Actual source code: spectraladjointassimilation.c
1: static char help[] = "Solves a simple data assimilation problem with one dimensional advection diffusion equation using TSAdjoint\n\n";
3: /*
5: Not yet tested in parallel
7: */
9: /* ------------------------------------------------------------------------
11: This program uses the one-dimensional advection-diffusion equation),
12: u_t = mu*u_xx - a u_x,
13: on the domain 0 <= x <= 1, with periodic boundary conditions
15: to demonstrate solving a data assimilation problem of finding the initial conditions
16: to produce a given solution at a fixed time.
18: The operators are discretized with the spectral element method
20: ------------------------------------------------------------------------- */
22: /*
23: Include "petscts.h" so that we can use the TS ODE integrators. Note that this file
24: automatically includes:
25: petscsys.h - base PETSc routines
26: petscis.h - index sets
27: petscvec.h - vectors
28: petscmat.h - matrices
29: petscpc.h - preconditioners
30: petscksp.h - linear solvers
31: petscsnes.h - nonlinear solvers
32: */
34: #include <petsctao.h>
35: #include <petscts.h>
36: #include <petscdt.h>
37: #include <petscdmda.h>
39: /*
40: User-defined application context - contains data needed by the
41: application-provided call-back routines.
42: */
44: typedef struct {
45: PetscInt n; /* number of nodes */
46: PetscReal *nodes; /* GLL nodes */
47: PetscReal *weights; /* GLL weights */
48: } PetscGLL;
50: typedef struct {
51: PetscInt N; /* grid points per elements*/
52: PetscInt E; /* number of elements */
53: PetscReal tol_L2, tol_max; /* error norms */
54: PetscInt steps; /* number of timesteps */
55: PetscReal Tend; /* endtime */
56: PetscReal mu; /* viscosity */
57: PetscReal a; /* advection speed */
58: PetscReal L; /* total length of domain */
59: PetscReal Le;
60: PetscReal Tadj;
61: } PetscParam;
63: typedef struct {
64: Vec reference; /* desired end state */
65: Vec grid; /* total grid */
66: Vec grad;
67: Vec ic;
68: Vec curr_sol;
69: Vec joe;
70: Vec true_solution; /* actual initial conditions for the final solution */
71: } PetscData;
73: typedef struct {
74: Vec grid; /* total grid */
75: Vec mass; /* mass matrix for total integration */
76: Mat stiff; /* stiffness matrix */
77: Mat advec;
78: Mat keptstiff;
79: PetscGLL gll;
80: } PetscSEMOperators;
82: typedef struct {
83: DM da; /* distributed array data structure */
84: PetscSEMOperators SEMop;
85: PetscParam param;
86: PetscData dat;
87: TS ts;
88: PetscReal initial_dt;
89: PetscReal *solutioncoefficients;
90: PetscInt ncoeff;
91: } AppCtx;
93: /*
94: User-defined routines
95: */
96: extern PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *, Vec, void *);
97: extern PetscErrorCode RHSLaplacian(TS, PetscReal, Vec, Mat, Mat, void *);
98: extern PetscErrorCode RHSAdvection(TS, PetscReal, Vec, Mat, Mat, void *);
99: extern PetscErrorCode InitialConditions(Vec, AppCtx *);
100: extern PetscErrorCode ComputeReference(TS, PetscReal, Vec, AppCtx *);
101: extern PetscErrorCode MonitorError(Tao, void *);
102: extern PetscErrorCode MonitorDestroy(PetscCtxRt);
103: extern PetscErrorCode ComputeSolutionCoefficients(AppCtx *);
104: extern PetscErrorCode RHSFunction(TS, PetscReal, Vec, Vec, void *);
105: extern PetscErrorCode RHSJacobian(TS, PetscReal, Vec, Mat, Mat, void *);
107: int main(int argc, char **argv)
108: {
109: AppCtx appctx; /* user-defined application context */
110: Tao tao;
111: Vec u; /* approximate solution vector */
112: PetscInt i, xs, xm, ind, j, lenglob;
113: PetscReal x, *wrk_ptr1, *wrk_ptr2;
114: MatNullSpace nsp;
116: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117: Initialize program and set problem parameters
118: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119: PetscFunctionBeginUser;
