Actual source code: tseig.c

petsc-3.9.1 2018-04-29
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  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: };


 17: /*@C
 18:    TSMonitorSPEigCtxCreate - Creates a context for use with TS to monitor the eigenvalues of the linearized operator

 20:    Collective on TS

 22:    Input Parameters:
 23: +  host - the X display to open, or null for the local machine
 24: .  label - the title to put in the title bar
 25: .  x, y - the screen coordinates of the upper left coordinate of the window
 26: .  m, n - the screen width and height in pixels
 27: -  howoften - if positive then determines the frequency of the plotting, if -1 then only at the final time

 29:    Output Parameter:
 30: .  ctx - the context

 32:    Options Database Key:
 33: .  -ts_monitor_sp_eig - plot egienvalues of linearized right hand side

 35:    Notes:
 36:    Use TSMonitorSPEigCtxDestroy() to destroy.

 38:    Currently only works if the Jacobian is provided explicitly.

 40:    Currently only works for ODEs u_t - F(t,u) = 0; that is with no mass matrix.

 42:    Level: intermediate

 44: .keywords: TS, monitor, line graph, residual, seealso

 46: .seealso: TSMonitorSPEigTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError()

 48: @*/
 49: PetscErrorCode  TSMonitorSPEigCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorSPEigCtx *ctx)
 50: {
 51:   PetscDraw      win;
 53:   PC             pc;

 56:   PetscNew(ctx);
 57:   PetscRandomCreate(comm,&(*ctx)->rand);
 58:   PetscRandomSetFromOptions((*ctx)->rand);
 59:   PetscDrawCreate(comm,host,label,x,y,m,n,&win);
 60:   PetscDrawSetFromOptions(win);
 61:   PetscDrawSPCreate(win,1,&(*ctx)->drawsp);
 62:   KSPCreate(comm,&(*ctx)->ksp);
 63:   KSPSetOptionsPrefix((*ctx)->ksp,"ts_monitor_sp_eig_"); /* this is wrong, used use also prefix from the TS */
 64:   KSPSetType((*ctx)->ksp,KSPGMRES);
 65:   KSPGMRESSetRestart((*ctx)->ksp,200);
 66:   KSPSetTolerances((*ctx)->ksp,1.e-10,PETSC_DEFAULT,PETSC_DEFAULT,200);
 67:   KSPSetComputeSingularValues((*ctx)->ksp,PETSC_TRUE);
 68:   KSPSetFromOptions((*ctx)->ksp);
 69:   KSPGetPC((*ctx)->ksp,&pc);
 70:   PCSetType(pc,PCNONE);

 72:   (*ctx)->howoften          = howoften;
 73:   (*ctx)->computeexplicitly = PETSC_FALSE;

 75:   PetscOptionsGetBool(NULL,NULL,"-ts_monitor_sp_eig_explicitly",&(*ctx)->computeexplicitly,NULL);

 77:   (*ctx)->comm = comm;
 78:   (*ctx)->xmin = -2.1;
 79:   (*ctx)->xmax = 1.1;
 80:   (*ctx)->ymin = -1.1;
 81:   (*ctx)->ymax = 1.1;
 82:   return(0);
 83: }

 85: static PetscErrorCode TSLinearStabilityIndicator(TS ts, PetscReal xr,PetscReal xi,PetscBool *flg)
 86: {
 88:   PetscReal      yr,yi;

 91:   TSComputeLinearStability(ts,xr,xi,&yr,&yi);
 92:   if ((yr*yr + yi*yi) <= 1.0) *flg = PETSC_TRUE;
 93:   else *flg = PETSC_FALSE;
 94:   return(0);
 95: }

 97: PetscErrorCode TSMonitorSPEig(TS ts,PetscInt step,PetscReal ptime,Vec v,void *monctx)
 98: {
 99:   TSMonitorSPEigCtx ctx = (TSMonitorSPEigCtx) monctx;
100:   PetscErrorCode    ierr;
101:   KSP               ksp = ctx->ksp;
102:   PetscInt          n,N,nits,neig,i,its = 200;
103:   PetscReal         *r,*c,time_step_save;
104:   PetscDrawSP       drawsp = ctx->drawsp;
105:   Mat               A,B;
106:   Vec               xdot;
107:   SNES              snes;

