Actual source code: ex8.c

  1: static char help[] = "Time-dependent PDE in 2d for calculating joint PDF. \n";
  2: /*
  3:    p_t = -x_t*p_x -y_t*p_y + f(t)*p_yy
  4:    xmin < x < xmax, ymin < y < ymax;

  6:    Boundary conditions:
  7:    Zero dirichlet in y using ghosted values
  8:    Periodic in x

 10:    Note that x_t and y_t in the above are given functions of x and y; they are not derivatives of x and y.
 11:    x_t = (y - ws)
 12:    y_t = (ws/2H)*(Pm - Pmax*sin(x) - D*(w - ws))

 14:    In this example, we can see the effect of a fault, that zeroes the electrical power output
 15:    Pmax*sin(x), on the PDF. The fault on/off times can be controlled by options -tf and -tcl respectively.

 17: */

 19: #include <petscdm.h>
 20: #include <petscdmda.h>
 21: #include <petscts.h>

 23: /*
 24:    User-defined data structures and routines
 25: */
 26: typedef struct {
 27:   PetscScalar ws;   /* Synchronous speed */
 28:   PetscScalar H;    /* Inertia constant */
 29:   PetscScalar D;    /* Damping constant */
 30:   PetscScalar Pmax,Pmax_s; /* Maximum power output of generator */
 31:   PetscScalar PM_min; /* Mean mechanical power input */
 32:   PetscScalar lambda; /* correlation time */
 33:   PetscScalar q;      /* noise strength */
 34:   PetscScalar mux;    /* Initial average angle */
 35:   PetscScalar sigmax; /* Standard deviation of initial angle */
 36:   PetscScalar muy;    /* Average speed */
 37:   PetscScalar sigmay; /* standard deviation of initial speed */
 38:   PetscScalar rho;    /* Cross-correlation coefficient */
 39:   PetscScalar xmin;   /* left boundary of angle */
 40:   PetscScalar xmax;   /* right boundary of angle */
 41:   PetscScalar ymin;   /* bottom boundary of speed */
 42:   PetscScalar ymax;   /* top boundary of speed */
 43:   PetscScalar dx;     /* x step size */
 44:   PetscScalar dy;     /* y step size */
 45:   PetscScalar disper_coe; /* Dispersion coefficient */
 46:   DM          da;
 47:   PetscInt    st_width; /* Stencil width */
 48:   DMBoundaryType bx; /* x boundary type */
 49:   DMBoundaryType by; /* y boundary type */
 50:   PetscReal        tf,tcl; /* Fault incidence and clearing times */
 51: } AppCtx;

 53: PetscErrorCode Parameter_settings(AppCtx*);
 54: PetscErrorCode ini_bou(Vec,AppCtx*);
 55: PetscErrorCode IFunction(TS,PetscReal,Vec,Vec,Vec,void*);
 56: PetscErrorCode IJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
 57: PetscErrorCode PostStep(TS);

 59: int main(int argc, char **argv)
 60: {
 61:   Vec         x;                /* Solution vector */
 62:   TS          ts;               /* Time-stepping context */
 63:   AppCtx      user;             /* Application context */
 64:   PetscViewer viewer;

 66:   PetscInitialize(&argc,&argv,"petscopt_ex8", help);

 68:   /* Get physics and time parameters */
 69:   Parameter_settings(&user);
 70:   /* Create a 2D DA with dof = 1 */
 71:   DMDACreate2d(PETSC_COMM_WORLD,user.bx,user.by,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,user.st_width,NULL,NULL,&user.da);
 72:   DMSetFromOptions(user.da);
 73:   DMSetUp(user.da);
 74:   /* Set x and y coordinates */
 75:   DMDASetUniformCoordinates(user.da,user.xmin,user.xmax,user.ymin,user.ymax,0,0);
 76:   DMDASetCoordinateName(user.da,0,"X - the angle");
 77:   DMDASetCoordinateName(user.da,1,"Y - the speed");

 79:   /* Get global vector x from DM  */
 80:   DMCreateGlobalVector(user.da,&x);