120: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
122: /*initialize parameters */
123: appctx.param.N = 10; /* order of the spectral element */
124: appctx.param.E = 8; /* number of elements */
125: appctx.param.L = 1.0; /* length of the domain */
126: appctx.param.mu = 0.00001; /* diffusion coefficient */
127: appctx.param.a = 0.0; /* advection speed */
128: appctx.initial_dt = 1e-4;
129: appctx.param.steps = PETSC_INT_MAX;
130: appctx.param.Tend = 0.01;
131: appctx.ncoeff = 2;
133: PetscCall(PetscOptionsGetInt(NULL, NULL, "-N", &appctx.param.N, NULL));
134: PetscCall(PetscOptionsGetInt(NULL, NULL, "-E", &appctx.param.E, NULL));
135: PetscCall(PetscOptionsGetInt(NULL, NULL, "-ncoeff", &appctx.ncoeff, NULL));
136: PetscCall(PetscOptionsGetReal(NULL, NULL, "-Tend", &appctx.param.Tend, NULL));
137: PetscCall(PetscOptionsGetReal(NULL, NULL, "-mu", &appctx.param.mu, NULL));
138: PetscCall(PetscOptionsGetReal(NULL, NULL, "-a", &appctx.param.a, NULL));
139: appctx.param.Le = appctx.param.L / appctx.param.E;
141: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: Create GLL data structures
143: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144: PetscCall(PetscMalloc2(appctx.param.N, &appctx.SEMop.gll.nodes, appctx.param.N, &appctx.SEMop.gll.weights));
145: PetscCall(PetscDTGaussLobattoLegendreQuadrature(appctx.param.N, PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA, appctx.SEMop.gll.nodes, appctx.SEMop.gll.weights));
146: appctx.SEMop.gll.n = appctx.param.N;
147: lenglob = appctx.param.E * (appctx.param.N - 1);
149: /*
150: Create distributed array (DMDA) to manage parallel grid and vectors
151: and to set up the ghost point communication pattern. There are E*(Nl-1)+1
152: total grid values spread equally among all the processors, except first and last
153: */
155: PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, lenglob, 1, 1, NULL, &appctx.da));
156: PetscCall(DMSetFromOptions(appctx.da));
157: PetscCall(DMSetUp(appctx.da));
159: /*
160: Extract global and local vectors from DMDA; we use these to store the
161: approximate solution. Then duplicate these for remaining vectors that
162: have the same types.
163: */
165: PetscCall(DMCreateGlobalVector(appctx.da, &u));
166: PetscCall(VecDuplicate(u, &appctx.dat.ic));
167: PetscCall(VecDuplicate(u, &appctx.dat.true_solution));
168: PetscCall(VecDuplicate(u, &appctx.dat.reference));
169: PetscCall(VecDuplicate(u, &appctx.SEMop.grid));
170: PetscCall(VecDuplicate(u, &appctx.SEMop.mass));
171: PetscCall(VecDuplicate(u, &appctx.dat.curr_sol));
172: PetscCall(VecDuplicate(u, &appctx.dat.joe));
174: PetscCall(DMDAGetCorners(appctx.da, &xs, NULL, NULL, &xm, NULL, NULL));
175: PetscCall(DMDAVecGetArray(appctx.da, appctx.SEMop.grid, &wrk_ptr1));
176: PetscCall(DMDAVecGetArray(appctx.da, appctx.SEMop.mass, &wrk_ptr2));
178: /* Compute function over the locally owned part of the grid */
180: xs = xs / (appctx.param.N - 1);
181: xm = xm / (appctx.param.N - 1);
183: /*
184: Build total grid and mass over entire mesh (multi-elemental)
185: */
187: for (i = xs; i < xs + xm; i++) {
188: for (j = 0; j < appctx.param.N - 1; j++) {
189: x = (appctx.param.Le / 2.0) * (appctx.SEMop.gll.nodes[j] + 1.0) + appctx.param.Le * i;
190: ind = i * (appctx.param.N - 1) + j;
191: wrk_ptr1[ind] = x;
192: wrk_ptr2[ind] = .5 * appctx.param.Le * appctx.SEMop.gll.weights[j];
193: if (j == 0) wrk_ptr2[ind] += .5 * appctx.param.Le * appctx.SEMop.gll.weights[j];
194: }
195: }
196: PetscCall(DMDAVecRestoreArray(appctx.da, appctx.SEMop.grid, &wrk_ptr1));
197: PetscCall(DMDAVecRestoreArray(appctx.da, appctx.SEMop.mass, &wrk_ptr2));
199: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
200: Create matrix data structure; set matrix evaluation routine.
