Actual source code: ex50.c
1: static char help[] = "Solves one dimensional Burger's equation compares with exact solution\n\n";
3: /*
4: Not yet tested in parallel
5: */
7: /* ------------------------------------------------------------------------
9: This program uses the one-dimensional Burger's equation
10: u_t = mu*u_xx - u u_x,
11: on the domain 0 <= x <= 1, with periodic boundary conditions
13: The operators are discretized with the spectral element method
15: See the paper PDE-CONSTRAINED OPTIMIZATION WITH SPECTRAL ELEMENTS USING PETSC AND TAO
16: by OANA MARIN, EMIL CONSTANTINESCU, AND BARRY SMITH for details on the exact solution
17: used
19: See src/tao/unconstrained/tutorials/burgers_spectral.c
21: ------------------------------------------------------------------------- */
23: #include <petscts.h>
24: #include <petscdt.h>
25: #include <petscdraw.h>
26: #include <petscdmda.h>
28: /*
29: User-defined application context - contains data needed by the
30: application-provided call-back routines.
31: */
33: typedef struct {
34: PetscInt n; /* number of nodes */
35: PetscReal *nodes; /* GLL nodes */
36: PetscReal *weights; /* GLL weights */
37: } PetscGLL;
39: typedef struct {
40: PetscInt N; /* grid points per elements*/
41: PetscInt E; /* number of elements */
42: PetscReal tol_L2, tol_max; /* error norms */
43: PetscInt steps; /* number of timesteps */
44: PetscReal Tend; /* endtime */
45: PetscReal mu; /* viscosity */
46: PetscReal L; /* total length of domain */
47: PetscReal Le;
48: PetscReal Tadj;
49: } PetscParam;
51: typedef struct {
52: Vec grid; /* total grid */
53: Vec curr_sol;
54: } PetscData;
56: typedef struct {
57: Vec grid; /* total grid */
58: Vec mass; /* mass matrix for total integration */
59: Mat stiff; /* stifness matrix */
60: Mat keptstiff;
61: Mat grad;
62: PetscGLL gll;
63: } PetscSEMOperators;
65: typedef struct {
66: DM da; /* distributed array data structure */
67: PetscSEMOperators SEMop;
68: PetscParam param;
69: PetscData dat;
70: TS ts;
71: PetscReal initial_dt;
72: } AppCtx;
74: /*
75: User-defined routines
76: */
77: extern PetscErrorCode RHSMatrixLaplaciangllDM(TS, PetscReal, Vec, Mat, Mat, void *);
78: extern PetscErrorCode RHSMatrixAdvectiongllDM(TS, PetscReal, Vec, Mat, Mat, void *);
79: extern PetscErrorCode TrueSolution(TS, PetscReal, Vec, AppCtx *);
80: extern PetscErrorCode RHSFunction(TS, PetscReal, Vec, Vec, void *);
81: extern PetscErrorCode RHSJacobian(TS, PetscReal, Vec, Mat, Mat, void *);
83: int main(int argc, char **argv)
84: {
85: AppCtx appctx; /* user-defined application context */
86: PetscInt i, xs, xm, ind, j, lenglob;
87: PetscReal x, *wrk_ptr1, *wrk_ptr2;
88: MatNullSpace nsp;
89: PetscMPIInt size;
91: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92: Initialize program and set problem parameters
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: PetscFunctionBeginUser;
95: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
97: /*initialize parameters */
98: appctx.param.N = 10; /* order of the spectral element */
99: appctx.param.E = 10; /* number of elements */
100: appctx.param.L = 4.0; /* length of the domain */
101: appctx.param.mu = 0.01; /* diffusion coefficient */
102: appctx.initial_dt = 5e-3;
103: appctx.param.steps = PETSC_INT_MAX;
104: appctx.param.Tend = 4;
106: PetscCall(PetscOptionsGetInt(NULL, NULL, "-N", &appctx.param.N, NULL));
