Date: 2022-03-04T17:39:43+00:00

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: {
     62:   Vec            x;  /* Solution vector */
     63:   TS             ts;   /* Time-stepping context */
     64:   AppCtx         user; /* Application context */
     65:   PetscViewer    viewer;

     67:   PetscInitialize(&argc,&argv,"petscopt_ex8", help);if (ierr) return ierr;

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

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

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

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

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

    104:   VecDestroy(&x);
    105:   DMDestroy(&user.da);
    106:   TSDestroy(&ts);
    107:   PetscFinalize();
    108:   return ierr;
    109: }

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

    120:   TSGetApplicationContext(ts,&user);
    121:   TSGetTime(ts,&t);
    122:   TSGetSolution(ts,&X);
    123:   /*
    124:   if (t >= .2) {
    125:     TSGetSolution(ts,&X);
    126:     VecView(X,PETSC_VIEWER_BINARY_WORLD);
    127:     exit(0);
    128:      results in initial conditions after fault in binaryoutput
    129:   }*/

    131:   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 */
    132:   else user->Pmax = user->Pmax_s;

    134:   VecSum(X,&asum);
    135:   PetscPrintf(PETSC_COMM_WORLD,"sum(p) at t = %f = %f\n",(double)t,(double)(asum));
    136:   return(0);
    137: }

    139: PetscErrorCode ini_bou(Vec X,AppCtx* user)
    140: {
    142:   DM             cda;
    143:   DMDACoor2d     **coors;
    144:   PetscScalar    **p;
    145:   Vec            gc;
    146:   PetscInt       M,N,Ir,J;
    147:   PetscMPIInt    rank;

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

    158:   /* Point mass at (mux,muy) */
    159:   PetscPrintf(PETSC_COMM_WORLD,"Original user->mux = %f, user->muy = %f\n",user->mux,user->muy);
    160:   DMDAGetLogicalCoordinate(user->da,user->mux,user->muy,0.0,&Ir,&J,NULL,&user->mux,&user->muy,NULL);
    161:   user->PM_min = user->Pmax*PetscSinScalar(user->mux);
    162:   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);
    163:   if (Ir > -1 && J > -1) {
    164:     p[J][Ir] = 1.0;
    165:   }

    167:   DMDAVecRestoreArrayRead(cda,gc,&coors);
    168:   DMDAVecRestoreArray(user->da,X,&p);
    169:   return(0);
    170: }

    172: /* First advection term */
    173: PetscErrorCode adv1(PetscScalar **p,PetscScalar y,PetscInt i,PetscInt j,PetscInt M,PetscScalar *p1,AppCtx *user)
    174: {
    175:   PetscScalar f,fpos,fneg;
    177:   f   =  (y - user->ws);
    178:   fpos = PetscMax(f,0);
    179:   fneg = PetscMin(f,0);
    180:   if (user->st_width == 1) {
    181:     *p1 = fpos*(p[j][i] - p[j][i-1])/user->dx + fneg*(p[j][i+1] - p[j][i])/user->dx;
    182:   } else if (user->st_width == 2) {
    183:     *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);
    184:   } else if (user->st_width == 3) {
    185:     *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);
    186:   }
    187:   /* *p1 = f*(p[j][i+1] - p[j][i-1])/user->dx;*/
    188:   return(0);
    189: }

    191: /* Second advection term */
    192: PetscErrorCode adv2(PetscScalar **p,PetscScalar x,PetscScalar y,PetscInt i,PetscInt j,PetscInt N,PetscScalar *p2,AppCtx *user)
    193: {
    194:   PetscScalar f,fpos,fneg;
    196:   f   = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(x) - user->D*(y - user->ws));
    197:   fpos = PetscMax(f,0);
    198:   fneg = PetscMin(f,0);
    199:   if (user->st_width == 1) {
    200:     *p2 = fpos*(p[j][i] - p[j-1][i])/user->dy + fneg*(p[j+1][i] - p[j][i])/user->dy;
    201:   } else if (user->st_width ==2) {
    202:     *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);
    203:   } else if (user->st_width == 3) {
    204:     *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);
    205:   }

    207:   /* *p2 = f*(p[j+1][i] - p[j-1][i])/user->dy;*/
    208:   return(0);
    209: }

