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:   PetscScalar        *f,r;
 36:   const PetscScalar  *u,*udot;
 37:   static PetscScalar R = .4;

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

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

 56: /*
 57:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 58: */
 59: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
 60: {
 61:   PetscInt          rowcol[] = {0,1};
 62:   PetscScalar       J[2][2];
 63:   const PetscScalar *u,*udot;

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

 73:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 74:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 75:   if (A != B) {
 76:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 77:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 78:   }
 79:   return 0;
 80: }

 82: int main(int argc,char **argv)
 83: {
 84:   TS             ts;            /* ODE integrator */
 85:   Vec            U;             /* solution will be stored here */
 86:   Mat            A;             /* Jacobian matrix */
 88:   PetscMPIInt    size;
 89:   PetscInt       n = 2;
 90:   AppCtx         ctx;
 91:   PetscScalar    *u;

 93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 94:      Initialize program
 95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 96:   PetscInitialize(&argc,&argv,(char*)0,help);
 97:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101:     Create necessary matrix and vectors
102:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103:   MatCreate(PETSC_COMM_WORLD,&A);
104:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
105:   MatSetFromOptions(A);
106:   MatSetUp(A);

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

110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
111:     Set runtime options
112:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
113:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Reaction options","");
114:   {
115:     ctx.omega_s = 1.0;
116:     PetscOptionsScalar("-omega_s","","",ctx.omega_s,&ctx.omega_s,NULL);
117:     ctx.H       = 1.0;
118:     PetscOptionsScalar("-H","","",ctx.H,&ctx.H,NULL);
119:     ctx.E       = 1.0;
120:     PetscOptionsScalar("-E","","",ctx.E,&ctx.E,NULL);
121:     ctx.V       = 1.0;
122:     PetscOptionsScalar("-V","","",ctx.V,&ctx.V,NULL);
123:     ctx.X       = 1.0;
124:     PetscOptionsScalar("-X","","",ctx.X,&ctx.X,NULL);

126:     VecGetArray(U,&u);
127:     u[0] = 1;
128:     u[1] = .7;
129:     VecRestoreArray(U,&u);
130:     PetscOptionsGetVec(NULL,NULL,"-initial",U,NULL);
131:   }
132:   PetscOptionsEnd();

134:   PetscRandomCreate(PETSC_COMM_WORLD,&ctx.rand);
135:   PetscRandomSetFromOptions(ctx.rand);

137:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138:      Create timestepping solver context
139:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
140:   TSCreate(PETSC_COMM_WORLD,&ts);
141:   TSSetProblemType(ts,TS_NONLINEAR);
142:   TSSetType(ts,TSROSW);
143:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
144:   TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);

146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147:      Set initial conditions
148:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149:   TSSetSolution(ts,U);

151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152:      Set solver options
153:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
154:   TSSetMaxTime(ts,2000.0);
155:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
156:   TSSetTimeStep(ts,.001);
157:   TSSetFromOptions(ts);

159:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160:      Solve nonlinear system
161:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
162:   TSSolve(ts,U);

164:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
166:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167:   MatDestroy(&A);
168:   VecDestroy(&U);
169:   TSDestroy(&ts);
170:   PetscRandomDestroy(&ctx.rand);
171:   PetscFinalize();
172:   return 0;
173: }

175: /*TEST

177:    build:
178:      requires: !complex !single

180:    test:
181:       args: -ksp_gmres_cgs_refinement_type refine_always -snes_type newtonls -ts_max_steps 10

183:    test:
184:       suffix: 2
185:       args: -ts_max_steps 10

187: TEST*/