107: PetscCall(PetscOptionsGetInt(NULL, NULL, "-E", &appctx.param.E, NULL));
108: PetscCall(PetscOptionsGetReal(NULL, NULL, "-Tend", &appctx.param.Tend, NULL));
109: PetscCall(PetscOptionsGetReal(NULL, NULL, "-mu", &appctx.param.mu, NULL));
110: appctx.param.Le = appctx.param.L / appctx.param.E;
112: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
113: PetscCheck((appctx.param.E % size) == 0, PETSC_COMM_WORLD, PETSC_ERR_ARG_WRONG, "Number of elements must be divisible by number of processes");
115: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116: Create GLL data structures
117: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
118: PetscCall(PetscMalloc2(appctx.param.N, &appctx.SEMop.gll.nodes, appctx.param.N, &appctx.SEMop.gll.weights));
119: PetscCall(PetscDTGaussLobattoLegendreQuadrature(appctx.param.N, PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA, appctx.SEMop.gll.nodes, appctx.SEMop.gll.weights));
120: appctx.SEMop.gll.n = appctx.param.N;
121: lenglob = appctx.param.E * (appctx.param.N - 1);
123: /*
124: Create distributed array (DMDA) to manage parallel grid and vectors
125: and to set up the ghost point communication pattern. There are E*(Nl-1)+1
126: total grid values spread equally among all the processors, except first and last
127: */
129: PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, lenglob, 1, 1, NULL, &appctx.da));
130: PetscCall(DMSetFromOptions(appctx.da));
131: PetscCall(DMSetUp(appctx.da));
133: /*
134: Extract global and local vectors from DMDA; we use these to store the
135: approximate solution. Then duplicate these for remaining vectors that
136: have the same types.
137: */
139: PetscCall(DMCreateGlobalVector(appctx.da, &appctx.dat.curr_sol));
140: PetscCall(VecDuplicate(appctx.dat.curr_sol, &appctx.SEMop.grid));
141: PetscCall(VecDuplicate(appctx.dat.curr_sol, &appctx.SEMop.mass));
143: PetscCall(DMDAGetCorners(appctx.da, &xs, NULL, NULL, &xm, NULL, NULL));
144: PetscCall(DMDAVecGetArray(appctx.da, appctx.SEMop.grid, &wrk_ptr1));
145: PetscCall(DMDAVecGetArray(appctx.da, appctx.SEMop.mass, &wrk_ptr2));
147: /* Compute function over the locally owned part of the grid */
149: xs = xs / (appctx.param.N - 1);
150: xm = xm / (appctx.param.N - 1);
152: /*
153: Build total grid and mass over entire mesh (multi-elemental)
154: */
156: for (i = xs; i < xs + xm; i++) {
157: for (j = 0; j < appctx.param.N - 1; j++) {
158: x = (appctx.param.Le / 2.0) * (appctx.SEMop.gll.nodes[j] + 1.0) + appctx.param.Le * i;
159: ind = i * (appctx.param.N - 1) + j;
160: wrk_ptr1[ind] = x;
161: wrk_ptr2[ind] = .5 * appctx.param.Le * appctx.SEMop.gll.weights[j];
162: if (j == 0) wrk_ptr2[ind] += .5 * appctx.param.Le * appctx.SEMop.gll.weights[j];
163: }
164: }
165: PetscCall(DMDAVecRestoreArray(appctx.da, appctx.SEMop.grid, &wrk_ptr1));
166: PetscCall(DMDAVecRestoreArray(appctx.da, appctx.SEMop.mass, &wrk_ptr2));
168: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
169: Create matrix data structure; set matrix evaluation routine.
170: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
171: PetscCall(DMSetMatrixPreallocateOnly(appctx.da, PETSC_TRUE));
172: PetscCall(DMCreateMatrix(appctx.da, &appctx.SEMop.stiff));
173: PetscCall(DMCreateMatrix(appctx.da, &appctx.SEMop.grad));
174: /*
175: For linear problems with a time-dependent f(u,t) in the equation
176: u_t = f(u,t), the user provides the discretized right-hand side
177: as a time-dependent matrix.