 82:   ini_bou(x,&user);
 83:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"ini_x",FILE_MODE_WRITE,&viewer);
 84:   VecView(x,viewer);
 85:   PetscViewerDestroy(&viewer);

 87:   TSCreate(PETSC_COMM_WORLD,&ts);
 88:   TSSetDM(ts,user.da);
 89:   TSSetProblemType(ts,TS_NONLINEAR);
 90:   TSSetType(ts,TSARKIMEX);
 91:   TSSetIFunction(ts,NULL,IFunction,&user);
 92:   /*  TSSetIJacobian(ts,NULL,NULL,IJacobian,&user); */
 93:   TSSetApplicationContext(ts,&user);
 94:   TSSetTimeStep(ts,.005);
 95:   TSSetFromOptions(ts);
 96:   TSSetPostStep(ts,PostStep);
 97:   TSSolve(ts,x);

 99:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"fin_x",FILE_MODE_WRITE,&viewer);
100:   VecView(x,viewer);
101:   PetscViewerDestroy(&viewer);

103:   VecDestroy(&x);
104:   DMDestroy(&user.da);
105:   TSDestroy(&ts);
106:   PetscFinalize();
107:   return 0;
108: }

110: PetscErrorCode PostStep(TS ts)
111: {
112:   Vec          X;
113:   AppCtx      *user;
114:   PetscReal    t;
115:   PetscScalar  asum;

117:   TSGetApplicationContext(ts,&user);
118:   TSGetTime(ts,&t);
119:   TSGetSolution(ts,&X);
120:   /*
121:   if (t >= .2) {
122:     TSGetSolution(ts,&X);
123:     VecView(X,PETSC_VIEWER_BINARY_WORLD);
124:     exit(0);
125:      results in initial conditions after fault in binaryoutput
126:   }*/

128:   if ((t > user->tf) && (t < user->tcl)) user->Pmax = 0.0; /* A short-circuit that drives the electrical power output (Pmax*sin(delta)) to zero */
129:   else user->Pmax = user->Pmax_s;

131:   VecSum(X,&asum);
132:   PetscPrintf(PETSC_COMM_WORLD,"sum(p) at t = %f = %f\n",(double)t,(double)(asum));
133:   return 0;
134: }

136: PetscErrorCode ini_bou(Vec X,AppCtx* user)
137: {
138:   DM            cda;
139:   DMDACoor2d  **coors;
140:   PetscScalar **p;
141:   Vec           gc;
142:   PetscInt      M,N,Ir,J;
143:   PetscMPIInt   rank;

146:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
147:   DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
148:   user->dx = (user->xmax - user->xmin)/(M-1); user->dy = (user->ymax - user->ymin)/(N-1);
149:   DMGetCoordinateDM(user->da,&cda);
150:   DMGetCoordinates(user->da,&gc);
151:   DMDAVecGetArrayRead(cda,gc,&coors);
152:   DMDAVecGetArray(user->da,X,&p);

154:   /* Point mass at (mux,muy) */
155:   PetscPrintf(PETSC_COMM_WORLD,"Original user->mux = %f, user->muy = %f\n",user->mux,user->muy);
156:   DMDAGetLogicalCoordinate(user->da,user->mux,user->muy,0.0,&Ir,&J,NULL,&user->mux,&user->muy,NULL);
157:   user->PM_min = user->Pmax*PetscSinScalar(user->mux);
158:   PetscPrintf(PETSC_COMM_WORLD,"Corrected user->mux = %f, user->muy = %f user->PM_min = %f,user->dx = %f\n",user->mux,user->muy,user->PM_min,user->dx);
159:   if (Ir > -1 && J > -1) {
160:     p[J][Ir] = 1.0;
161:   }

163:   DMDAVecRestoreArrayRead(cda,gc,&coors);
164:   DMDAVecRestoreArray(user->da,X,&p);
165:   return 0;
166: }

