Actual source code: ex36A.c


  2: static char help[] = "Transistor amplifier (autonomous).\n";

  4: /*F
  5:   M y'=f(y)

  7:   Useful options: -ts_monitor_lg_solution -ts_monitor_lg_timestep -lg_indicate_data_points 0
  8: F*/

 10: /*
 11:    Include "petscts.h" so that we can use TS solvers.  Note that this
 12:    file automatically includes:
 13:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 14:      petscmat.h - matrices
 15:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 16:      petscviewer.h - viewers               petscpc.h  - preconditioners
 17:      petscksp.h   - linear solvers
 18: */
 19: #include <petscts.h>

 21: FILE *gfilepointer_data, *gfilepointer_info;

 23: /* Defines the source  */
 24: PetscErrorCode Ue(PetscScalar t, PetscScalar *U)
 25: {
 27:   U = 0.4 * sin(200 * pi * t);
 28:   return 0;
 29: }
 30: * /

 32:   /*
 33:      Defines the DAE passed to the time solver
 34: */
 35:   static PetscErrorCode IFunctionImplicit(TS ts, PetscReal t, Vec Y, Vec Ydot, Vec F, void *ctx)
 36: {
 37:   const PetscScalar *y, *ydot;
 38:   PetscScalar       *f;

 41:   /*  The next three lines allow us to access the entries of the vectors directly */
 42:   VecGetArrayRead(Y, &y);
 43:   VecGetArrayRead(Ydot, &ydot);
 44:   VecGetArray(F, &f);

 46:   f[0] = PetscSinReal(200 * PETSC_PI * y[5]) / 2500. - y[0] / 1000. - ydot[0] / 1.e6 + ydot[1] / 1.e6;
 47:   f[1] = 0.0006666766666666667 - PetscExpReal((500 * (y[1] - y[2])) / 13.) / 1.e8 - y[1] / 4500. + ydot[0] / 1.e6 - ydot[1] / 1.e6;
 48:   f[2] = -1.e-6 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 1.e6 - y[2] / 9000. - ydot[2] / 500000.;
 49:   f[3] = 0.0006676566666666666 - (99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 1.e8 - y[3] / 9000. - (3 * ydot[3]) / 1.e6 + (3 * ydot[4]) / 1.e6;
 50:   f[4] = -y[4] / 9000. + (3 * ydot[3]) / 1.e6 - (3 * ydot[4]) / 1.e6;
 51:   f[5] = -1 + ydot[5];

 53:   VecRestoreArrayRead(Y, &y);
 54:   VecRestoreArrayRead(Ydot, &ydot);
 55:   VecRestoreArray(F, &f);
 56:   return 0;
 57: }

 59: /*
 60:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 61: */
 62: static PetscErrorCode IJacobianImplicit(TS ts, PetscReal t, Vec Y, Vec Ydot, PetscReal a, Mat A, Mat B, void *ctx)
 63: {
 64:   PetscInt           rowcol[] = {0, 1, 2, 3, 4, 5};
 65:   const PetscScalar *y, *ydot;
 66:   PetscScalar        J[6][6];

 69:   VecGetArrayRead(Y, &y);
 70:   VecGetArrayRead(Ydot, &ydot);

 72:   PetscMemzero(J, sizeof(J));

 74:   J[0][0] = -0.001 - a / 1.e6;
 75:   J[0][1] = a / 1.e6;
 76:   J[0][5] = (2 * PETSC_PI * PetscCosReal(200 * PETSC_PI * y[5])) / 25.;
 77:   J[1][0] = a / 1.e6;
 78:   J[1][1] = -0.00022222222222222223 - a / 1.e6 - PetscExpReal((500 * (y[1] - y[2])) / 13.) / 2.6e6;
 79:   J[1][2] = PetscExpReal((500 * (y[1] - y[2])) / 13.) / 2.6e6;
 80:   J[2][1] = PetscExpReal((500 * (y[1] - y[2])) / 13.) / 26000.;
 81:   J[2][2] = -0.00011111111111111112 - a / 500000. - PetscExpReal((500 * (y[1] - y[2])) / 13.) / 26000.;
 82:   J[3][1] = (-99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 2.6e6;
 83:   J[3][2] = (99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 2.6e6;
 84:   J[3][3] = -0.00011111111111111112 - (3 * a) / 1.e6;
 85:   J[3][4] = (3 * a) / 1.e6;
 86:   J[4][3] = (3 * a) / 1.e6;
 87:   J[4][4] = -0.00011111111111111112 - (3 * a) / 1.e6;
 88:   J[5][5] = a;

 90:   MatSetValues(B, 6, rowcol, 6, rowcol, &J[0][0], INSERT_VALUES);

 92:   VecRestoreArrayRead(Y, &y);
 93:   VecRestoreArrayRead(Ydot, &ydot);

 95:   MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
 96:   MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
 97:   if (A != B) {
 98:     MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
 99:     MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
100:   }
101:   return 0;
102: }

104: int main(int argc, char **argv)
105: {
106:   TS           ts; /* ODE integrator */
107:   Vec          Y;  /* solution will be stored here */
108:   Mat          A;  /* Jacobian matrix */
109:   PetscMPIInt  size;
110:   PetscInt     n = 6;
111:   PetscScalar *y;

113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114:      Initialize program
115:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
117:   PetscInitialize(&argc, &argv, (char *)0, help);
118:   MPI_Comm_size(PETSC_COMM_WORLD, &size);

121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
122:     Create necessary matrix and vectors
123:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
124:   MatCreate(PETSC_COMM_WORLD, &A);
125:   MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE);
126:   MatSetFromOptions(A);
127:   MatSetUp(A);

129:   MatCreateVecs(A, &Y, NULL);

131:   VecGetArray(Y, &y);
132:   y[0] = 0.0;
133:   y[1] = 3.0;
134:   y[2] = y[1];
135:   y[3] = 6.0;
136:   y[4] = 0.0;
137:   y[5] = 0.0;
138:   VecRestoreArray(Y, &y);

140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141:      Create timestepping solver context
142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143:   TSCreate(PETSC_COMM_WORLD, &ts);
144:   TSSetProblemType(ts, TS_NONLINEAR);
145:   TSSetType(ts, TSARKIMEX);
146:   TSSetEquationType(ts, TS_EQ_DAE_IMPLICIT_INDEX1);
147:   TSARKIMEXSetFullyImplicit(ts, PETSC_TRUE);
148:   /*TSSetType(ts,TSROSW);*/
149:   TSSetIFunction(ts, NULL, IFunctionImplicit, NULL);
150:   TSSetIJacobian(ts, A, A, IJacobianImplicit, NULL);

152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153:      Set initial conditions
154:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155:   TSSetSolution(ts, Y);

157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158:      Set solver options
159:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160:   TSSetMaxTime(ts, 0.15);
161:   TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER);
162:   TSSetTimeStep(ts, .001);
163:   TSSetFromOptions(ts);

165:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166:      Do Time stepping
167:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
168:   TSSolve(ts, Y);

170:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
172:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
173:   MatDestroy(&A);
174:   VecDestroy(&Y);
175:   TSDestroy(&ts);
176:   PetscFinalize();
177:   return 0;
178: }