178: */
179: PetscCall(RHSMatrixLaplaciangllDM(appctx.ts, 0.0, appctx.dat.curr_sol, appctx.SEMop.stiff, appctx.SEMop.stiff, &appctx));
180: PetscCall(RHSMatrixAdvectiongllDM(appctx.ts, 0.0, appctx.dat.curr_sol, appctx.SEMop.grad, appctx.SEMop.grad, &appctx));
181: /*
182: For linear problems with a time-dependent f(u,t) in the equation
183: u_t = f(u,t), the user provides the discretized right-hand side
184: as a time-dependent matrix.
185: */
187: PetscCall(MatDuplicate(appctx.SEMop.stiff, MAT_COPY_VALUES, &appctx.SEMop.keptstiff));
189: /* attach the null space to the matrix, this probably is not needed but does no harm */
190: PetscCall(MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, NULL, &nsp));
191: PetscCall(MatSetNullSpace(appctx.SEMop.stiff, nsp));
192: PetscCall(MatSetNullSpace(appctx.SEMop.keptstiff, nsp));
193: PetscCall(MatNullSpaceTest(nsp, appctx.SEMop.stiff, NULL));
194: PetscCall(MatNullSpaceDestroy(&nsp));
195: /* attach the null space to the matrix, this probably is not needed but does no harm */
196: PetscCall(MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, NULL, &nsp));
197: PetscCall(MatSetNullSpace(appctx.SEMop.grad, nsp));
198: PetscCall(MatNullSpaceTest(nsp, appctx.SEMop.grad, NULL));
199: PetscCall(MatNullSpaceDestroy(&nsp));
201: /* Create the TS solver that solves the ODE and its adjoint; set its options */
202: PetscCall(TSCreate(PETSC_COMM_WORLD, &appctx.ts));
203: PetscCall(TSSetProblemType(appctx.ts, TS_NONLINEAR));
204: PetscCall(TSSetType(appctx.ts, TSRK));
205: PetscCall(TSSetDM(appctx.ts, appctx.da));
206: PetscCall(TSSetTime(appctx.ts, 0.0));
207: PetscCall(TSSetTimeStep(appctx.ts, appctx.initial_dt));
208: PetscCall(TSSetMaxSteps(appctx.ts, appctx.param.steps));
209: PetscCall(TSSetMaxTime(appctx.ts, appctx.param.Tend));
210: PetscCall(TSSetExactFinalTime(appctx.ts, TS_EXACTFINALTIME_MATCHSTEP));
211: PetscCall(TSSetTolerances(appctx.ts, 1e-7, NULL, 1e-7, NULL));
212: PetscCall(TSSetSaveTrajectory(appctx.ts));
213: PetscCall(TSSetFromOptions(appctx.ts));
214: PetscCall(TSSetRHSFunction(appctx.ts, NULL, RHSFunction, &appctx));
215: PetscCall(TSSetRHSJacobian(appctx.ts, appctx.SEMop.stiff, appctx.SEMop.stiff, RHSJacobian, &appctx));
217: /* Set Initial conditions for the problem */
218: PetscCall(TrueSolution(appctx.ts, 0, appctx.dat.curr_sol, &appctx));
220: PetscCall(TSSetSolutionFunction(appctx.ts, (PetscErrorCode (*)(TS, PetscReal, Vec, void *))TrueSolution, &appctx));
221: PetscCall(TSSetTime(appctx.ts, 0.0));
222: PetscCall(TSSetStepNumber(appctx.ts, 0));
224: PetscCall(TSSolve(appctx.ts, appctx.dat.curr_sol));
226: PetscCall(MatDestroy(&appctx.SEMop.stiff));
227: PetscCall(MatDestroy(&appctx.SEMop.keptstiff));
228: PetscCall(MatDestroy(&appctx.SEMop.grad));
229: PetscCall(VecDestroy(&appctx.SEMop.grid));
230: PetscCall(VecDestroy(&appctx.SEMop.mass));
231: PetscCall(VecDestroy(&appctx.dat.curr_sol));
232: PetscCall(PetscFree2(appctx.SEMop.gll.nodes, appctx.SEMop.gll.weights));
233: PetscCall(DMDestroy(&appctx.da));
234: PetscCall(TSDestroy(&appctx.ts));
236: /*
237: Always call PetscFinalize() before exiting a program. This routine
238: - finalizes the PETSc libraries as well as MPI
239: - provides summary and diagnostic information if certain runtime
240: options are chosen (e.g., -log_view).
