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*/