Actual source code: ex1.c

      1: static char help[] = "An example of hybrid system using TS event.\n";

      3: /*
      4:   The dynamics is described by the ODE
      5:                   u_t = A_i u

      7:   where A_1 = [ 1  -100
      8:                 10  1  ],
      9:         A_2 = [ 1    10
     10:                -100  1 ].
     11:   The index i changes from 1 to 2 when u[1]=2.75u[0] and from 2 to 1 when u[1]=0.36u[0].
     12:   Initially u=[0 1]^T and i=1.

     14:   Reference:
     15:   I. A. Hiskens, M.A. Pai, Trajectory Sensitivity Analysis of Hybrid Systems, IEEE Transactions on Circuits and Systems, Vol 47, No 2, February 2000
     16: */

     18: #include <petscts.h>

     20: typedef struct {
     21:   PetscScalar lambda1;
     22:   PetscScalar lambda2;
     23:   PetscInt    mode; /* mode flag*/
     24: } AppCtx;

     26: PetscErrorCode EventFunction(TS ts, PetscReal t, Vec U, PetscReal *fvalue, void *ctx)
     27: {
     28:   AppCtx            *actx = (AppCtx *)ctx;
     29:   const PetscScalar *u;

     31:   PetscFunctionBegin;
     32:   PetscCall(VecGetArrayRead(U, &u));
     33:   if (actx->mode == 1) {
     34:     fvalue[0] = PetscRealPart(u[1] - actx->lambda1 * u[0]);
     35:   } else if (actx->mode == 2) {
     36:     fvalue[0] = PetscRealPart(u[1] - actx->lambda2 * u[0]);
     37:   }
     38:   PetscCall(VecRestoreArrayRead(U, &u));
     39:   PetscFunctionReturn(PETSC_SUCCESS);
     40: }

     42: PetscErrorCode PostEventFunction(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec U, PetscBool forwardsolve, void *ctx)
     43: {
     44:   AppCtx *actx = (AppCtx *)ctx;

     46:   PetscFunctionBegin;
     47:   if (actx->mode == 1) {
     48:     actx->mode = 2;
     49:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Change from mode 1 to 2 at t = %f \n", (double)t));
     50:   } else if (actx->mode == 2) {
     51:     actx->mode = 1;
     52:     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Change from mode 2 to 1 at t = %f \n", (double)t));
     53:   }
     54:   PetscFunctionReturn(PETSC_SUCCESS);
     55: }

     57: /*
     58:      Defines the ODE passed to the ODE solver
     59: */
     60: static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, void *ctx)
     61: {
     62:   AppCtx            *actx = (AppCtx *)ctx;
     63:   PetscScalar       *f;
     64:   const PetscScalar *u, *udot;

     66:   PetscFunctionBegin;
     67:   /*  The next three lines allow us to access the entries of the vectors directly */
     68:   PetscCall(VecGetArrayRead(U, &u));
     69:   PetscCall(VecGetArrayRead(Udot, &udot));
     70:   PetscCall(VecGetArray(F, &f));

     72:   if (actx->mode == 1) {
     73:     f[0] = udot[0] - u[0] + 100 * u[1];
     74:     f[1] = udot[1] - 10 * u[0] - u[1];
     75:   } else if (actx->mode == 2) {
     76:     f[0] = udot[0] - u[0] - 10 * u[1];
     77:     f[1] = udot[1] + 100 * u[0] - u[1];
     78:   }

     80:   PetscCall(VecRestoreArrayRead(U, &u));
     81:   PetscCall(VecRestoreArrayRead(Udot, &udot));
     82:   PetscCall(VecRestoreArray(F, &f));
     83:   PetscFunctionReturn(PETSC_SUCCESS);
     84: }

     86: /*
     87:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
     88: */
     89: static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, void *ctx)
     90: {
     91:   AppCtx            *actx     = (AppCtx *)ctx;
     92:   PetscInt           rowcol[] = {0, 1};
     93:   PetscScalar        J[2][2];
     94:   const PetscScalar *u, *udot;