241: */
242: PetscCall(PetscFinalize());
243: return 0;
244: }
246: /*
247: TrueSolution() computes the true solution for the PDE
249: Input Parameter:
250: u - uninitialized solution vector (global)
251: appctx - user-defined application context
253: Output Parameter:
254: u - vector with solution at initial time (global)
255: */
256: PetscErrorCode TrueSolution(TS ts, PetscReal t, Vec u, AppCtx *appctx)
257: {
258: PetscScalar *s;
259: const PetscScalar *xg;
260: PetscInt i, xs, xn;
262: PetscFunctionBeginUser;
263: PetscCall(DMDAVecGetArray(appctx->da, u, &s));
264: PetscCall(DMDAVecGetArrayRead(appctx->da, appctx->SEMop.grid, (void *)&xg));
265: PetscCall(DMDAGetCorners(appctx->da, &xs, NULL, NULL, &xn, NULL, NULL));
266: for (i = xs; i < xs + xn; i++) {
267: s[i] = 2.0 * appctx->param.mu * PETSC_PI * PetscSinScalar(PETSC_PI * xg[i]) * PetscExpReal(-appctx->param.mu * PETSC_PI * PETSC_PI * t) / (2.0 + PetscCosScalar(PETSC_PI * xg[i]) * PetscExpReal(-appctx->param.mu * PETSC_PI * PETSC_PI * t));
268: }
269: PetscCall(DMDAVecRestoreArray(appctx->da, u, &s));
270: PetscCall(DMDAVecRestoreArrayRead(appctx->da, appctx->SEMop.grid, (void *)&xg));
271: PetscFunctionReturn(PETSC_SUCCESS);
272: }
274: PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec globalin, Vec globalout, void *ctx)
275: {
276: AppCtx *appctx = (AppCtx *)ctx;
278: PetscFunctionBeginUser;
279: PetscCall(MatMult(appctx->SEMop.grad, globalin, globalout)); /* grad u */
280: PetscCall(VecPointwiseMult(globalout, globalin, globalout)); /* u grad u */
281: PetscCall(VecScale(globalout, -1.0));
282: PetscCall(MatMultAdd(appctx->SEMop.keptstiff, globalin, globalout, globalout));
283: PetscFunctionReturn(PETSC_SUCCESS);
284: }
286: /*
288: K is the discretiziation of the Laplacian
289: G is the discretization of the gradient
291: Computes Jacobian of K u + diag(u) G u which is given by
292: K + diag(u)G + diag(Gu)
293: */
294: PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec globalin, Mat A, Mat B, void *ctx)
295: {
296: AppCtx *appctx = (AppCtx *)ctx;
297: Vec Gglobalin;
299: PetscFunctionBeginUser;
300: /* A = diag(u) G */
302: PetscCall(MatCopy(appctx->SEMop.grad, A, SAME_NONZERO_PATTERN));
303: PetscCall(MatDiagonalScale(A, globalin, NULL));
305: /* A = A + diag(Gu) */
306: PetscCall(VecDuplicate(globalin, &Gglobalin));
307: PetscCall(MatMult(appctx->SEMop.grad, globalin, Gglobalin));
308: PetscCall(MatDiagonalSet(A, Gglobalin, ADD_VALUES));
309: PetscCall(VecDestroy(&Gglobalin));
311: /* A = K - A */
312: PetscCall(MatScale(A, -1.0));
313: PetscCall(MatAXPY(A, 0.0, appctx->SEMop.keptstiff, SAME_NONZERO_PATTERN));
314: PetscFunctionReturn(PETSC_SUCCESS);
315: }
317: #include <petscblaslapack.h>
318: /*
319: Matrix free operation of 1d Laplacian and Grad for GLL spectral elements
320: */
321: PetscErrorCode MatMult_Laplacian(Mat A, Vec x, Vec y)
322: {
323: AppCtx *appctx;
324: PetscReal **temp, vv;
325: PetscInt i, j, xs, xn;
326: Vec xlocal, ylocal;
327: const PetscScalar *xl;
328: PetscScalar *yl;
329: PetscBLASInt _One = 1, n;
330: PetscScalar _DOne = 1;
332: PetscFunctionBeginUser;
333: PetscCall(MatShellGetContext(A, &appctx));
334: PetscCall(DMGetLocalVector(appctx->da, &xlocal));
