Actual source code: ex42.c

      1: static char help[] = "Meinhard't activator-inhibitor model to test TS domain error feature.\n";

      3: /*
      4:    The activator-inhibitor on a line is described by the PDE:

      6:    da/dt = \alpha a^2 / (1 + \beta h) + \rho_a - \mu_a a + D_a d^2 a/ dx^2
      7:    dh/dt = \alpha a^2 + \rho_h - \mu_h h + D_h d^2 h/ dx^2

      9:    The PDE part will be solve by finite-difference on the line of cells.
     10:  */

     12: #include <petscts.h>

     14: typedef struct {
     15:   PetscInt  nb_cells;
     16:   PetscReal alpha;
     17:   PetscReal beta;
     18:   PetscReal rho_a;
     19:   PetscReal rho_h;
     20:   PetscReal mu_a;
     21:   PetscReal mu_h;
     22:   PetscReal D_a;
     23:   PetscReal D_h;
     24: } AppCtx;

     26: PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec X, Vec DXDT, void* ptr)
     27: {
     28:   AppCtx*           user = (AppCtx*)ptr;
     29:   PetscInt          nb_cells, i;
     30:   PetscReal         alpha, beta;
     31:   PetscReal         rho_a, mu_a, D_a;
     32:   PetscReal         rho_h, mu_h, D_h;
     33:   PetscReal         a, h, da, dh, d2a, d2h;
     34:   PetscScalar       *dxdt;
     35:   const PetscScalar *x;

     37:   nb_cells = user->nb_cells;
     38:   alpha    = user->alpha;
     39:   beta     = user->beta;
     40:   rho_a    = user->rho_a;
     41:   mu_a     = user->mu_a;
     42:   D_a      = user->D_a;
     43:   rho_h    = user->rho_h;
     44:   mu_h     = user->mu_h;
     45:   D_h      = user->D_h;

     47:   VecGetArrayRead(X, &x);
     48:   VecGetArray(DXDT, &dxdt);

     50:   for (i = 0 ; i < nb_cells ; i++) {
     51:     a = x[2*i];
     52:     h = x[2*i+1];
     53:     // Reaction:
     54:     da = alpha * a*a / (1. + beta * h) + rho_a - mu_a * a;
     55:     dh = alpha * a*a + rho_h - mu_h*h;
     56:     // Diffusion:
     57:     d2a = d2h = 0.;
     58:     if (i > 0) {
     59:       d2a += (x[2*(i-1)] - a);
     60:       d2h += (x[2*(i-1)+1] - h);
     61:     }
     62:     if (i < nb_cells-1) {
     63:       d2a += (x[2*(i+1)] - a);
     64:       d2h += (x[2*(i+1)+1] - h);
     65:     }
     66:     dxdt[2*i] = da + D_a*d2a;
     67:     dxdt[2*i+1] = dh + D_h*d2h;
     68:   }
     69:   VecRestoreArray(DXDT, &dxdt);
     70:   VecRestoreArrayRead(X, &x);
     71:   return 0;
     72: }

     74: PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec X, Mat J, Mat B, void *ptr)
     75: {
     76:   AppCtx            *user = (AppCtx*)ptr;
     77:   PetscInt          nb_cells, i, idx;
     78:   PetscReal         alpha, beta;
     79:   PetscReal         mu_a, D_a;
     80:   PetscReal         mu_h, D_h;
     81:   PetscReal         a, h;
     82:   const PetscScalar *x;
     83:   PetscScalar       va[4], vh[4];
     84:   PetscInt          ca[4], ch[4], rowa, rowh;

     86:   nb_cells = user->nb_cells;
     87:   alpha    = user->alpha;
     88:   beta     = user->beta;
     89:   mu_a     = user->mu_a;
     90:   D_a      = user->D_a;
     91:   mu_h     = user->mu_h;
     92:   D_h      = user->D_h;

     94:   VecGetArrayRead(X, &x);
     95:   for (i = 0; i < nb_cells ; ++i) {
     96:     rowa = 2*i;
     97:     rowh = 2*i+1;
     98:     a = x[2*i];
     99:     h = x[2*i+1];
    100:     ca[0] = ch[1] = 2*i;
    101:     va[0] = 2*alpha*a / (1.+beta*h) - mu_a;
    102:     vh[1] = 2*alpha*a;
    103:     ca[1] = ch[0] = 2*i+1;
    104:     va[1] = -beta*alpha*a*a / ((1.+beta*h)*(1.+beta*h));
    105:     vh[0] = -mu_h;
    106:     idx = 2;
    107:     if (i > 0) {
    108:       ca[idx] = 2*(i-1);
    109:       ch[idx] = 2*(i-1)+1;
    110:       va[idx] = D_a;
    111:       vh[idx] = D_h;
    112:       va[0] -= D_a;
    113:       vh[0] -= D_h;
    114:       idx++;
    115:     }
    116:     if (i < nb_cells-1) {
    117:       ca[idx] = 2*(i+1);
    118:       ch[idx] = 2*(i+1)+1;
    119:       va[idx] = D_a;
    120:       vh[idx] = D_h;
    121:       va[0] -= D_a;
    122:       vh[0] -= D_h;
    123:       idx++;
    124:     }
    125:     MatSetValues(B, 1, &rowa, idx, ca, va, INSERT_VALUES);
    126:     MatSetValues(B, 1, &rowh, idx, ch, vh, INSERT_VALUES);
    127:   }
    128:   VecRestoreArrayRead(X, &x);
    129:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    130:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    131:   if (J != B) {
    132:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    133:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
    134:   }
    135:   return 0;
    136: }