     96:   PetscFunctionBegin;
     97:   PetscCall(VecGetArrayRead(U, &u));
     98:   PetscCall(VecGetArrayRead(Udot, &udot));

    100:   if (actx->mode == 1) {
    101:     J[0][0] = a - 1;
    102:     J[0][1] = 100;
    103:     J[1][0] = -10;
    104:     J[1][1] = a - 1;
    105:   } else if (actx->mode == 2) {
    106:     J[0][0] = a - 1;
    107:     J[0][1] = -10;
    108:     J[1][0] = 100;
    109:     J[1][1] = a - 1;
    110:   }
    111:   PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));

    113:   PetscCall(VecRestoreArrayRead(U, &u));
    114:   PetscCall(VecRestoreArrayRead(Udot, &udot));

    116:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    117:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
    118:   if (A != B) {
    119:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    120:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    121:   }
    122:   PetscFunctionReturn(PETSC_SUCCESS);
    123: }

    125: int main(int argc, char **argv)
    126: {
    127:   TS           ts; /* ODE integrator */
    128:   Vec          U;  /* solution will be stored here */
    129:   Mat          A;  /* Jacobian matrix */
    130:   PetscMPIInt  size;
    131:   PetscInt     n = 2;
    132:   PetscScalar *u;
    133:   AppCtx       app;
    134:   PetscInt     direction[1];
    135:   PetscBool    terminate[1];

    137:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    138:      Initialize program
    139:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    140:   PetscFunctionBeginUser;
    141:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
    142:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
    143:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");
    144:   app.mode    = 1;
    145:   app.lambda1 = 2.75;
    146:   app.lambda2 = 0.36;
    147:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex1 options", "");
    148:   {
    149:     PetscCall(PetscOptionsReal("-lambda1", "", "", app.lambda1, &app.lambda1, NULL));
    150:     PetscCall(PetscOptionsReal("-lambda2", "", "", app.lambda2, &app.lambda2, NULL));
    151:   }
    152:   PetscOptionsEnd();

    154:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    155:     Create necessary matrix and vectors
    156:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    157:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
    158:   PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
    159:   PetscCall(MatSetType(A, MATDENSE));
    160:   PetscCall(MatSetFromOptions(A));
    161:   PetscCall(MatSetUp(A));

    163:   PetscCall(MatCreateVecs(A, &U, NULL));

    165:   PetscCall(VecGetArray(U, &u));
    166:   u[0] = 0;
    167:   u[1] = 1;
    168:   PetscCall(VecRestoreArray(U, &u));
    169:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    170:      Create timestepping solver context
    171:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    172:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
    173:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
    174:   PetscCall(TSSetType(ts, TSCN));
    175:   PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &app));
    176:   PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &app));

    178:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    179:      Set initial conditions
    180:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    181:   PetscCall(TSSetSolution(ts, U));

    183:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    184:      Set solver options
    185:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    186:   PetscCall(TSSetMaxTime(ts, 0.125));
    187:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
    188:   PetscCall(TSSetTimeStep(ts, 1. / 256.));
    189:   PetscCall(TSSetFromOptions(ts));

    191:   /* Set directions and terminate flags for the two events */
    192:   direction[0] = 0;
    193:   terminate[0] = PETSC_FALSE;
    194:   PetscCall(TSSetEventHandler(ts, 1, direction, terminate, EventFunction, PostEventFunction, (void *)&app));

    196:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    197:      Run timestepping solver
    198:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    199:   PetscCall(TSSolve(ts, U));

    201:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    202:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    203:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    204:   PetscCall(MatDestroy(&A));
    205:   PetscCall(VecDestroy(&U));
    206:   PetscCall(TSDestroy(&ts));

    208:   PetscCall(PetscFinalize());
    209:   return 0;
    210: }

    212: /*TEST

    214:    build:
    215:       requires: !complex
    216:    test:
    217:       args: -ts_monitor

    219:    test:
    220:       suffix: 2
    221:       args: -ts_monitor_lg_solution -1
    222:       requires: x

    224: TEST*/