335: PetscCall(DMGlobalToLocalBegin(appctx->da, x, INSERT_VALUES, xlocal));
336: PetscCall(DMGlobalToLocalEnd(appctx->da, x, INSERT_VALUES, xlocal));
337: PetscCall(DMGetLocalVector(appctx->da, &ylocal));
338: PetscCall(VecSet(ylocal, 0.0));
339: PetscCall(PetscGaussLobattoLegendreElementLaplacianCreate(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
340: for (i = 0; i < appctx->param.N; i++) {
341: vv = -appctx->param.mu * 2.0 / appctx->param.Le;
342: for (j = 0; j < appctx->param.N; j++) temp[i][j] = temp[i][j] * vv;
343: }
344: PetscCall(DMDAVecGetArrayRead(appctx->da, xlocal, (void *)&xl));
345: PetscCall(DMDAVecGetArray(appctx->da, ylocal, &yl));
346: PetscCall(DMDAGetCorners(appctx->da, &xs, NULL, NULL, &xn, NULL, NULL));
347: PetscCall(PetscBLASIntCast(appctx->param.N, &n));
348: for (j = xs; j < xs + xn; j += appctx->param.N - 1) PetscCallBLAS("BLASgemv", BLASgemv_("N", &n, &n, &_DOne, &temp[0][0], &n, &xl[j], &_One, &_DOne, &yl[j], &_One));
349: PetscCall(DMDAVecRestoreArrayRead(appctx->da, xlocal, (void *)&xl));
350: PetscCall(DMDAVecRestoreArray(appctx->da, ylocal, &yl));
351: PetscCall(PetscGaussLobattoLegendreElementLaplacianDestroy(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
352: PetscCall(VecSet(y, 0.0));
353: PetscCall(DMLocalToGlobalBegin(appctx->da, ylocal, ADD_VALUES, y));
354: PetscCall(DMLocalToGlobalEnd(appctx->da, ylocal, ADD_VALUES, y));
355: PetscCall(DMRestoreLocalVector(appctx->da, &xlocal));
356: PetscCall(DMRestoreLocalVector(appctx->da, &ylocal));
357: PetscCall(VecPointwiseDivide(y, y, appctx->SEMop.mass));
358: PetscFunctionReturn(PETSC_SUCCESS);
359: }
361: PetscErrorCode MatMult_Advection(Mat A, Vec x, Vec y)
362: {
363: AppCtx *appctx;
364: PetscReal **temp;
365: PetscInt j, xs, xn;
366: Vec xlocal, ylocal;
367: const PetscScalar *xl;
368: PetscScalar *yl;
369: PetscBLASInt _One = 1, n;
370: PetscScalar _DOne = 1;
372: PetscFunctionBeginUser;
373: PetscCall(MatShellGetContext(A, &appctx));
374: PetscCall(DMGetLocalVector(appctx->da, &xlocal));
375: PetscCall(DMGlobalToLocalBegin(appctx->da, x, INSERT_VALUES, xlocal));
376: PetscCall(DMGlobalToLocalEnd(appctx->da, x, INSERT_VALUES, xlocal));
377: PetscCall(DMGetLocalVector(appctx->da, &ylocal));
378: PetscCall(VecSet(ylocal, 0.0));
379: PetscCall(PetscGaussLobattoLegendreElementAdvectionCreate(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
380: PetscCall(DMDAVecGetArrayRead(appctx->da, xlocal, (void *)&xl));
381: PetscCall(DMDAVecGetArray(appctx->da, ylocal, &yl));
382: PetscCall(DMDAGetCorners(appctx->da, &xs, NULL, NULL, &xn, NULL, NULL));
383: PetscCall(PetscBLASIntCast(appctx->param.N, &n));
384: for (j = xs; j < xs + xn; j += appctx->param.N - 1) PetscCallBLAS("BLASgemv", BLASgemv_("N", &n, &n, &_DOne, &temp[0][0], &n, &xl[j], &_One, &_DOne, &yl[j], &_One));
385: PetscCall(DMDAVecRestoreArrayRead(appctx->da, xlocal, (void *)&xl));
386: PetscCall(DMDAVecRestoreArray(appctx->da, ylocal, &yl));
387: PetscCall(PetscGaussLobattoLegendreElementAdvectionDestroy(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
388: PetscCall(VecSet(y, 0.0));
389: PetscCall(DMLocalToGlobalBegin(appctx->da, ylocal, ADD_VALUES, y));