201: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
202: PetscCall(DMSetMatrixPreallocateOnly(appctx.da, PETSC_TRUE));
203: PetscCall(DMCreateMatrix(appctx.da, &appctx.SEMop.stiff));
204: PetscCall(DMCreateMatrix(appctx.da, &appctx.SEMop.advec));
206: /*
207: For linear problems with a time-dependent f(u,t) in the equation
208: u_t = f(u,t), the user provides the discretized right-hand side
209: as a time-dependent matrix.
210: */
211: PetscCall(RHSLaplacian(appctx.ts, 0.0, u, appctx.SEMop.stiff, appctx.SEMop.stiff, &appctx));
212: PetscCall(RHSAdvection(appctx.ts, 0.0, u, appctx.SEMop.advec, appctx.SEMop.advec, &appctx));
213: PetscCall(MatAXPY(appctx.SEMop.stiff, -1.0, appctx.SEMop.advec, DIFFERENT_NONZERO_PATTERN));
214: PetscCall(MatDuplicate(appctx.SEMop.stiff, MAT_COPY_VALUES, &appctx.SEMop.keptstiff));
216: /* attach the null space to the matrix, this probably is not needed but does no harm */
217: PetscCall(MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, NULL, &nsp));
218: PetscCall(MatSetNullSpace(appctx.SEMop.stiff, nsp));
219: PetscCall(MatNullSpaceTest(nsp, appctx.SEMop.stiff, NULL));
220: PetscCall(MatNullSpaceDestroy(&nsp));
222: /* Create the TS solver that solves the ODE and its adjoint; set its options */
223: PetscCall(TSCreate(PETSC_COMM_WORLD, &appctx.ts));
224: PetscCall(TSSetSolutionFunction(appctx.ts, (PetscErrorCode (*)(TS, PetscReal, Vec, void *))ComputeReference, &appctx));
225: PetscCall(TSSetProblemType(appctx.ts, TS_LINEAR));
226: PetscCall(TSSetType(appctx.ts, TSRK));
227: PetscCall(TSSetDM(appctx.ts, appctx.da));
228: PetscCall(TSSetTime(appctx.ts, 0.0));
229: PetscCall(TSSetTimeStep(appctx.ts, appctx.initial_dt));
230: PetscCall(TSSetMaxSteps(appctx.ts, appctx.param.steps));
231: PetscCall(TSSetMaxTime(appctx.ts, appctx.param.Tend));
232: PetscCall(TSSetExactFinalTime(appctx.ts, TS_EXACTFINALTIME_MATCHSTEP));
233: PetscCall(TSSetTolerances(appctx.ts, 1e-7, NULL, 1e-7, NULL));
234: PetscCall(TSSetFromOptions(appctx.ts));
235: /* Need to save initial timestep user may have set with -ts_time_step so it can be reset for each new TSSolve() */
236: PetscCall(TSGetTimeStep(appctx.ts, &appctx.initial_dt));
237: PetscCall(TSSetRHSFunction(appctx.ts, NULL, TSComputeRHSFunctionLinear, &appctx));
238: PetscCall(TSSetRHSJacobian(appctx.ts, appctx.SEMop.stiff, appctx.SEMop.stiff, TSComputeRHSJacobianConstant, &appctx));