    211: /* Diffusion term */
    212: PetscErrorCode diffuse(PetscScalar **p,PetscInt i,PetscInt j,PetscReal t,PetscScalar *p_diff,AppCtx * user)
    213: {
    215:   if (user->st_width == 1) {
    216:     *p_diff = user->disper_coe*((p[j-1][i] - 2*p[j][i] + p[j+1][i])/(user->dy*user->dy));
    217:   } else if (user->st_width == 2) {
    218:     *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));
    219:   } else if (user->st_width == 3) {
    220:     *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));
    221:   }
    222:   return(0);
    223: }

    225: PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
    226: {
    228:   AppCtx         *user=(AppCtx*)ctx;
    229:   DM             cda;
    230:   DMDACoor2d     **coors;
    231:   PetscScalar    **p,**f,**pdot;
    232:   PetscInt       i,j;
    233:   PetscInt       xs,ys,xm,ym,M,N;
    234:   Vec            localX,gc,localXdot;
    235:   PetscScalar    p_adv1 = 0.0,p_adv2 = 0.0,p_diff = 0;
    236:   PetscScalar    diffuse1,gamma;

    239:   DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
    240:   DMGetCoordinateDM(user->da,&cda);
    241:   DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);

    243:   DMGetLocalVector(user->da,&localX);
    244:   DMGetLocalVector(user->da,&localXdot);

    246:   DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
    247:   DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
    248:   DMGlobalToLocalBegin(user->da,Xdot,INSERT_VALUES,localXdot);
    249:   DMGlobalToLocalEnd(user->da,Xdot,INSERT_VALUES,localXdot);

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

    253:   DMDAVecGetArrayRead(cda,gc,&coors);
    254:   DMDAVecGetArrayRead(user->da,localX,&p);
    255:   DMDAVecGetArrayRead(user->da,localXdot,&pdot);
    256:   DMDAVecGetArray(user->da,F,&f);

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

    262:   for (i=xs; i < xs+xm; i++) {
    263:     for (j=ys; j < ys+ym; j++) {
    264:       adv1(p,coors[j][i].y,i,j,M,&p_adv1,user);
    265:       adv2(p,coors[j][i].x,coors[j][i].y,i,j,N,&p_adv2,user);
    266:       diffuse(p,i,j,t,&p_diff,user);
    267:       f[j][i] = -p_adv1 - p_adv2  + p_diff - pdot[j][i];
    268:     }
    269:   }
    270:   DMDAVecRestoreArrayRead(user->da,localX,&p);
    271:   DMDAVecRestoreArrayRead(user->da,localX,&pdot);
    272:   DMRestoreLocalVector(user->da,&localX);
    273:   DMRestoreLocalVector(user->da,&localXdot);
    274:   DMDAVecRestoreArray(user->da,F,&f);
    275:   DMDAVecRestoreArrayRead(cda,gc,&coors);

    277:   return(0);
    278: }

    280: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ctx)
    281: {
    283:   AppCtx         *user=(AppCtx*)ctx;
    284:   DM             cda;
    285:   DMDACoor2d     **coors;
    286:   PetscInt       i,j;
    287:   PetscInt       xs,ys,xm,ym,M,N;
    288:   Vec            gc;
    289:   PetscScalar    val[5],xi,yi;
    290:   MatStencil     row,col[5];
    291:   PetscScalar    c1,c3,c5,c1pos,c1neg,c3pos,c3neg;

    294:   DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
    295:   DMGetCoordinateDM(user->da,&cda);
    296:   DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);

    298:   DMGetCoordinatesLocal(user->da,&gc);
    299:   DMDAVecGetArrayRead(cda,gc,&coors);
    300:   for (i=xs; i < xs+xm; i++) {
    301:     for (j=ys; j < ys+ym; j++) {
    302:       PetscInt nc = 0;
    303:       xi = coors[j][i].x; yi = coors[j][i].y;
    304:       row.i = i; row.j = j;
    305:       c1        = (yi-user->ws)/user->dx;
    306:       c1pos    = PetscMax(c1,0);
    307:       c1neg    = PetscMin(c1,0);
    308:       c3        = (user->ws/(2.0*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(xi) - user->D*(yi - user->ws))/user->dy;
    309:       c3pos    = PetscMax(c3,0);
    310:       c3neg    = PetscMin(c3,0);
    311:       c5        = (PetscPowScalar((user->lambda*user->ws)/(2*user->H),2)*user->q*(1.0-PetscExpScalar(-t/user->lambda)))/(user->dy*user->dy);
    312:       col[nc].i = i-1; col[nc].j = j;   val[nc++] = c1pos;
    313:       col[nc].i = i+1; col[nc].j = j;   val[nc++] = -c1neg;
    314:       col[nc].i = i;   col[nc].j = j-1; val[nc++] = c3pos + c5;
    315:       col[nc].i = i;   col[nc].j = j+1; val[nc++] = -c3neg + c5;
    316:       col[nc].i = i;   col[nc].j = j;   val[nc++] = -c1pos + c1neg -c3pos + c3neg -2*c5 -a;
    317:       MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES);
    318:     }
    319:   }
    320:   DMDAVecRestoreArrayRead(cda,gc,&coors);