    138: PetscErrorCode DomainErrorFunction(TS ts, PetscReal t, Vec Y, PetscBool *accept)
    139: {
    140:   AppCtx            *user;
    141:   PetscReal         dt;
    142:   const PetscScalar *x;
    143:   PetscInt          nb_cells, i;

    145:   TSGetApplicationContext(ts, &user);
    146:   nb_cells = user->nb_cells;
    147:   VecGetArrayRead(Y, &x);
    148:   for (i = 0 ; i < 2*nb_cells ; ++i) {
    149:     if (PetscRealPart(x[i]) < 0) {
    150:       TSGetTimeStep(ts, &dt);
    151:       PetscPrintf(PETSC_COMM_WORLD, " ** Domain Error at time %g\n", (double)t);
    152:       *accept = PETSC_FALSE;
    153:       break;
    154:     }
    155:   }
    156:   VecRestoreArrayRead(Y, &x);
    157:   return 0;
    158: }

    160: PetscErrorCode FormInitialState(Vec X, AppCtx* user)
    161: {
    162:   PetscRandom    R;

    164:   PetscRandomCreate(PETSC_COMM_WORLD, &R);
    165:   PetscRandomSetFromOptions(R);
    166:   PetscRandomSetInterval(R, 0., 10.);

    168:   /*
    169:    * Initialize the state vector
    170:    */
    171:   VecSetRandom(X, R);
    172:   PetscRandomDestroy(&R);
    173:   return 0;
    174: }

    176: PetscErrorCode PrintSolution(Vec X, AppCtx *user)
    177: {
    178:   const PetscScalar *x;
    179:   PetscInt          i;
    180:   PetscInt          nb_cells = user->nb_cells;

    182:   VecGetArrayRead(X, &x);
    183:   PetscPrintf(PETSC_COMM_WORLD, "Activator,Inhibitor\n");
    184:   for (i = 0 ; i < nb_cells ; i++) {
    185:     PetscPrintf(PETSC_COMM_WORLD, "%5.6e,%5.6e\n", (double)x[2*i], (double)x[2*i+1]);
    186:   }
    187:   VecRestoreArrayRead(X, &x);
    188:   return 0;
    189: }

    191: int main(int argc, char **argv)
    192: {
    193:   TS             ts;       /* time-stepping context */
    194:   Vec            x;       /* State vector */
    195:   Mat            J; /* Jacobian matrix */
    196:   AppCtx         user; /* user-defined context */
    198:   PetscReal      ftime;
    199:   PetscInt       its;
    200:   PetscMPIInt    size;

    202:   PetscInitialize(&argc, &argv, NULL, help);
    203:   MPI_Comm_size(PETSC_COMM_WORLD, &size);

    206:   /*
    207:    * Allow user to set the grid dimensions and the equations parameters
    208:    */

    210:   user.nb_cells = 50;
    211:   user.alpha = 10.;
    212:   user.beta = 1.;
    213:   user.rho_a = 1.;
    214:   user.rho_h = 2.;
    215:   user.mu_a = 2.;
    216:   user.mu_h = 3.;
    217:   user.D_a = 0.;
    218:   user.D_h = 30.;

    220:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Problem settings", "PROBLEM");
    221:   PetscOptionsInt("-nb_cells", "Number of cells", "ex42.c",user.nb_cells, &user.nb_cells,NULL);
    222:   PetscOptionsReal("-alpha", "Autocatalysis factor", "ex42.c",user.alpha, &user.alpha,NULL);
    223:   PetscOptionsReal("-beta", "Inhibition factor", "ex42.c",user.beta, &user.beta,NULL);
    224:   PetscOptionsReal("-rho_a", "Default production of the activator", "ex42.c",user.rho_a, &user.rho_a,NULL);
    225:   PetscOptionsReal("-mu_a", "Degradation rate of the activator", "ex42.c",user.mu_a, &user.mu_a,NULL);
    226:   PetscOptionsReal("-D_a", "Diffusion rate of the activator", "ex42.c",user.D_a, &user.D_a,NULL);
    227:   PetscOptionsReal("-rho_h", "Default production of the inhibitor", "ex42.c",user.rho_h, &user.rho_h,NULL);
    228:   PetscOptionsReal("-mu_h", "Degradation rate of the inhibitor", "ex42.c",user.mu_h, &user.mu_h,NULL);
    229:   PetscOptionsReal("-D_h", "Diffusion rate of the inhibitor", "ex42.c",user.D_h, &user.D_h,NULL);
    230:   PetscOptionsEnd();