390: PetscCall(DMLocalToGlobalEnd(appctx->da, ylocal, ADD_VALUES, y));
391: PetscCall(DMRestoreLocalVector(appctx->da, &xlocal));
392: PetscCall(DMRestoreLocalVector(appctx->da, &ylocal));
393: PetscCall(VecPointwiseDivide(y, y, appctx->SEMop.mass));
394: PetscCall(VecScale(y, -1.0));
395: PetscFunctionReturn(PETSC_SUCCESS);
396: }
398: /*
399: RHSMatrixLaplacian - User-provided routine to compute the right-hand-side
400: matrix for the Laplacian operator
402: Input Parameters:
403: ts - the TS context
404: t - current time (ignored)
405: X - current solution (ignored)
406: dummy - optional user-defined context, as set by TSetRHSJacobian()
408: Output Parameters:
409: AA - Jacobian matrix
410: BB - optionally different matrix from which the preconditioner is built
412: */
413: PetscErrorCode RHSMatrixLaplaciangllDM(TS ts, PetscReal t, Vec X, Mat A, Mat BB, void *ctx)
414: {
415: PetscReal **temp;
416: PetscReal vv;
417: AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */
418: PetscInt i, xs, xn, l, j;
419: PetscInt *rowsDM;
420: PetscBool flg = PETSC_FALSE;
422: PetscFunctionBeginUser;
423: PetscCall(PetscOptionsGetBool(NULL, NULL, "-gll_mf", &flg, NULL));
425: if (!flg) {
426: /*
427: Creates the element stiffness matrix for the given gll
428: */
429: PetscCall(PetscGaussLobattoLegendreElementLaplacianCreate(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
430: /* workaround for clang analyzer warning: Division by zero */
431: PetscCheck(appctx->param.N > 1, PETSC_COMM_WORLD, PETSC_ERR_ARG_WRONG, "Spectral element order should be > 1");
433: /* scale by the size of the element */
434: for (i = 0; i < appctx->param.N; i++) {
435: vv = -appctx->param.mu * 2.0 / appctx->param.Le;
436: for (j = 0; j < appctx->param.N; j++) temp[i][j] = temp[i][j] * vv;
437: }
439: PetscCall(MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
440: PetscCall(DMDAGetCorners(appctx->da, &xs, NULL, NULL, &xn, NULL, NULL));
442: xs = xs / (appctx->param.N - 1);
443: xn = xn / (appctx->param.N - 1);
445: PetscCall(PetscMalloc1(appctx->param.N, &rowsDM));
446: /*
447: loop over local elements
448: */
449: for (j = xs; j < xs + xn; j++) {
450: for (l = 0; l < appctx->param.N; l++) rowsDM[l] = 1 + (j - xs) * (appctx->param.N - 1) + l;
451: PetscCall(MatSetValuesLocal(A, appctx->param.N, rowsDM, appctx->param.N, rowsDM, &temp[0][0], ADD_VALUES));
452: }
453: PetscCall(PetscFree(rowsDM));
454: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
455: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
456: PetscCall(VecReciprocal(appctx->SEMop.mass));
457: PetscCall(MatDiagonalScale(A, appctx->SEMop.mass, 0));
458: PetscCall(VecReciprocal(appctx->SEMop.mass));
460: PetscCall(PetscGaussLobattoLegendreElementLaplacianDestroy(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
461: } else {
462: PetscCall(MatSetType(A, MATSHELL));
463: PetscCall(MatSetUp(A));
464: PetscCall(MatShellSetContext(A, appctx));
465: PetscCall(MatShellSetOperation(A, MATOP_MULT, (void (*)(void))MatMult_Laplacian));
466: }
467: PetscFunctionReturn(PETSC_SUCCESS);
468: }
470: /*
471: RHSMatrixAdvection - User-provided routine to compute the right-hand-side
472: matrix for the Advection (gradient) operator.