168: /* First advection term */
169: PetscErrorCode adv1(PetscScalar **p,PetscScalar y,PetscInt i,PetscInt j,PetscInt M,PetscScalar *p1,AppCtx *user)
170: {
171:   PetscScalar f,fpos,fneg;
172:   f   =  (y - user->ws);
173:   fpos = PetscMax(f,0);
174:   fneg = PetscMin(f,0);
175:   if (user->st_width == 1) {
176:     *p1 = fpos*(p[j][i] - p[j][i-1])/user->dx + fneg*(p[j][i+1] - p[j][i])/user->dx;
177:   } else if (user->st_width == 2) {
178:     *p1 = fpos*(3*p[j][i] - 4*p[j][i-1] + p[j][i-2])/(2*user->dx) + fneg*(-p[j][i+2] + 4*p[j][i+1] - 3*p[j][i])/(2*user->dx);
179:   } else if (user->st_width == 3) {
180:     *p1 = fpos*(2*p[j][i+1] + 3*p[j][i] - 6*p[j][i-1] + p[j][i-2])/(6*user->dx) + fneg*(-p[j][i+2] + 6*p[j][i+1] - 3*p[j][i] - 2*p[j][i-1])/(6*user->dx);
181:   }
182:   /* *p1 = f*(p[j][i+1] - p[j][i-1])/user->dx;*/
183:   return 0;
184: }

186: /* Second advection term */
187: PetscErrorCode adv2(PetscScalar **p,PetscScalar x,PetscScalar y,PetscInt i,PetscInt j,PetscInt N,PetscScalar *p2,AppCtx *user)
188: {
189:   PetscScalar f,fpos,fneg;
190:   f   = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(x) - user->D*(y - user->ws));
191:   fpos = PetscMax(f,0);
192:   fneg = PetscMin(f,0);
193:   if (user->st_width == 1) {
194:     *p2 = fpos*(p[j][i] - p[j-1][i])/user->dy + fneg*(p[j+1][i] - p[j][i])/user->dy;
195:   } else if (user->st_width ==2) {
196:     *p2 = fpos*(3*p[j][i] - 4*p[j-1][i] + p[j-2][i])/(2*user->dy) + fneg*(-p[j+2][i] + 4*p[j+1][i] - 3*p[j][i])/(2*user->dy);
197:   } else if (user->st_width == 3) {
198:     *p2 = fpos*(2*p[j+1][i] + 3*p[j][i] - 6*p[j-1][i] + p[j-2][i])/(6*user->dy) + fneg*(-p[j+2][i] + 6*p[j+1][i] - 3*p[j][i] - 2*p[j-1][i])/(6*user->dy);
199:   }

201:   /* *p2 = f*(p[j+1][i] - p[j-1][i])/user->dy;*/
202:   return 0;
203: }

205: /* Diffusion term */
206: PetscErrorCode diffuse(PetscScalar **p,PetscInt i,PetscInt j,PetscReal t,PetscScalar *p_diff,AppCtx * user)
207: {
209:   if (user->st_width == 1) {
210:     *p_diff = user->disper_coe*((p[j-1][i] - 2*p[j][i] + p[j+1][i])/(user->dy*user->dy));
211:   } else if (user->st_width == 2) {
212:     *p_diff = user->disper_coe*((-p[j-2][i] + 16*p[j-1][i] - 30*p[j][i] + 16*p[j+1][i] - p[j+2][i])/(12.0*user->dy*user->dy));
213:   } else if (user->st_width == 3) {
214:     *p_diff = user->disper_coe*((2*p[j-3][i] - 27*p[j-2][i] + 270*p[j-1][i] - 490*p[j][i] + 270*p[j+1][i] - 27*p[j+2][i] + 2*p[j+3][i])/(180.0*user->dy*user->dy));
215:   }
216:   return 0;
217: }