    232:   PetscPrintf(PETSC_COMM_WORLD, "nb_cells: %D\n", user.nb_cells);
    233:   PetscPrintf(PETSC_COMM_WORLD, "alpha: %5.5g\n", (double)user.alpha);
    234:   PetscPrintf(PETSC_COMM_WORLD, "beta:  %5.5g\n", (double)user.beta);
    235:   PetscPrintf(PETSC_COMM_WORLD, "rho_a: %5.5g\n", (double)user.rho_a);
    236:   PetscPrintf(PETSC_COMM_WORLD, "mu_a:  %5.5g\n", (double)user.mu_a);
    237:   PetscPrintf(PETSC_COMM_WORLD, "D_a:   %5.5g\n", (double)user.D_a);
    238:   PetscPrintf(PETSC_COMM_WORLD, "rho_h: %5.5g\n", (double)user.rho_h);
    239:   PetscPrintf(PETSC_COMM_WORLD, "mu_h:  %5.5g\n", (double)user.mu_h);
    240:   PetscPrintf(PETSC_COMM_WORLD, "D_h:   %5.5g\n", (double)user.D_h);

    242:   /*
    243:    * Create vector to hold the solution
    244:    */
    245:   VecCreateSeq(PETSC_COMM_WORLD, 2*user.nb_cells, &x);

    247:   /*
    248:    * Create time-stepper context
    249:    */
    250:   TSCreate(PETSC_COMM_WORLD, &ts);
    251:   TSSetProblemType(ts, TS_NONLINEAR);

    253:   /*
    254:    * Tell the time-stepper context where to compute the solution
    255:    */
    256:   TSSetSolution(ts, x);

    258:   /*
    259:    * Allocate the jacobian matrix
    260:    */
    261:   MatCreateSeqAIJ(PETSC_COMM_WORLD, 2*user.nb_cells, 2*user.nb_cells, 4, 0, &J);

    263:   /*
    264:    * Provide the call-back for the non-linear function we are evaluating.
    265:    */
    266:   TSSetRHSFunction(ts, NULL, RHSFunction, &user);

    268:   /*
    269:    * Set the Jacobian matrix and the function user to compute Jacobians
    270:    */
    271:   TSSetRHSJacobian(ts, J, J, RHSJacobian, &user);

    273:   /*
    274:    * Set the function checking the domain
    275:    */
    276:   TSSetFunctionDomainError(ts, &DomainErrorFunction);

    278:   /*
    279:    * Initialize the problem with random values
    280:    */
    281:   FormInitialState(x, &user);

    283:   /*
    284:    * Read the solver type from options
    285:    */
    286:   TSSetType(ts, TSPSEUDO);

    288:   /*
    289:    * Set a large number of timesteps and final duration time to insure
    290:    * convergenge to steady state
    291:    */
    292:   TSSetMaxSteps(ts, 2147483647);
    293:   TSSetMaxTime(ts, 1.e12);
    294:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);

    296:   /*
    297:    * Set a larger number of potential errors
    298:    */
    299:   TSSetMaxStepRejections(ts, 50);

    301:   /*
    302:    * Also start with a very small dt
    303:    */
    304:   TSSetTimeStep(ts, 0.05);

    306:   /*
    307:    * Set a larger time step increment
    308:    */
    309:   TSPseudoSetTimeStepIncrement(ts, 1.5);

    311:   /*
    312:    * Let the user personalise TS
    313:    */
    314:   TSSetFromOptions(ts);

    316:   /*
    317:    * Set the context for the time stepper
    318:    */
    319:   TSSetApplicationContext(ts, &user);

    321:   /*
    322:    * Setup the time stepper, ready for evaluation
    323:    */
    324:   TSSetUp(ts);

    326:   /*
    327:    * Perform the solve.
    328:    */
    329:   TSSolve(ts, x);
    330:   TSGetSolveTime(ts, &ftime);
    331:   TSGetStepNumber(ts,&its);
    332:   PetscPrintf(PETSC_COMM_WORLD, "Number of time steps = %D, final time: %4.2e\nResult:\n\n", its, (double)ftime);
    333:   PrintSolution(x, &user);

    335:   /*
    336:    * Free the data structures
    337:    */
    338:   VecDestroy(&x);
    339:   MatDestroy(&J);
    340:   TSDestroy(&ts);
    341:   PetscFinalize();
    342:   return 0;
    343: }

    345: /*TEST
    346:     build:
    347:       requires: !single !complex

    349:     test:
    350:       args: -ts_max_steps 8
    351:       output_file: output/ex42.out

    353: TEST*/