Actual source code: ex1.c

      2: static char help[] = "Basic equation for generator stability analysis.\n";

\begin{eqnarray}
\frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - \frac{EV}{X} \sin(\theta) \\
\frac{d \theta}{dt} = \omega - \omega_s
\end{eqnarray}

     13: /*
     14:    Include "petscts.h" so that we can use TS solvers.  Note that this
     15:    file automatically includes:
     16:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     17:      petscmat.h - matrices
     18:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     19:      petscviewer.h - viewers               petscpc.h  - preconditioners
     20:      petscksp.h   - linear solvers
     21: */

     23: #include <petscts.h>

     25: typedef struct {
     26:   PetscScalar H,omega_s,E,V,X;
     27:   PetscRandom rand;
     28: } AppCtx;

     30: /*
     31:      Defines the ODE passed to the ODE solver
     32: */
     33: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
     34: {
     35:   PetscErrorCode     ierr;
     36:   PetscScalar        *f,r;
     37:   const PetscScalar  *u,*udot;
     38:   static PetscScalar R = .4;

     41:   PetscRandomGetValue(ctx->rand,&r);
     42:   if (r > .9) R = .5;
     43:   if (r < .1) R = .4;
     44:   R = .4;
     45:   /*  The next three lines allow us to access the entries of the vectors directly */
     46:   VecGetArrayRead(U,&u);
     47:   VecGetArrayRead(Udot,&udot);
     48:   VecGetArray(F,&f);
     49:   f[0] = 2.0*ctx->H*udot[0]/ctx->omega_s + ctx->E*ctx->V*PetscSinScalar(u[1])/ctx->X - R;
     50:   f[1] = udot[1] - u[0] + ctx->omega_s;

     52:   VecRestoreArrayRead(U,&u);
     53:   VecRestoreArrayRead(Udot,&udot);
     54:   VecRestoreArray(F,&f);
     55:   return(0);
     56: }

     58: /*
     59:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
     60: */
     61: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
     62: {
     63:   PetscErrorCode    ierr;
     64:   PetscInt          rowcol[] = {0,1};
     65:   PetscScalar       J[2][2];
     66:   const PetscScalar *u,*udot;

     69:   VecGetArrayRead(U,&u);
     70:   VecGetArrayRead(Udot,&udot);
     71:   J[0][0] = 2.0*ctx->H*a/ctx->omega_s;   J[0][1] = -ctx->E*ctx->V*PetscCosScalar(u[1])/ctx->X;
     72:   J[1][0] = -1.0;                        J[1][1] = a;
     73:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
     74:   VecRestoreArrayRead(U,&u);
     75:   VecRestoreArrayRead(Udot,&udot);

     77:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     78:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     79:   if (A != B) {
     80:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     81:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     82:   }
     83:   return(0);
     84: }

     86: int main(int argc,char **argv)
     87: {
     88:   TS             ts;            /* ODE integrator */
     89:   Vec            U;             /* solution will be stored here */
     90:   Mat            A;             /* Jacobian matrix */
     92:   PetscMPIInt    size;
     93:   PetscInt       n = 2;
     94:   AppCtx         ctx;
     95:   PetscScalar    *u;

     97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     98:      Initialize program
     99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    100:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
    101:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
    102:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

    104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:     Create necessary matrix and vectors
    106:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    107:   MatCreate(PETSC_COMM_WORLD,&A);
    108:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
    109:   MatSetFromOptions(A);
    110:   MatSetUp(A);

    112:   MatCreateVecs(A,&U,NULL);

    114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    115:     Set runtime options
    116:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    117:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Reaction options","");
    118:   {
    119:     ctx.omega_s = 1.0;
    120:     PetscOptionsScalar("-omega_s","","",ctx.omega_s,&ctx.omega_s,NULL);
    121:     ctx.H       = 1.0;
    122:     PetscOptionsScalar("-H","","",ctx.H,&ctx.H,NULL);
    123:     ctx.E       = 1.0;
    124:     PetscOptionsScalar("-E","","",ctx.E,&ctx.E,NULL);
    125:     ctx.V       = 1.0;
    126:     PetscOptionsScalar("-V","","",ctx.V,&ctx.V,NULL);
    127:     ctx.X       = 1.0;
    128:     PetscOptionsScalar("-X","","",ctx.X,&ctx.X,NULL);

    130:     VecGetArray(U,&u);
    131:     u[0] = 1;
    132:     u[1] = .7;
    133:     VecRestoreArray(U,&u);
    134:     PetscOptionsGetVec(NULL,NULL,"-initial",U,NULL);
    135:   }
    136:   PetscOptionsEnd();

    138:   PetscRandomCreate(PETSC_COMM_WORLD,&ctx.rand);
    139:   PetscRandomSetFromOptions(ctx.rand);

    141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    142:      Create timestepping solver context
    143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    144:   TSCreate(PETSC_COMM_WORLD,&ts);
    145:   TSSetProblemType(ts,TS_NONLINEAR);
    146:   TSSetType(ts,TSROSW);
    147:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
    148:   TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);

    150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    151:      Set initial conditions
    152:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    153:   TSSetSolution(ts,U);

    155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    156:      Set solver options
    157:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    158:   TSSetMaxTime(ts,2000.0);
    159:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    160:   TSSetTimeStep(ts,.001);
    161:   TSSetFromOptions(ts);

    163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164:      Solve nonlinear system
    165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    166:   TSSolve(ts,U);

    168:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    169:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    170:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    171:   MatDestroy(&A);
    172:   VecDestroy(&U);
    173:   TSDestroy(&ts);
    174:   PetscRandomDestroy(&ctx.rand);
    175:   PetscFinalize();
    176:   return ierr;
    177: }

    180: /*TEST

    182:    build:
    183:      requires: !complex !single

    185:    test:
    186:       args: -ksp_gmres_cgs_refinement_type refine_always -snes_type newtonls -ts_max_steps 10

    188:    test:
    189:       suffix: 2
    190:       args: -ts_max_steps 10

    192: TEST*/