    322:    MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
    323:   MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
    324:   if (J != Jpre) {
    325:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    326:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
    327:   }
    328:   return(0);
    329: }

    331: PetscErrorCode Parameter_settings(AppCtx *user)
    332: {
    334:   PetscBool      flg;

    338:   /* Set default parameters */
    339:   user->ws     = 1.0;
    340:   user->H      = 5.0;
    341:   user->D      = 0.0;
    342:   user->Pmax = user->Pmax_s  = 2.1;
    343:   user->PM_min = 1.0;
    344:   user->lambda = 0.1;
    345:   user->q      = 1.0;
    346:   user->mux    = PetscAsinScalar(user->PM_min/user->Pmax);
    347:   user->sigmax = 0.1;
    348:   user->sigmay = 0.1;
    349:   user->rho    = 0.0;
    350:   user->xmin   = -PETSC_PI;
    351:   user->xmax   = PETSC_PI;
    352:   user->bx     = DM_BOUNDARY_PERIODIC;
    353:   user->by     = DM_BOUNDARY_GHOSTED;
    354:   user->tf = user->tcl = -1;
    355:   user->ymin   = -2.0;
    356:   user->ymax   = 2.0;
    357:   user->st_width = 1;

    359:   PetscOptionsGetScalar(NULL,NULL,"-ws",&user->ws,&flg);
    360:   PetscOptionsGetScalar(NULL,NULL,"-Inertia",&user->H,&flg);
    361:   PetscOptionsGetScalar(NULL,NULL,"-D",&user->D,&flg);
    362:   PetscOptionsGetScalar(NULL,NULL,"-Pmax",&user->Pmax,&flg);
    363:   PetscOptionsGetScalar(NULL,NULL,"-PM_min",&user->PM_min,&flg);
    364:   PetscOptionsGetScalar(NULL,NULL,"-lambda",&user->lambda,&flg);
    365:   PetscOptionsGetScalar(NULL,NULL,"-q",&user->q,&flg);
    366:   PetscOptionsGetScalar(NULL,NULL,"-mux",&user->mux,&flg);
    367:   PetscOptionsGetScalar(NULL,NULL,"-muy",&user->muy,&flg);
    368:   if (flg == 0) {
    369:     user->muy = user->ws;
    370:   }
    371:   PetscOptionsGetScalar(NULL,NULL,"-xmin",&user->xmin,&flg);
    372:   PetscOptionsGetScalar(NULL,NULL,"-xmax",&user->xmax,&flg);
    373:   PetscOptionsGetScalar(NULL,NULL,"-ymin",&user->ymin,&flg);
    374:   PetscOptionsGetScalar(NULL,NULL,"-ymax",&user->ymax,&flg);
    375:   PetscOptionsGetInt(NULL,NULL,"-stencil_width",&user->st_width,&flg);
    376:   PetscOptionsGetEnum(NULL,NULL,"-bx",DMBoundaryTypes,(PetscEnum*)&user->bx,&flg);
    377:   PetscOptionsGetEnum(NULL,NULL,"-by",DMBoundaryTypes,(PetscEnum*)&user->by,&flg);
    378:   PetscOptionsGetReal(NULL,NULL,"-tf",&user->tf,&flg);
    379:   PetscOptionsGetReal(NULL,NULL,"-tcl",&user->tcl,&flg);
    380:   return(0);
    381: }

    383: /*TEST

    385:    build:
    386:       requires: !complex x

    388:    test:
    389:       args: -ts_max_steps 1
    390:       localrunfiles: petscopt_ex8
    391:       timeoutfactor: 3

    393: TEST*/