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: PetscFunctionBeginUser;
63: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
64: appctx.a = 1.0;
65: appctx.d = 0.0;
66: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-a", &appctx.a, NULL));
67: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-d", &appctx.d, NULL));
68: appctx.upwind = PETSC_TRUE;
69: PetscCall(PetscOptionsGetBool(NULL, NULL, "-upwind", &appctx.upwind, NULL));
71: PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 60, 1, 1, NULL, &da));
72: PetscCall(DMSetFromOptions(da));
73: PetscCall(DMSetUp(da));
74: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
75: Create vector data structures
76: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
78: /*
79: Create vector data structures for approximate and exact solutions
80: */
81: PetscCall(DMCreateGlobalVector(da, &U));
83: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
84: Create timestepping solver context
85: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
87: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
88: PetscCall(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: PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx));
96: PetscCall(TSSetRHSJacobian(ts, NULL, NULL, RHSMatrixHeat, &appctx));
97: PetscCall(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: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
109: dt = .48 / (M * M);
110: PetscCall(TSSetTimeStep(ts, dt));
111: PetscCall(TSSetMaxSteps(ts, 1000));
112: PetscCall(TSSetMaxTime(ts, 100.0));
113: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
114: PetscCall(TSSetType(ts, TSARKIMEX));
115: PetscCall(TSSetFromOptions(ts));
117: /*
118: Evaluate initial conditions
119: */
120: PetscCall(InitialConditions(ts, U, &appctx));
122: /*
123: Run the timestepping solver
124: */
125: PetscCall(TSSolve(ts, U));
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Free work space. All PETSc objects should be destroyed when they
129: are no longer needed.
130: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132: PetscCall(TSDestroy(&ts));
133: PetscCall(VecDestroy(&U));
134: PetscCall(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: PetscCall(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: PetscFunctionBeginUser;
163: PetscCall(TSGetDM(ts, &da));
164: PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0));
165: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
166: h = 1.0 / M;
167: mend = mstart + xm;
168: /*
169: Get a pointer to vector data.
170: - For default PETSc vectors, VecGetArray() returns a pointer to
171: the data array. Otherwise, the routine is implementation dependent.
172: - You MUST call VecRestoreArray() when you no longer need access to
173: the array.
174: - Note that the Fortran interface to VecGetArray() differs from the
175: C version. See the users manual for details.
176: */
177: PetscCall(DMDAVecGetArray(da, U, &u));
179: /*
180: We initialize the solution array by simply writing the solution
181: directly into the array locations. Alternatively, we could use
182: VecSetValues() or VecSetValuesLocal().
183: */
184: for (i = mstart; i < mend; i++) u[i] = PetscSinScalar(PETSC_PI * i * 6. * h) + 3. * PetscSinScalar(PETSC_PI * i * 2. * h);
186: /*
187: Restore vector
188: */
189: PetscCall(DMDAVecRestoreArray(da, U, &u));
190: PetscFunctionReturn(PETSC_SUCCESS);
191: }
192: /* --------------------------------------------------------------------- */
193: /*
194: Solution - Computes the exact solution at a given time.
196: Input Parameters:
197: t - current time
198: solution - vector in which exact solution will be computed
199: appctx - user-defined application context
201: Output Parameter:
202: solution - vector with the newly computed exact solution
203: */
204: PetscErrorCode Solution(TS ts, PetscReal t, Vec U, AppCtx *appctx)
205: {
206: PetscScalar *u, ex1, ex2, sc1, sc2, h;
207: PetscInt i, mstart, mend, xm, M;
208: DM da;
210: PetscFunctionBeginUser;
211: PetscCall(TSGetDM(ts, &da));
212: PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0));
213: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
214: h = 1.0 / M;
215: mend = mstart + xm;
216: /*
217: Get a pointer to vector data.
218: */
219: PetscCall(DMDAVecGetArray(da, U, &u));
221: /*
222: Simply write the solution directly into the array locations.
223: Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
224: */
225: ex1 = PetscExpScalar(-36. * PETSC_PI * PETSC_PI * appctx->d * t);
226: ex2 = PetscExpScalar(-4. * PETSC_PI * PETSC_PI * appctx->d * t);
227: sc1 = PETSC_PI * 6. * h;
228: 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: PetscCall(DMDAVecRestoreArray(da, U, &u));
235: PetscFunctionReturn(PETSC_SUCCESS);
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;
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, 0, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
270: PetscCall(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;
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, 0, 0, &xm, 0, 0));
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*/