Actual source code: ex3.c
1: static char help[] = "Model Equations for Advection-Diffusion\n";
3: /*
4: Page 9, Section 1.2 Model Equations for Advection-Diffusion
6: u_t = a u_x + d u_xx
8: The initial conditions used here different then in the book.
10: */
12: /*
13: Helpful runtime linear solver options:
14: -pc_type mg -da_refine 2 -snes_monitor -ksp_monitor -ts_view (geometric multigrid with three levels)
16: */
18: /*
19: Include "petscts.h" so that we can use the TS ODE integrators. Note that this file
20: automatically includes:
21: petscsys.h - base PETSc routines
22: petscis.h - index sets
23: petscvec.h - vectors
24: petscmat.h - matrices
25: petscpc.h - preconditioners
26: petscksp.h - linear solvers
27: petscsnes.h - nonlinear solvers
28: */
30: #include <petscts.h>
31: #include <petscdm.h>
32: #include <petscdmda.h>
34: /*
35: User-defined application context - contains data needed by the
36: application-provided call-back routines.
37: */
38: typedef struct {
39: PetscScalar a, d; /* advection and diffusion strength */
40: PetscBool upwind;
41: } AppCtx;
43: /*
44: User-defined routines
45: */
46: extern PetscErrorCode InitialConditions(TS, Vec, AppCtx *);
47: extern PetscErrorCode RHSMatrixHeat(TS, PetscReal, Vec, Mat, Mat, void *);
48: extern PetscErrorCode Solution(TS, PetscReal, Vec, AppCtx *);
50: int main(int argc, char **argv)
51: {
52: AppCtx appctx; /* user-defined application context */
53: TS ts; /* timestepping context */
54: Vec U; /* approximate solution vector */
55: PetscReal dt;
56: DM da;
57: PetscInt M;
59: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: Initialize program and set problem parameters
61: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
63: PetscFunctionBeginUser;
64: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
65: appctx.a = 1.0;
66: appctx.d = 0.0;
67: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-a", &appctx.a, NULL));
68: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-d", &appctx.d, NULL));
69: appctx.upwind = PETSC_TRUE;
70: PetscCall(PetscOptionsGetBool(NULL, NULL, "-upwind", &appctx.upwind, NULL));
72: PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 60, 1, 1, NULL, &da));
73: PetscCall(DMSetFromOptions(da));
74: PetscCall(DMSetUp(da));
75: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76: Create vector data structures
77: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
79: /*
80: Create vector data structures for approximate and exact solutions
81: */
82: PetscCall(DMCreateGlobalVector(da, &U));
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Create timestepping solver context
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
88: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
89: PetscCall(TSSetDM(ts, da));
91: /*
92: For linear problems with a time-dependent f(U,t) in the equation
93: u_t = f(u,t), the user provides the discretized right-hand side
94: as a time-dependent matrix.
95: */
96: PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx));
97: PetscCall(TSSetRHSJacobian(ts, NULL, NULL, RHSMatrixHeat, &appctx));
98: PetscCall(TSSetSolutionFunction(ts, (PetscErrorCode (*)(TS, PetscReal, Vec, void *))Solution, &appctx));
100: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101: Customize timestepping solver:
102: - Set timestepping duration info
103: Then set runtime options, which can override these defaults.
104: For example,
105: -ts_max_steps <maxsteps> -ts_max_time <maxtime>
106: to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
107: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
109: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
110: dt = .48 / (M * M);
111: PetscCall(TSSetTimeStep(ts, dt));
112: PetscCall(TSSetMaxSteps(ts, 1000));
113: PetscCall(TSSetMaxTime(ts, 100.0));
114: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
115: PetscCall(TSSetType(ts, TSARKIMEX));
116: PetscCall(TSSetFromOptions(ts));
118: /*
119: Evaluate initial conditions
120: */
121: PetscCall(InitialConditions(ts, U, &appctx));
123: /*
124: Run the timestepping solver
125: */
126: PetscCall(TSSolve(ts, U));
128: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129: Free work space. All PETSc objects should be destroyed when they
130: are no longer needed.
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133: PetscCall(TSDestroy(&ts));
134: PetscCall(VecDestroy(&U));
135: PetscCall(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: PetscCall(PetscFinalize());
144: return 0;
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;
160: PetscInt i, mstart, mend, xm, M;
161: DM da;
163: PetscFunctionBeginUser;
164: PetscCall(TSGetDM(ts, &da));
165: PetscCall(DMDAGetCorners(da, &mstart, NULL, NULL, &xm, NULL, NULL));
166: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
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: PetscCall(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: PetscCall(DMDAVecRestoreArray(da, U, &u));
191: PetscFunctionReturn(PETSC_SUCCESS);
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;
208: PetscInt i, mstart, mend, xm, M;
209: DM da;
211: PetscFunctionBeginUser;
212: PetscCall(TSGetDM(ts, &da));
213: PetscCall(DMDAGetCorners(da, &mstart, NULL, NULL, &xm, NULL, NULL));
214: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
215: h = 1.0 / M;
216: mend = mstart + xm;
217: /*
218: Get a pointer to vector data.