110:   if (step < 0) return(0); /* -1 indicates interpolated solution */
111:   if (!step) return(0);
112:   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
113:     VecDuplicate(v,&xdot);
114:     TSGetSNES(ts,&snes);
115:     SNESGetJacobian(snes,&A,&B,NULL,NULL);
116:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&B);
117:     /*
118:        This doesn't work because methods keep and use internal information about the shift so it
119:        seems we would need code for each method to trick the correct Jacobian in being computed.
120:      */
121:     time_step_save = ts->time_step;
122:     ts->time_step  = PETSC_MAX_REAL;

124:     SNESComputeJacobian(snes,v,A,B);

126:     ts->time_step  = time_step_save;

128:     KSPSetOperators(ksp,B,B);
129:     VecGetSize(v,&n);
130:     if (n < 200) its = n;
131:     KSPSetTolerances(ksp,1.e-10,PETSC_DEFAULT,PETSC_DEFAULT,its);
132:     VecSetRandom(xdot,ctx->rand);
133:     KSPSolve(ksp,xdot,xdot);
134:     VecDestroy(&xdot);
135:     KSPGetIterationNumber(ksp,&nits);
136:     N    = nits+2;

138:     if (nits) {
139:       PetscDraw     draw;
140:       PetscReal     pause;
141:       PetscDrawAxis axis;
142:       PetscReal     xmin,xmax,ymin,ymax;

144:       PetscDrawSPReset(drawsp);
145:       PetscDrawSPSetLimits(drawsp,ctx->xmin,ctx->xmax,ctx->ymin,ctx->ymax);
146:       PetscMalloc2(PetscMax(n,N),&r,PetscMax(n,N),&c);
147:       if (ctx->computeexplicitly) {
148:         KSPComputeEigenvaluesExplicitly(ksp,n,r,c);
149:         neig = n;
150:       } else {
151:         KSPComputeEigenvalues(ksp,N,r,c,&neig);
152:       }
153:       /* We used the positive operator to be able to reuse KSPs that require positive definiteness, now flip the spectrum as is conventional for ODEs */
154:       for (i=0; i<neig; i++) r[i] = -r[i];
155:       for (i=0; i<neig; i++) {
156:         if (ts->ops->linearstability) {
157:           PetscReal fr,fi;
158:           TSComputeLinearStability(ts,r[i],c[i],&fr,&fi);
159:           if ((fr*fr + fi*fi) > 1.0) {
160:             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));
161:           }
162:         }
163:         PetscDrawSPAddPoint(drawsp,r+i,c+i);
164:       }
165:       PetscFree2(r,c);
166:       PetscDrawSPGetDraw(drawsp,&draw);
167:       PetscDrawGetPause(draw,&pause);
168:       PetscDrawSetPause(draw,0.0);
169:       PetscDrawSPDraw(drawsp,PETSC_TRUE);
170:       PetscDrawSetPause(draw,pause);
171:       if (ts->ops->linearstability) {
172:         PetscDrawSPGetAxis(drawsp,&axis);
173:         PetscDrawAxisGetLimits(axis,&xmin,&xmax,&ymin,&ymax);
174:         PetscDrawIndicatorFunction(draw,xmin,xmax,ymin,ymax,PETSC_DRAW_CYAN,(PetscErrorCode (*)(void*,PetscReal,PetscReal,PetscBool*))TSLinearStabilityIndicator,ts);
175:         PetscDrawSPDraw(drawsp,PETSC_FALSE);
176:       }
177:       PetscDrawSPSave(drawsp);
178:     }
179:     MatDestroy(&B);
180:   }
181:   return(0);
182: }

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

187:    Collective on TSMonitorSPEigCtx

189:    Input Parameter:
190: .  ctx - the monitor context

192:    Level: intermediate

194: .keywords: TS, monitor, line graph, destroy

196: .seealso: TSMonitorSPEigCtxCreate(),  TSMonitorSet(), TSMonitorSPEig();
197: @*/
198: PetscErrorCode  TSMonitorSPEigCtxDestroy(TSMonitorSPEigCtx *ctx)
199: {
200:   PetscDraw      draw;

204:   PetscDrawSPGetDraw((*ctx)->drawsp,&draw);
205:   PetscDrawDestroy(&draw);
206:   PetscDrawSPDestroy(&(*ctx)->drawsp);
207:   KSPDestroy(&(*ctx)->ksp);
208:   PetscRandomDestroy(&(*ctx)->rand);
209:   PetscFree(*ctx);
210:   return(0);
211: }