239: /* PetscCall(TSSetRHSFunction(appctx.ts,NULL,RHSFunction,&appctx));
240: PetscCall(TSSetRHSJacobian(appctx.ts,appctx.SEMop.stiff,appctx.SEMop.stiff,RHSJacobian,&appctx)); */
242: /* Set random initial conditions as initial guess, compute analytic reference solution and analytic (true) initial conditions */
243: PetscCall(ComputeSolutionCoefficients(&appctx));
244: PetscCall(InitialConditions(appctx.dat.ic, &appctx));
245: PetscCall(ComputeReference(appctx.ts, appctx.param.Tend, appctx.dat.reference, &appctx));
246: PetscCall(ComputeReference(appctx.ts, 0.0, appctx.dat.true_solution, &appctx));
248: /* Set up to save trajectory before TSSetFromOptions() so that TSTrajectory options can be captured */
249: PetscCall(TSSetSaveTrajectory(appctx.ts));
250: PetscCall(TSSetFromOptions(appctx.ts));
252: /* Create TAO solver and set desired solution method */
253: PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
254: PetscCall(TaoMonitorSet(tao, MonitorError, &appctx, MonitorDestroy));
255: PetscCall(TaoSetType(tao, TAOBQNLS));
256: PetscCall(TaoSetSolution(tao, appctx.dat.ic));
257: /* Set routine for function and gradient evaluation */
258: PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, (void *)&appctx));
259: /* Check for any TAO command line options */
260: PetscCall(TaoSetTolerances(tao, 1e-8, PETSC_CURRENT, PETSC_CURRENT));
261: PetscCall(TaoSetFromOptions(tao));
262: PetscCall(TaoSolve(tao));
264: PetscCall(TaoDestroy(&tao));
265: PetscCall(PetscFree(appctx.solutioncoefficients));
266: PetscCall(MatDestroy(&appctx.SEMop.advec));
267: PetscCall(MatDestroy(&appctx.SEMop.stiff));
268: PetscCall(MatDestroy(&appctx.SEMop.keptstiff));
269: PetscCall(VecDestroy(&u));
270: PetscCall(VecDestroy(&appctx.dat.ic));
271: PetscCall(VecDestroy(&appctx.dat.joe));
272: PetscCall(VecDestroy(&appctx.dat.true_solution));
273: PetscCall(VecDestroy(&appctx.dat.reference));
274: PetscCall(VecDestroy(&appctx.SEMop.grid));
275: PetscCall(VecDestroy(&appctx.SEMop.mass));
276: PetscCall(VecDestroy(&appctx.dat.curr_sol));
277: PetscCall(PetscFree2(appctx.SEMop.gll.nodes, appctx.SEMop.gll.weights));
278: PetscCall(DMDestroy(&appctx.da));
279: PetscCall(TSDestroy(&appctx.ts));
281: /*
282: Always call PetscFinalize() before exiting a program. This routine
283: - finalizes the PETSc libraries as well as MPI
284: - provides summary and diagnostic information if certain runtime
285: options are chosen (e.g., -log_view).
