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) 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));
151:         }
152:         PetscDrawSPAddPoint(drawsp, r + i, c + i);
153:       }
154:       PetscFree2(r, c);
155:       PetscDrawSPGetDraw(drawsp, &draw);
156:       PetscDrawGetPause(draw, &pause);
157:       PetscDrawSetPause(draw, 0.0);
158:       PetscDrawSPDraw(drawsp, PETSC_TRUE);
159:       PetscDrawSetPause(draw, pause);
160:       if (ts->ops->linearstability) {
161:         PetscDrawSPGetAxis(drawsp, &axis);
162:         PetscDrawAxisGetLimits(axis, &xmin, &xmax, &ymin, &ymax);
163:         PetscDrawIndicatorFunction(draw, xmin, xmax, ymin, ymax, PETSC_DRAW_CYAN, (PetscErrorCode(*)(void *, PetscReal, PetscReal, PetscBool *))TSLinearStabilityIndicator, ts);
164:         PetscDrawSPDraw(drawsp, PETSC_FALSE);
165:       }
166:       PetscDrawSPSave(drawsp);
167:     }
168:     MatDestroy(&B);
169:   }
170:   return 0;
171: }

173: /*@C
174:    TSMonitorSPEigCtxDestroy - Destroys a scatter plot context that was created with TSMonitorSPEigCtxCreate().

176:    Collective on TSMonitorSPEigCtx

178:    Input Parameter:
179: .  ctx - the monitor context

181:    Level: intermediate

183: .seealso: `TSMonitorSPEigCtxCreate()`, `TSMonitorSet()`, `TSMonitorSPEig();`
184: @*/
185: PetscErrorCode TSMonitorSPEigCtxDestroy(TSMonitorSPEigCtx *ctx)
186: {
187:   PetscDraw draw;

189:   PetscDrawSPGetDraw((*ctx)->drawsp, &draw);
190:   PetscDrawDestroy(&draw);
191:   PetscDrawSPDestroy(&(*ctx)->drawsp);
192:   KSPDestroy(&(*ctx)->ksp);
193:   PetscRandomDestroy(&(*ctx)->rand);
194:   PetscFree(*ctx);
195:   return 0;
196: }