219: PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
220: {
221:   AppCtx       *user   = (AppCtx*)ctx;
222:   DM            cda;
223:   DMDACoor2d  **coors;
224:   PetscScalar **p,**f,**pdot;
225:   PetscInt      i,j;
226:   PetscInt      xs,ys,xm,ym,M,N;
227:   Vec           localX,gc,localXdot;
228:   PetscScalar   p_adv1 = 0.0,p_adv2 = 0.0,p_diff = 0;
229:   PetscScalar   diffuse1,gamma;

232:   DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
233:   DMGetCoordinateDM(user->da,&cda);
234:   DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);

236:   DMGetLocalVector(user->da,&localX);
237:   DMGetLocalVector(user->da,&localXdot);

239:   DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
240:   DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
241:   DMGlobalToLocalBegin(user->da,Xdot,INSERT_VALUES,localXdot);
242:   DMGlobalToLocalEnd(user->da,Xdot,INSERT_VALUES,localXdot);

244:   DMGetCoordinatesLocal(user->da,&gc);

246:   DMDAVecGetArrayRead(cda,gc,&coors);
247:   DMDAVecGetArrayRead(user->da,localX,&p);
248:   DMDAVecGetArrayRead(user->da,localXdot,&pdot);
249:   DMDAVecGetArray(user->da,F,&f);

251:   gamma = user->D*user->ws/(2*user->H);
252:   diffuse1 = user->lambda*user->lambda*user->q/(user->lambda*gamma+1)*(1.0 - PetscExpScalar(-t*(gamma+1.0)/user->lambda));
253:   user->disper_coe = user->ws*user->ws/(4*user->H*user->H)*diffuse1;

255:   for (i=xs; i < xs+xm; i++) {
256:     for (j=ys; j < ys+ym; j++) {
257:       adv1(p,coors[j][i].y,i,j,M,&p_adv1,user);
258:       adv2(p,coors[j][i].x,coors[j][i].y,i,j,N,&p_adv2,user);
259:       diffuse(p,i,j,t,&p_diff,user);
260:       f[j][i] = -p_adv1 - p_adv2  + p_diff - pdot[j][i];
261:     }
262:   }
263:   DMDAVecRestoreArrayRead(user->da,localX,&p);
264:   DMDAVecRestoreArrayRead(user->da,localX,&pdot);
265:   DMRestoreLocalVector(user->da,&localX);
266:   DMRestoreLocalVector(user->da,&localXdot);
267:   DMDAVecRestoreArray(user->da,F,&f);
268:   DMDAVecRestoreArrayRead(cda,gc,&coors);

270:   return 0;
271: }

273: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ctx)
274: {
275:   AppCtx         *user=(AppCtx*)ctx;
276:   DM             cda;
277:   DMDACoor2d     **coors;
278:   PetscInt       i,j;
279:   PetscInt       xs,ys,xm,ym,M,N;
280:   Vec            gc;
281:   PetscScalar    val[5],xi,yi;
282:   MatStencil     row,col[5];
283:   PetscScalar    c1,c3,c5,c1pos,c1neg,c3pos,c3neg;

286:   DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
287:   DMGetCoordinateDM(user->da,&cda);
288:   DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);

290:   DMGetCoordinatesLocal(user->da,&gc);
291:   DMDAVecGetArrayRead(cda,gc,&coors);
292:   for (i=xs; i < xs+xm; i++) {
293:     for (j=ys; j < ys+ym; j++) {
294:       PetscInt nc = 0;
295:       xi = coors[j][i].x; yi = coors[j][i].y;
296:       row.i = i; row.j = j;
297:       c1        = (yi-user->ws)/user->dx;
298:       c1pos    = PetscMax(c1,0);
299:       c1neg    = PetscMin(c1,0);
300:       c3        = (user->ws/(2.0*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(xi) - user->D*(yi - user->ws))/user->dy;
301:       c3pos    = PetscMax(c3,0);
302:       c3neg    = PetscMin(c3,0);
303:       c5        = (PetscPowScalar((user->lambda*user->ws)/(2*user->H),2)*user->q*(1.0-PetscExpScalar(-t/user->lambda)))/(user->dy*user->dy);
304:       col[nc].i = i-1; col[nc].j = j;   val[nc++] = c1pos;
305:       col[nc].i = i+1; col[nc].j = j;   val[nc++] = -c1neg;
306:       col[nc].i = i;   col[nc].j = j-1; val[nc++] = c3pos + c5;
307:       col[nc].i = i;   col[nc].j = j+1; val[nc++] = -c3neg + c5;
308:       col[nc].i = i;   col[nc].j = j;   val[nc++] = -c1pos + c1neg -c3pos + c3neg -2*c5 -a;
309:       MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES);
310:     }
311:   }
312:   DMDAVecRestoreArrayRead(cda,gc,&coors);