286: */
287: PetscCall(PetscFinalize());
288: return 0;
289: }
291: /*
292: Computes the coefficients for the analytic solution to the PDE
293: */
294: PetscErrorCode ComputeSolutionCoefficients(AppCtx *appctx)
295: {
296: PetscRandom rand;
297: PetscInt i;
299: PetscFunctionBegin;
300: PetscCall(PetscMalloc1(appctx->ncoeff, &appctx->solutioncoefficients));
301: PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rand));
302: PetscCall(PetscRandomSetInterval(rand, .9, 1.0));
303: for (i = 0; i < appctx->ncoeff; i++) PetscCall(PetscRandomGetValue(rand, &appctx->solutioncoefficients[i]));
304: PetscCall(PetscRandomDestroy(&rand));
305: PetscFunctionReturn(PETSC_SUCCESS);
306: }
308: /* --------------------------------------------------------------------- */
309: /*
310: InitialConditions - Computes the (random) initial conditions for the Tao optimization solve (these are also initial conditions for the first TSSolve()
312: Input Parameter:
313: u - uninitialized solution vector (global)
314: appctx - user-defined application context
316: Output Parameter:
317: u - vector with solution at initial time (global)
318: */
319: PetscErrorCode InitialConditions(Vec u, AppCtx *appctx)
320: {
321: PetscScalar *s;
322: const PetscScalar *xg;
323: PetscInt i, j, lenglob;
324: PetscReal sum, val;
325: PetscRandom rand;
327: PetscFunctionBegin;
328: PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rand));
329: PetscCall(PetscRandomSetInterval(rand, .9, 1.0));
330: PetscCall(DMDAVecGetArray(appctx->da, u, &s));
331: PetscCall(DMDAVecGetArrayRead(appctx->da, appctx->SEMop.grid, (void *)&xg));
332: lenglob = appctx->param.E * (appctx->param.N - 1);
333: for (i = 0; i < lenglob; i++) {
334: s[i] = 0;
335: for (j = 0; j < appctx->ncoeff; j++) {
336: PetscCall(PetscRandomGetValue(rand, &val));
337: s[i] += val * PetscSinScalar(2 * (j + 1) * PETSC_PI * xg[i]);
338: }
339: }
340: PetscCall(PetscRandomDestroy(&rand));
341: PetscCall(DMDAVecRestoreArray(appctx->da, u, &s));
342: PetscCall(DMDAVecRestoreArrayRead(appctx->da, appctx->SEMop.grid, (void *)&xg));
343: /* make sure initial conditions do not contain the constant functions, since with periodic boundary conditions the constant functions introduce a null space */
344: PetscCall(VecSum(u, &sum));
345: PetscCall(VecShift(u, -sum / lenglob));
346: PetscFunctionReturn(PETSC_SUCCESS);
347: }
349: /*
350: TrueSolution() computes the true solution for the Tao optimization solve which means they are the initial conditions for the objective function.
352: InitialConditions() computes the initial conditions for the beginning of the Tao iterations
354: Input Parameter:
355: u - uninitialized solution vector (global)
356: appctx - user-defined application context
358: Output Parameter:
359: u - vector with solution at initial time (global)
360: */
361: PetscErrorCode TrueSolution(Vec u, AppCtx *appctx)
362: {
363: PetscScalar *s;
364: const PetscScalar *xg;
365: PetscInt i, j, lenglob;
366: PetscReal sum;
368: PetscFunctionBegin;
369: PetscCall(DMDAVecGetArray(appctx->da, u, &s));
370: PetscCall(DMDAVecGetArrayRead(appctx->da, appctx->SEMop.grid, (void *)&xg));
371: lenglob = appctx->param.E * (appctx->param.N - 1);
372: for (i = 0; i < lenglob; i++) {
373: s[i] = 0;
374: for (j = 0; j < appctx->ncoeff; j++) s[i] += appctx->solutioncoefficients[j] * PetscSinScalar(2 * (j + 1) * PETSC_PI * xg[i]);
375: }
376: PetscCall(DMDAVecRestoreArray(appctx->da, u, &s));
377: PetscCall(DMDAVecRestoreArrayRead(appctx->da, appctx->SEMop.grid, (void *)&xg));
378: /* make sure initial conditions do not contain the constant functions, since with periodic boundary conditions the constant functions introduce a null space */
379: PetscCall(VecSum(u, &sum));
380: PetscCall(VecShift(u, -sum / lenglob));
381: PetscFunctionReturn(PETSC_SUCCESS);
382: }
383: /* --------------------------------------------------------------------- */
384: /*
385: Sets the desired profile for the final end time
387: Input Parameters:
388: t - final time
389: obj - vector storing the desired profile
390: appctx - user-defined application context