474: Input Parameters:
475: ts - the TS context
476: t - current time
477: global_in - global input vector
478: dummy - optional user-defined context, as set by TSetRHSJacobian()
480: Output Parameters:
481: AA - Jacobian matrix
482: BB - optionally different preconditioning matrix
484: */
485: PetscErrorCode RHSMatrixAdvectiongllDM(TS ts, PetscReal t, Vec X, Mat A, Mat BB, void *ctx)
486: {
487: PetscReal **temp;
488: AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */
489: PetscInt xs, xn, l, j;
490: PetscInt *rowsDM;
491: PetscBool flg = PETSC_FALSE;
493: PetscFunctionBeginUser;
494: PetscCall(PetscOptionsGetBool(NULL, NULL, "-gll_mf", &flg, NULL));
496: if (!flg) {
497: /*
498: Creates the advection matrix for the given gll
499: */
500: PetscCall(PetscGaussLobattoLegendreElementAdvectionCreate(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
501: PetscCall(MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
502: PetscCall(DMDAGetCorners(appctx->da, &xs, NULL, NULL, &xn, NULL, NULL));
503: xs = xs / (appctx->param.N - 1);
504: xn = xn / (appctx->param.N - 1);
506: PetscCall(PetscMalloc1(appctx->param.N, &rowsDM));
507: for (j = xs; j < xs + xn; j++) {
508: for (l = 0; l < appctx->param.N; l++) rowsDM[l] = 1 + (j - xs) * (appctx->param.N - 1) + l;
509: PetscCall(MatSetValuesLocal(A, appctx->param.N, rowsDM, appctx->param.N, rowsDM, &temp[0][0], ADD_VALUES));
510: }
511: PetscCall(PetscFree(rowsDM));
512: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
513: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
515: PetscCall(VecReciprocal(appctx->SEMop.mass));
516: PetscCall(MatDiagonalScale(A, appctx->SEMop.mass, 0));
517: PetscCall(VecReciprocal(appctx->SEMop.mass));
519: PetscCall(PetscGaussLobattoLegendreElementAdvectionDestroy(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
520: } else {
521: PetscCall(MatSetType(A, MATSHELL));
522: PetscCall(MatSetUp(A));
523: PetscCall(MatShellSetContext(A, appctx));
524: PetscCall(MatShellSetOperation(A, MATOP_MULT, (void (*)(void))MatMult_Advection));
525: }
526: PetscFunctionReturn(PETSC_SUCCESS);
527: }
529: /*TEST
531: build:
532: requires: !complex
534: test:
535: suffix: 1
536: requires: !single
538: test:
539: suffix: 2
540: nsize: 5
541: requires: !single
543: test:
544: suffix: 3
545: requires: !single
546: args: -ts_view -ts_type beuler -gll_mf -pc_type none -ts_max_steps 5 -ts_monitor_error
548: test:
549: suffix: 4
550: requires: !single
551: args: -ts_view -ts_type beuler -pc_type none -ts_max_steps 5 -ts_monitor_error
553: TEST*/