Actual source code: tseig.c
2: #include <petsc/private/tsimpl.h>
3: #include <petscdraw.h>
5: /* ------------------------------------------------------------------------*/
6: struct _n_TSMonitorSPEigCtx {
7: PetscDrawSP drawsp;
8: KSP ksp;
9: PetscInt howoften; /* when > 0 uses step % howoften, when negative only final solution plotted */
10: PetscBool computeexplicitly;
11: MPI_Comm comm;
12: PetscRandom rand;
13: PetscReal xmin, xmax, ymin, ymax;
14: };
16: /*@C
17: TSMonitorSPEigCtxCreate - Creates a context for use with `TS` to monitor the eigenvalues of the linearized operator
19: Collective
21: Input Parameters:
22: + host - the X display to open, or `NULL` for the local machine
23: . label - the title to put in the title bar
24: . x, y - the screen coordinates of the upper left coordinate of the window
25: . m, n - the screen width and height in pixels
26: - howoften - if positive then determines the frequency of the plotting, if -1 then only at the final time
28: Output Parameter:
29: . ctx - the context
31: Options Database Key:
32: . -ts_monitor_sp_eig - plot egienvalues of linearized right hand side
34: Level: intermediate
36: Notes:
37: Use `TSMonitorSPEigCtxDestroy()` to destroy the context
39: Currently only works if the Jacobian is provided explicitly.
41: Currently only works for ODEs u_t - F(t,u) = 0; that is with no mass matrix.
43: .seealso: [](chapter_ts), `TSMonitorSPEigTimeStep()`, `TSMonitorSet()`, `TSMonitorLGSolution()`, `TSMonitorLGError()`
44: @*/
45: PetscErrorCode TSMonitorSPEigCtxCreate(MPI_Comm comm, const char host[], const char label[], int x, int y, int m, int n, PetscInt howoften, TSMonitorSPEigCtx *ctx)
46: {
47: PetscDraw win;
48: PC pc;
50: PetscFunctionBegin;
51: PetscCall(PetscNew(ctx));
52: PetscCall(PetscRandomCreate(comm, &(*ctx)->rand));
53: PetscCall(PetscRandomSetFromOptions((*ctx)->rand));
54: PetscCall(PetscDrawCreate(comm, host, label, x, y, m, n, &win));
55: PetscCall(PetscDrawSetFromOptions(win));
56: PetscCall(PetscDrawSPCreate(win, 1, &(*ctx)->drawsp));
57: PetscCall(KSPCreate(comm, &(*ctx)->ksp));
58: PetscCall(KSPSetOptionsPrefix((*ctx)->ksp, "ts_monitor_sp_eig_")); /* this is wrong, used use also prefix from the TS */
59: PetscCall(KSPSetType((*ctx)->ksp, KSPGMRES));
60: PetscCall(KSPGMRESSetRestart((*ctx)->ksp, 200));
61: PetscCall(KSPSetTolerances((*ctx)->ksp, 1.e-10, PETSC_DEFAULT, PETSC_DEFAULT, 200));
62: PetscCall(KSPSetComputeSingularValues((*ctx)->ksp, PETSC_TRUE));
63: PetscCall(KSPSetFromOptions((*ctx)->ksp));
64: PetscCall(KSPGetPC((*ctx)->ksp, &pc));
65: PetscCall(PCSetType(pc, PCNONE));
67: (*ctx)->howoften = howoften;
68: (*ctx)->computeexplicitly = PETSC_FALSE;
70: PetscCall(PetscOptionsGetBool(NULL, NULL, "-ts_monitor_sp_eig_explicitly", &(*ctx)->computeexplicitly, NULL));
72: (*ctx)->comm = comm;
73: (*ctx)->xmin = -2.1;
74: (*ctx)->xmax = 1.1;
75: (*ctx)->ymin = -1.1;
76: (*ctx)->ymax = 1.1;
77: PetscFunctionReturn(PETSC_SUCCESS);
78: }
80: static PetscErrorCode TSLinearStabilityIndicator(TS ts, PetscReal xr, PetscReal xi, PetscBool *flg)
81: {
82: PetscReal yr, yi;
84: PetscFunctionBegin;
85: PetscCall(TSComputeLinearStability(ts, xr, xi, &yr, &yi));
86: if ((yr * yr + yi * yi) <= 1.0) *flg = PETSC_TRUE;
87: else *flg = PETSC_FALSE;
88: PetscFunctionReturn(PETSC_SUCCESS);
89: }
91: PetscErrorCode TSMonitorSPEig(TS ts, PetscInt step, PetscReal ptime, Vec v, void *monctx)
92: {
93: TSMonitorSPEigCtx ctx = (TSMonitorSPEigCtx)monctx;
94: KSP ksp = ctx->ksp;
95: PetscInt n, N, nits, neig, i, its = 200;
96: PetscReal *r, *c, time_step_save;
97: PetscDrawSP drawsp = ctx->drawsp;
98: Mat A, B;
99: Vec xdot;
100: SNES snes;
102: PetscFunctionBegin;
103: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS); /* -1 indicates interpolated solution */
104: if (!step) PetscFunctionReturn(PETSC_SUCCESS);
105: if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
106: PetscCall(VecDuplicate(v, &xdot));
107: PetscCall(TSGetSNES(ts, &snes));
108: PetscCall(SNESGetJacobian(snes, &A, &B, NULL, NULL));
109: PetscCall(MatDuplicate(A, MAT_DO_NOT_COPY_VALUES, &B));
110: /*
111: This doesn't work because methods keep and use internal information about the shift so it
112: seems we would need code for each method to trick the correct Jacobian in being computed.