392: */
393: PetscErrorCode ComputeReference(TS ts, PetscReal t, Vec obj, AppCtx *appctx)
394: {
395: PetscScalar *s, tc;
396: const PetscScalar *xg;
397: PetscInt i, j, lenglob;
399: PetscFunctionBegin;
400: PetscCall(DMDAVecGetArray(appctx->da, obj, &s));
401: PetscCall(DMDAVecGetArrayRead(appctx->da, appctx->SEMop.grid, (void *)&xg));
402: lenglob = appctx->param.E * (appctx->param.N - 1);
403: for (i = 0; i < lenglob; i++) {
404: s[i] = 0;
405: for (j = 0; j < appctx->ncoeff; j++) {
406: tc = -appctx->param.mu * (j + 1) * (j + 1) * 4.0 * PETSC_PI * PETSC_PI * t;
407: s[i] += appctx->solutioncoefficients[j] * PetscSinScalar(2 * (j + 1) * PETSC_PI * (xg[i] + appctx->param.a * t)) * PetscExpReal(tc);
408: }
409: }
410: PetscCall(DMDAVecRestoreArray(appctx->da, obj, &s));
411: PetscCall(DMDAVecRestoreArrayRead(appctx->da, appctx->SEMop.grid, (void *)&xg));
412: PetscFunctionReturn(PETSC_SUCCESS);
413: }
415: PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec globalin, Vec globalout, PetscCtx ctx)
416: {
417: AppCtx *appctx = (AppCtx *)ctx;
419: PetscFunctionBegin;
420: PetscCall(MatMult(appctx->SEMop.keptstiff, globalin, globalout));
421: PetscFunctionReturn(PETSC_SUCCESS);
422: }
424: PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec globalin, Mat A, Mat B, PetscCtx ctx)
425: {
426: AppCtx *appctx = (AppCtx *)ctx;
428: PetscFunctionBegin;
429: PetscCall(MatCopy(appctx->SEMop.keptstiff, A, DIFFERENT_NONZERO_PATTERN));
430: PetscFunctionReturn(PETSC_SUCCESS);
431: }
433: /* --------------------------------------------------------------------- */
435: /*
436: RHSLaplacian - matrix for diffusion
438: Input Parameters:
439: ts - the TS context
440: t - current time (ignored)
441: X - current solution (ignored)
442: dummy - optional user-defined context, as set by TSetRHSJacobian()
444: Output Parameters:
445: AA - Jacobian matrix
446: BB - optionally different matrix from which the preconditioner is built
448: Scales by the inverse of the mass matrix (perhaps that should be pulled out)
450: */
451: PetscErrorCode RHSLaplacian(TS ts, PetscReal t, Vec X, Mat A, Mat BB, PetscCtx ctx)
452: {
453: PetscReal **temp;
454: PetscReal vv;
455: AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */
456: PetscInt i, xs, xn, l, j;
457: PetscInt *rowsDM;
459: PetscFunctionBegin;
460: /*
461: Creates the element stiffness matrix for the given gll
462: */
463: PetscCall(PetscGaussLobattoLegendreElementLaplacianCreate(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
465: /* scale by the size of the element */
466: for (i = 0; i < appctx->param.N; i++) {
467: vv = -appctx->param.mu * 2.0 / appctx->param.Le;
468: for (j = 0; j < appctx->param.N; j++) temp[i][j] = temp[i][j] * vv;
469: }
471: PetscCall(MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
472: PetscCall(DMDAGetCorners(appctx->da, &xs, NULL, NULL, &xn, NULL, NULL));
474: PetscCheck(appctx->param.N - 1 >= 1, PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Polynomial order must be at least 2");
475: xs = xs / (appctx->param.N - 1);
476: xn = xn / (appctx->param.N - 1);
478: PetscCall(PetscMalloc1(appctx->param.N, &rowsDM));
479: /*
480: loop over local elements
481: */
482: for (j = xs; j < xs + xn; j++) {
483: for (l = 0; l < appctx->param.N; l++) rowsDM[l] = 1 + (j - xs) * (appctx->param.N - 1) + l;
484: PetscCall(MatSetValuesLocal(A, appctx->param.N, rowsDM, appctx->param.N, rowsDM, &temp[0][0], ADD_VALUES));
485: }
486: PetscCall(PetscFree(rowsDM));
487: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
488: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
489: PetscCall(VecReciprocal(appctx->SEMop.mass));
490: PetscCall(MatDiagonalScale(A, appctx->SEMop.mass, NULL));
491: PetscCall(VecReciprocal(appctx->SEMop.mass));
493: PetscCall(PetscGaussLobattoLegendreElementLaplacianDestroy(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
494: PetscFunctionReturn(PETSC_SUCCESS);
495: }
497: /*
498: Almost identical to Laplacian
500: Note that the element matrix is NOT scaled by the size of element like the Laplacian term.
