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 on TS
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: Notes:
35: Use TSMonitorSPEigCtxDestroy() to destroy.
37: Currently only works if the Jacobian is provided explicitly.
39: Currently only works for ODEs u_t - F(t,u) = 0; that is with no mass matrix.
41: Level: intermediate
43: .seealso: TSMonitorSPEigTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError()
45: @*/
46: PetscErrorCode TSMonitorSPEigCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorSPEigCtx *ctx)
47: {
48: PetscDraw win;
49: PC pc;
51: PetscNew(ctx);
52: PetscRandomCreate(comm,&(*ctx)->rand);
53: PetscRandomSetFromOptions((*ctx)->rand);
54: PetscDrawCreate(comm,host,label,x,y,m,n,&win);
55: PetscDrawSetFromOptions(win);
56: PetscDrawSPCreate(win,1,&(*ctx)->drawsp);
57: KSPCreate(comm,&(*ctx)->ksp);
58: KSPSetOptionsPrefix((*ctx)->ksp,"ts_monitor_sp_eig_"); /* this is wrong, used use also prefix from the TS */
59: KSPSetType((*ctx)->ksp,KSPGMRES);
60: KSPGMRESSetRestart((*ctx)->ksp,200);
61: KSPSetTolerances((*ctx)->ksp,1.e-10,PETSC_DEFAULT,PETSC_DEFAULT,200);
62: KSPSetComputeSingularValues((*ctx)->ksp,PETSC_TRUE);
63: KSPSetFromOptions((*ctx)->ksp);
64: KSPGetPC((*ctx)->ksp,&pc);
65: PCSetType(pc,PCNONE);
67: (*ctx)->howoften = howoften;
68: (*ctx)->computeexplicitly = PETSC_FALSE;
70: 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: return 0;
78: }
80: static PetscErrorCode TSLinearStabilityIndicator(TS ts, PetscReal xr,PetscReal xi,PetscBool *flg)
81: {
82: PetscReal yr,yi;
84: TSComputeLinearStability(ts,xr,xi,&yr,&yi);
85: if ((yr*yr + yi*yi) <= 1.0) *flg = PETSC_TRUE;
86: else *flg = PETSC_FALSE;
87: return 0;
88: }
90: PetscErrorCode TSMonitorSPEig(TS ts,PetscInt step,PetscReal ptime,Vec v,void *monctx)
91: {
92: TSMonitorSPEigCtx ctx = (TSMonitorSPEigCtx) monctx;
93: KSP ksp = ctx->ksp;
94: PetscInt n,N,nits,neig,i,its = 200;
95: PetscReal *r,*c,time_step_save;
96: PetscDrawSP drawsp = ctx->drawsp;
97: Mat A,B;
98: Vec xdot;
99: SNES snes;
101: if (step < 0) return 0; /* -1 indicates interpolated solution */
102: if (!step) return 0;
103: if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
104: VecDuplicate(v,&xdot);
105: TSGetSNES(ts,&snes);
106: SNESGetJacobian(snes,&A,&B,NULL,NULL);
107: MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&B);
108: /*
109: This doesn't work because methods keep and use internal information about the shift so it
110: seems we would need code for each method to trick the correct Jacobian in being computed.
111: */
112: time_step_save = ts->time_step;
113: ts->time_step = PETSC_MAX_REAL;
115: SNESComputeJacobian(snes,v,A,B);
117: ts->time_step = time_step_save;
119: KSPSetOperators(ksp,B,B);
120: VecGetSize(v,&n);
121: if (n < 200) its = n;
122: KSPSetTolerances(ksp,1.e-10,PETSC_DEFAULT,PETSC_DEFAULT,its);
123: VecSetRandom(xdot,ctx->rand);
124: KSPSolve(ksp,xdot,xdot);
125: VecDestroy(&xdot);
126: KSPGetIterationNumber(ksp,&nits);
127: N = nits+2;
129: if (nits) {
130: PetscDraw draw;
131: PetscReal pause;
132: PetscDrawAxis axis;
133: PetscReal xmin,xmax,ymin,ymax;
135: PetscDrawSPReset(drawsp);
136: PetscDrawSPSetLimits(drawsp,ctx->xmin,ctx->xmax,ctx->ymin,ctx->ymax);
137: PetscMalloc2(PetscMax(n,N),&r,PetscMax(n,N),&c);
138: if (ctx->computeexplicitly) {
139: KSPComputeEigenvaluesExplicitly(ksp,n,r,c);
140: neig = n;
141: } else {
142: KSPComputeEigenvalues(ksp,N,r,c,&neig);
143: }
144: /* We used the positive operator to be able to reuse KSPs that require positive definiteness, now flip the spectrum as is conventional for ODEs */
145: for (i=0; i<neig; i++) r[i] = -r[i];
146: for (i=0; i<neig; i++) {
147: if (ts->ops->linearstability) {
148: PetscReal fr,fi;
149: TSComputeLinearStability(ts,r[i],c[i],&fr,&fi);
150: if ((fr*fr + fi*fi) > 1.0) {
151: 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));
152: }
153: }
154: PetscDrawSPAddPoint(drawsp,r+i,c+i);
155: }
156: PetscFree2(r,c);
157: PetscDrawSPGetDraw(drawsp,&draw);
158: PetscDrawGetPause(draw,&pause);
159: PetscDrawSetPause(draw,0.0);
160: PetscDrawSPDraw(drawsp,PETSC_TRUE);
161: PetscDrawSetPause(draw,pause);
162: if (ts->ops->linearstability) {
163: PetscDrawSPGetAxis(drawsp,&axis);
164: PetscDrawAxisGetLimits(axis,&xmin,&xmax,&ymin,&ymax);
165: PetscDrawIndicatorFunction(draw,xmin,xmax,ymin,ymax,PETSC_DRAW_CYAN,(PetscErrorCode (*)(void*,PetscReal,PetscReal,PetscBool*))TSLinearStabilityIndicator,ts);
166: PetscDrawSPDraw(drawsp,PETSC_FALSE);
167: }
168: PetscDrawSPSave(drawsp);
169: }
170: MatDestroy(&B);
171: }
172: return 0;
173: }
175: /*@C
176: TSMonitorSPEigCtxDestroy - Destroys a scatter plot context that was created with TSMonitorSPEigCtxCreate().
178: Collective on TSMonitorSPEigCtx
180: Input Parameter:
181: . ctx - the monitor context
183: Level: intermediate
185: .seealso: TSMonitorSPEigCtxCreate(), TSMonitorSet(), TSMonitorSPEig();
186: @*/
187: PetscErrorCode TSMonitorSPEigCtxDestroy(TSMonitorSPEigCtx *ctx)
188: {
189: PetscDraw draw;
191: PetscDrawSPGetDraw((*ctx)->drawsp,&draw);
192: PetscDrawDestroy(&draw);
193: PetscDrawSPDestroy(&(*ctx)->drawsp);
194: KSPDestroy(&(*ctx)->ksp);
195: PetscRandomDestroy(&(*ctx)->rand);
196: PetscFree(*ctx);
197: return 0;
198: }