219: */
220: PetscCall(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;
229: sc2 = PETSC_PI * 2. * h;
230: 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;
232: /*
233: Restore vector
234: */
235: PetscCall(DMDAVecRestoreArray(da, U, &u));
236: PetscFunctionReturn(PETSC_SUCCESS);
237: }
239: /* --------------------------------------------------------------------- */
240: /*
241: RHSMatrixHeat - User-provided routine to compute the right-hand-side
242: matrix for the heat equation.
244: Input Parameters:
245: ts - the TS context
246: t - current time
247: global_in - global input vector
248: dummy - optional user-defined context, as set by TSetRHSJacobian()
250: Output Parameters:
251: AA - Jacobian matrix
252: BB - optionally different matrix used to construct the preconditioner
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, PetscCtx ctx)
259: {
260: Mat A = AA; /* Jacobian matrix */
261: AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */
262: PetscInt mstart, mend;
263: PetscInt i, idx[3], M, xm;
264: PetscScalar v[3], h;
265: DM da;
267: PetscFunctionBeginUser;
268: PetscCall(TSGetDM(ts, &da));
269: PetscCall(DMDAGetInfo(da, NULL, &M, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
270: PetscCall(DMDAGetCorners(da, &mstart, NULL, NULL, &xm, NULL, NULL));
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;
286: idx[1] = 0;
287: idx[2] = 1;
288: PetscCall(MatSetValues(A, 1, &mstart, 3, idx, v, INSERT_VALUES));
289: mstart++;
290: }
292: if (mend == M) {
293: mend--;
294: idx[0] = M - 2;
295: idx[1] = M - 1;
296: idx[2] = 0;
297: PetscCall(MatSetValues(A, 1, &mend, 3, idx, v, INSERT_VALUES));
298: }
300: /*
301: Set matrix rows corresponding to interior data. We construct the
302: matrix one row at a time.
303: */
304: for (i = mstart; i < mend; i++) {
305: idx[0] = i - 1;
306: idx[1] = i;
307: idx[2] = i + 1;
308: PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES));
309: }
310: PetscCall(MatAssemblyBegin(A, MAT_FLUSH_ASSEMBLY));
311: PetscCall(MatAssemblyEnd(A, MAT_FLUSH_ASSEMBLY));
313: PetscCall(DMDAGetCorners(da, &mstart, NULL, NULL, &xm, NULL, NULL));
314: mend = mstart + xm;
315: if (!appctx->upwind) {
316: /* advection -- centered differencing */
317: v[0] = -.5 * appctx->a / (h);
318: v[1] = .5 * appctx->a / (h);
319: if (!mstart) {
320: idx[0] = M - 1;
321: idx[1] = 1;
322: PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES));
323: mstart++;
324: }
326: if (mend == M) {
327: mend--;
328: idx[0] = M - 2;
329: idx[1] = 0;
330: PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES));
331: }
333: for (i = mstart; i < mend; i++) {
334: idx[0] = i - 1;
335: idx[1] = i + 1;
336: PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES));
337: }
338: } else {
339: /* advection -- upwinding */
340: v[0] = -appctx->a / (h);
341: v[1] = appctx->a / (h);
342: if (!mstart) {
343: idx[0] = 0;
344: idx[1] = 1;
345: PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES));
346: mstart++;
347: }
349: if (mend == M) {
350: mend--;
351: idx[0] = M - 1;
352: idx[1] = 0;
353: PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES));
354: }
356: for (i = mstart; i < mend; i++) {
357: idx[0] = i;
358: idx[1] = i + 1;
359: PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES));
360: }
361: }
363: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
364: Complete the matrix assembly process and set some options
365: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
366: /*
367: Assemble matrix, using the 2-step process:
368: MatAssemblyBegin(), MatAssemblyEnd()
369: Computations can be done while messages are in transition
370: by placing code between these two statements.
371: */
372: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
373: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
375: /*
376: Set and option to indicate that we will never add a new nonzero location
377: to the matrix. If we do, it will generate an error.
378: */
379: PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
380: PetscFunctionReturn(PETSC_SUCCESS);
381: }
383: /*TEST
385: test:
386: args: -pc_type mg -da_refine 2 -ts_view -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
387: requires: double
388: filter: grep -v "total number of"
390: test:
391: suffix: 2
392: 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
393: requires: x
394: output_file: output/ex3_1.out
395: requires: double
396: filter: grep -v "total number of"
398: TEST*/