501: */
502: PetscErrorCode RHSAdvection(TS ts, PetscReal t, Vec X, Mat A, Mat BB, PetscCtx ctx)
503: {
504: PetscReal **temp;
505: PetscReal vv;
506: AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */
507: PetscInt i, xs, xn, l, j;
508: PetscInt *rowsDM;
510: PetscFunctionBegin;
511: /*
512: Creates the element stiffness matrix for the given gll
513: */
514: PetscCall(PetscGaussLobattoLegendreElementAdvectionCreate(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
516: /* scale by the size of the element */
517: for (i = 0; i < appctx->param.N; i++) {
518: vv = -appctx->param.a;
519: for (j = 0; j < appctx->param.N; j++) temp[i][j] = temp[i][j] * vv;
520: }
522: PetscCall(MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
523: PetscCall(DMDAGetCorners(appctx->da, &xs, NULL, NULL, &xn, NULL, NULL));
525: PetscCheck(appctx->param.N - 1 >= 1, PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Polynomial order must be at least 2");
526: xs = xs / (appctx->param.N - 1);
527: xn = xn / (appctx->param.N - 1);
529: PetscCall(PetscMalloc1(appctx->param.N, &rowsDM));
530: /*
531: loop over local elements
532: */
533: for (j = xs; j < xs + xn; j++) {
534: for (l = 0; l < appctx->param.N; l++) rowsDM[l] = 1 + (j - xs) * (appctx->param.N - 1) + l;
535: PetscCall(MatSetValuesLocal(A, appctx->param.N, rowsDM, appctx->param.N, rowsDM, &temp[0][0], ADD_VALUES));
536: }
537: PetscCall(PetscFree(rowsDM));
538: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
539: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
540: PetscCall(VecReciprocal(appctx->SEMop.mass));
541: PetscCall(MatDiagonalScale(A, appctx->SEMop.mass, NULL));
542: PetscCall(VecReciprocal(appctx->SEMop.mass));
544: PetscCall(PetscGaussLobattoLegendreElementAdvectionDestroy(appctx->SEMop.gll.n, appctx->SEMop.gll.nodes, appctx->SEMop.gll.weights, &temp));
545: PetscFunctionReturn(PETSC_SUCCESS);
546: }
548: /* ------------------------------------------------------------------ */
549: /*
550: FormFunctionGradient - Evaluates the function and corresponding gradient.
552: Input Parameters:
553: tao - the Tao context
554: ic - the input vector
555: ctx - optional user-defined context, as set when calling TaoSetObjectiveAndGradient()
557: Output Parameters:
558: f - the newly evaluated function
559: G - the newly evaluated gradient
561: Notes:
563: The forward equation is
564: M u_t = F(U)
565: which is converted to
566: u_t = M^{-1} F(u)
567: in the user code since TS has no direct way of providing a mass matrix. The Jacobian of this is
568: M^{-1} J
569: where J is the Jacobian of F. Now the adjoint equation is
570: M v_t = J^T v
571: but TSAdjoint does not solve this since it can only solve the transposed system for the
572: Jacobian the user provided. Hence TSAdjoint solves
573: w_t = J^T M^{-1} w (where w = M v)
574: since there is no way to indicate the mass matrix as a separate entity to TS. Thus one
575: must be careful in initializing the "adjoint equation" and using the result. This is
576: why
577: G = -2 M(u(T) - u_d)
578: below (instead of -2(u(T) - u_d)
580: */
581: PetscErrorCode FormFunctionGradient(Tao tao, Vec ic, PetscReal *f, Vec G, PetscCtx ctx)