113: */
114: time_step_save = ts->time_step;
115: ts->time_step = PETSC_MAX_REAL;
117: PetscCall(SNESComputeJacobian(snes, v, A, B));
119: ts->time_step = time_step_save;
121: PetscCall(KSPSetOperators(ksp, B, B));
122: PetscCall(VecGetSize(v, &n));
123: if (n < 200) its = n;
124: PetscCall(KSPSetTolerances(ksp, 1.e-10, PETSC_DEFAULT, PETSC_DEFAULT, its));
125: PetscCall(VecSetRandom(xdot, ctx->rand));
126: PetscCall(KSPSolve(ksp, xdot, xdot));
127: PetscCall(VecDestroy(&xdot));
128: PetscCall(KSPGetIterationNumber(ksp, &nits));
129: N = nits + 2;
131: if (nits) {
132: PetscDraw draw;
133: PetscReal pause;
134: PetscDrawAxis axis;
135: PetscReal xmin, xmax, ymin, ymax;
137: PetscCall(PetscDrawSPReset(drawsp));
138: PetscCall(PetscDrawSPSetLimits(drawsp, ctx->xmin, ctx->xmax, ctx->ymin, ctx->ymax));
139: PetscCall(PetscMalloc2(PetscMax(n, N), &r, PetscMax(n, N), &c));
140: if (ctx->computeexplicitly) {
141: PetscCall(KSPComputeEigenvaluesExplicitly(ksp, n, r, c));
142: neig = n;
143: } else {
144: PetscCall(KSPComputeEigenvalues(ksp, N, r, c, &neig));
145: }
146: /* We used the positive operator to be able to reuse KSPs that require positive definiteness, now flip the spectrum as is conventional for ODEs */
147: for (i = 0; i < neig; i++) r[i] = -r[i];
148: for (i = 0; i < neig; i++) {
149: if (ts->ops->linearstability) {
150: PetscReal fr, fi;
151: PetscCall(TSComputeLinearStability(ts, r[i], c[i], &fr, &fi));
152: if ((fr * fr + fi * fi) > 1.0) PetscCall(PetscPrintf(ctx->comm, "Linearized Eigenvalue %g + %g i linear stability function %g norm indicates unstable scheme \n", (double)r[i], (double)c[i], (double)(fr * fr + fi * fi)));
153: }
154: PetscCall(PetscDrawSPAddPoint(drawsp, r + i, c + i));
155: }
156: PetscCall(PetscFree2(r, c));
157: PetscCall(PetscDrawSPGetDraw(drawsp, &draw));
158: PetscCall(PetscDrawGetPause(draw, &pause));
159: PetscCall(PetscDrawSetPause(draw, 0.0));
160: PetscCall(PetscDrawSPDraw(drawsp, PETSC_TRUE));
161: PetscCall(PetscDrawSetPause(draw, pause));
162: if (ts->ops->linearstability) {
163: PetscCall(PetscDrawSPGetAxis(drawsp, &axis));
164: PetscCall(PetscDrawAxisGetLimits(axis, &xmin, &xmax, &ymin, &ymax));
165: PetscCall(PetscDrawIndicatorFunction(draw, xmin, xmax, ymin, ymax, PETSC_DRAW_CYAN, (PetscErrorCode(*)(void *, PetscReal, PetscReal, PetscBool *))TSLinearStabilityIndicator, ts));
166: PetscCall(PetscDrawSPDraw(drawsp, PETSC_FALSE));
167: }
168: PetscCall(PetscDrawSPSave(drawsp));
169: }
170: PetscCall(MatDestroy(&B));
171: }
172: PetscFunctionReturn(PETSC_SUCCESS);
173: }
175: /*@C
176: TSMonitorSPEigCtxDestroy - Destroys a scatter plot context that was created with `TSMonitorSPEigCtxCreate()`.
178: Collective
180: Input Parameter:
181: . ctx - the monitor context
183: Level: intermediate
185: Note:
186: Should be passed to `TSMonitorSet()` along with `TSMonitorSPEig()` an the context created with `TSMonitorSPEigCtxCreate()`
188: .seealso: [](chapter_ts), `TSMonitorSPEigCtxCreate()`, `TSMonitorSet()`, `TSMonitorSPEig();`
189: @*/
190: PetscErrorCode TSMonitorSPEigCtxDestroy(TSMonitorSPEigCtx *ctx)
191: {
192: PetscDraw draw;
194: PetscFunctionBegin;
195: PetscCall(PetscDrawSPGetDraw((*ctx)->drawsp, &draw));
196: PetscCall(PetscDrawDestroy(&draw));
197: PetscCall(PetscDrawSPDestroy(&(*ctx)->drawsp));
198: PetscCall(KSPDestroy(&(*ctx)->ksp));
199: PetscCall(PetscRandomDestroy(&(*ctx)->rand));
200: PetscCall(PetscFree(*ctx));
201: PetscFunctionReturn(PETSC_SUCCESS);
202: }