314:   MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
315:   MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
316:   if (J != Jpre) {
317:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
318:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
319:   }
320:   return 0;
321: }

323: PetscErrorCode Parameter_settings(AppCtx *user)
324: {
325:   PetscBool flg;

328:   /* Set default parameters */
329:   user->ws     = 1.0;
330:   user->H      = 5.0;
331:   user->D      = 0.0;
332:   user->Pmax = user->Pmax_s  = 2.1;
333:   user->PM_min = 1.0;
334:   user->lambda = 0.1;
335:   user->q      = 1.0;
336:   user->mux    = PetscAsinScalar(user->PM_min/user->Pmax);
337:   user->sigmax = 0.1;
338:   user->sigmay = 0.1;
339:   user->rho    = 0.0;
340:   user->xmin   = -PETSC_PI;
341:   user->xmax   = PETSC_PI;
342:   user->bx     = DM_BOUNDARY_PERIODIC;
343:   user->by     = DM_BOUNDARY_GHOSTED;
344:   user->tf = user->tcl = -1;
345:   user->ymin   = -2.0;
346:   user->ymax   = 2.0;
347:   user->st_width = 1;

349:   PetscOptionsGetScalar(NULL,NULL,"-ws",&user->ws,&flg);
350:   PetscOptionsGetScalar(NULL,NULL,"-Inertia",&user->H,&flg);
351:   PetscOptionsGetScalar(NULL,NULL,"-D",&user->D,&flg);
352:   PetscOptionsGetScalar(NULL,NULL,"-Pmax",&user->Pmax,&flg);
353:   PetscOptionsGetScalar(NULL,NULL,"-PM_min",&user->PM_min,&flg);
354:   PetscOptionsGetScalar(NULL,NULL,"-lambda",&user->lambda,&flg);
355:   PetscOptionsGetScalar(NULL,NULL,"-q",&user->q,&flg);
356:   PetscOptionsGetScalar(NULL,NULL,"-mux",&user->mux,&flg);
357:   PetscOptionsGetScalar(NULL,NULL,"-muy",&user->muy,&flg);
358:   if (flg == 0) user->muy = user->ws;
359:   PetscOptionsGetScalar(NULL,NULL,"-xmin",&user->xmin,&flg);
360:   PetscOptionsGetScalar(NULL,NULL,"-xmax",&user->xmax,&flg);
361:   PetscOptionsGetScalar(NULL,NULL,"-ymin",&user->ymin,&flg);
362:   PetscOptionsGetScalar(NULL,NULL,"-ymax",&user->ymax,&flg);
363:   PetscOptionsGetInt(NULL,NULL,"-stencil_width",&user->st_width,&flg);
364:   PetscOptionsGetEnum(NULL,NULL,"-bx",DMBoundaryTypes,(PetscEnum*)&user->bx,&flg);
365:   PetscOptionsGetEnum(NULL,NULL,"-by",DMBoundaryTypes,(PetscEnum*)&user->by,&flg);
366:   PetscOptionsGetReal(NULL,NULL,"-tf",&user->tf,&flg);
367:   PetscOptionsGetReal(NULL,NULL,"-tcl",&user->tcl,&flg);
368:   return 0;
369: }

371: /*TEST

373:    build:
374:       requires: !complex x

376:    test:
377:       args: -ts_max_steps 1
378:       localrunfiles: petscopt_ex8
379:       timeoutfactor: 3

381: TEST*/