582: {
583: AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */
584: Vec temp;
586: PetscFunctionBegin;
587: PetscCall(TSSetTime(appctx->ts, 0.0));
588: PetscCall(TSSetStepNumber(appctx->ts, 0));
589: PetscCall(TSSetTimeStep(appctx->ts, appctx->initial_dt));
590: PetscCall(VecCopy(ic, appctx->dat.curr_sol));
592: PetscCall(TSSolve(appctx->ts, appctx->dat.curr_sol));
593: PetscCall(VecCopy(appctx->dat.curr_sol, appctx->dat.joe));
595: /* Compute the difference between the current ODE solution and target ODE solution */
596: PetscCall(VecWAXPY(G, -1.0, appctx->dat.curr_sol, appctx->dat.reference));
598: /* Compute the objective/cost function */
599: PetscCall(VecDuplicate(G, &temp));
600: PetscCall(VecPointwiseMult(temp, G, G));
601: PetscCall(VecDot(temp, appctx->SEMop.mass, f));
602: PetscCall(VecDestroy(&temp));
604: /* Compute initial conditions for the adjoint integration. See Notes above */
605: PetscCall(VecScale(G, -2.0));
606: PetscCall(VecPointwiseMult(G, G, appctx->SEMop.mass));
607: PetscCall(TSSetCostGradients(appctx->ts, 1, &G, NULL));
609: PetscCall(TSAdjointSolve(appctx->ts));
610: /* PetscCall(VecPointwiseDivide(G,G,appctx->SEMop.mass));*/
611: PetscFunctionReturn(PETSC_SUCCESS);
612: }
614: PetscErrorCode MonitorError(Tao tao, PetscCtx ctx)
615: {
616: AppCtx *appctx = (AppCtx *)ctx;
617: Vec temp, grad;
618: PetscReal nrm;
619: PetscInt its;
620: PetscReal fct, gnorm;
622: PetscFunctionBegin;
623: PetscCall(VecDuplicate(appctx->dat.ic, &temp));
624: PetscCall(VecWAXPY(temp, -1.0, appctx->dat.ic, appctx->dat.true_solution));
625: PetscCall(VecPointwiseMult(temp, temp, temp));
626: PetscCall(VecDot(temp, appctx->SEMop.mass, &nrm));
627: nrm = PetscSqrtReal(nrm);
628: PetscCall(TaoGetGradient(tao, &grad, NULL, NULL));
629: PetscCall(VecPointwiseMult(temp, temp, temp));
630: PetscCall(VecDot(temp, appctx->SEMop.mass, &gnorm));
631: gnorm = PetscSqrtReal(gnorm);
632: PetscCall(VecDestroy(&temp));
633: PetscCall(TaoGetIterationNumber(tao, &its));
634: PetscCall(TaoGetSolutionStatus(tao, NULL, &fct, NULL, NULL, NULL, NULL));
635: if (!its) {
636: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%% Iteration Error Objective Gradient-norm\n"));
637: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "history = [\n"));
638: }
639: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%3" PetscInt_FMT " %g %g %g\n", its, (double)nrm, (double)fct, (double)gnorm));
640: PetscFunctionReturn(PETSC_SUCCESS);
641: }
643: PetscErrorCode MonitorDestroy(PetscCtxRt ctx)
644: {
645: PetscFunctionBegin;
646: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "];\n"));
647: PetscFunctionReturn(PETSC_SUCCESS);
648: }
650: /*TEST
652: build:
653: requires: !complex
655: test:
656: requires: !single
657: args: -ts_adapt_dt_max 3.e-3 -E 10 -N 8 -ncoeff 5 -tao_bqnls_mat_lmvm_scale_type none
659: test:
660: suffix: cn
661: requires: !single
662: args: -ts_type cn -ts_time_step .003 -pc_type lu -E 10 -N 8 -ncoeff 5 -tao_bqnls_mat_lmvm_scale_type none
664: test:
665: suffix: 2
666: requires: !single
667: args: -ts_adapt_dt_max 3.e-3 -E 10 -N 8 -ncoeff 5 -a .1 -tao_bqnls_mat_lmvm_scale_type none
669: TEST*/