write the solution directly into the array locations.
224:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
225:   */
226:   ex1 = PetscExpScalar(-36.*PETSC_PI*PETSC_PI*appctx->d*t);
227:   ex2 = PetscExpScalar(-4.*PETSC_PI*PETSC_PI*appctx->d*t);
228:   sc1 = PETSC_PI*6.*h;                 sc2 = PETSC_PI*2.*h;
229:   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;

231:   /*
232:      Restore vector
233:   */
234:   DMDAVecRestoreArray(da,U,&u);
235:   return 0;
236: }

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

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

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

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

268:   TSGetDM(ts,&da);
269:   DMDAGetInfo(da,0,&M,0,0,0,0,0,0,0,0,0,0,0);
270:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
271:   h    = 1.0/M;
272:   mend = mstart + xm;
273:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
274:      Compute entries for the locally owned part of the matrix
275:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
276:   /*
277:      Set matrix rows corresponding to boundary data
278:   */

280:   /* diffusion */
281:   v[0] = appctx->d/(h*h);
282:   v[1] = -2.0*appctx->d/(h*h);
283:   v[2] = appctx->d/(h*h);
284:   if (!mstart) {
285:     idx[0] = M-1; idx[1] = 0; idx[2] = 1;
286:     MatSetValues(A,1,&mstart,3,idx,v,INSERT_VALUES);
287:     mstart++;
288:   }

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

296:   /*
297:      Set matrix rows corresponding to interior data.  We construct the
298:      matrix one row at a time.
299:   */
300:   for (i=mstart; i<mend; i++) {
301:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
302:     MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
303:   }
304:   MatAssemblyBegin(A,MAT_FLUSH_ASSEMBLY);
305:   MatAssemblyEnd(A,MAT_FLUSH_ASSEMBLY);

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

319:     if (mend == M) {
320:       mend--;
321:       idx[0] = M-2; idx[1] = 0;
322:       MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);
323:     }

325:     for (i=mstart; i<mend; i++) {
326:       idx[0] = i-1; idx[1] = i+1;
327:       MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);
328:     }
329:   } else {
330:     /* advection -- upwinding */
331:     v[0] = -appctx->a/(h);
332:     v[1] = appctx->a/(h);
333:     if (!mstart) {
334:       idx[0] = 0; idx[1] = 1;
335:       MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES);
336:       mstart++;
337:     }

339:     if (mend == M) {
340:       mend--;
341:       idx[0] = M-1; idx[1] = 0;
342:       MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);
343:     }

345:     for (i=mstart; i<mend; i++) {
346:       idx[0] = i; idx[1] = i+1;
347:       MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);
348:     }
349:   }


352:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
353:      Complete the matrix assembly process and set some options
354:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
355:   /*
356:      Assemble matrix, using the 2-step process:
357:        MatAssemblyBegin(), MatAssemblyEnd()
358:      Computations can be done while messages are in transition
359:      by placing code between these two statements.
360:   */
361:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
362:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

364:   /*
365:      Set and option to indicate that we will never add a new nonzero location
366:      to the matrix. If we do, it will generate an error.
367:   */
368:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
369:   return 0;
370: }


373: /*TEST

375:    test:
376:       args: -pc_type mg -da_refine 2  -ts_view  -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
377:       requires: double

379:    test:
380:      suffix: 2
381:      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 
382:      requires: x
383:      output_file: output/ex3_1.out
384:      requires: double

386: TEST*/