Actual source code: ex36.c


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

  4: /*F
  5:  ` This example illustrates the implementation of an implicit DAE index-1 of form M y'=f(t,y) with singular mass matrix, where

  7:      [ -C1  C1           ]
  8:      [  C1 -C1           ]
  9:   M =[        -C2        ]; Ck = k * 1e-06
 10:      [            -C3  C3]
 11:      [             C3 -C3]

 13:         [ -(U(t) - y[0])/1000                    ]
 14:         [ -6/R + y[1]/4500 + 0.01 * h(y[1]-y[2]) ]
 15: f(t,y)= [ y[2]/R - h(y[1]-y[2]) ]
 16:         [ (y[3]-6)/9000 + 0.99 * h([y1]-y[2]) ]
 17:         [ y[4]/9000 ]

 19: U(t) = 0.4 * Sin(200 Pi t); h[V] = 1e-06 * Exp(V/0.026 - 1) `

 21:   Useful options: -ts_monitor_lg_solution -ts_monitor_lg_timestep -lg_indicate_data_points 0
 22: F*/

 24: /*
 25:    Include "petscts.h" so that we can use TS solvers.  Note that this
 26:    file automatically includes:
 27:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 28:      petscmat.h - matrices
 29:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 30:      petscviewer.h - viewers               petscpc.h  - preconditioners
 31:      petscksp.h   - linear solvers
 32: */
 33: #include <petscts.h>

 35: FILE *gfilepointer_data, *gfilepointer_info;

 37: /* Defines the source  */
 38: PetscErrorCode Ue(PetscScalar t, PetscScalar *U)
 39: {
 41:   *U = 0.4 * PetscSinReal(200 * PETSC_PI * t);
 42:   return 0;
 43: }

 45: /*
 46:      Defines the DAE passed to the time solver
 47: */
 48: static PetscErrorCode IFunctionImplicit(TS ts, PetscReal t, Vec Y, Vec Ydot, Vec F, void *ctx)
 49: {
 50:   const PetscScalar *y, *ydot;
 51:   PetscScalar       *f;

 54:   /*  The next three lines allow us to access the entries of the vectors directly */
 55:   VecGetArrayRead(Y, &y);
 56:   VecGetArrayRead(Ydot, &ydot);
 57:   VecGetArrayWrite(F, &f);

 59:   f[0] = ydot[0] / 1.e6 - ydot[1] / 1.e6 - PetscSinReal(200 * PETSC_PI * t) / 2500. + y[0] / 1000.;
 60:   f[1] = -ydot[0] / 1.e6 + ydot[1] / 1.e6 - 0.0006666766666666667 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 1.e8 + y[1] / 4500.;
 61:   f[2] = ydot[2] / 500000. + 1.e-6 - PetscExpReal((500 * (y[1] - y[2])) / 13.) / 1.e6 + y[2] / 9000.;
 62:   f[3] = (3 * ydot[3]) / 1.e6 - (3 * ydot[4]) / 1.e6 - 0.0006676566666666666 + (99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 1.e8 + y[3] / 9000.;
 63:   f[4] = (3 * ydot[4]) / 1.e6 - (3 * ydot[3]) / 1.e6 + y[4] / 9000.;

 65:   VecRestoreArrayRead(Y, &y);
 66:   VecRestoreArrayRead(Ydot, &ydot);
 67:   VecRestoreArrayWrite(F, &f);
 68:   return 0;
 69: }

 71: /*
 72:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 73: */
 74: static PetscErrorCode IJacobianImplicit(TS ts, PetscReal t, Vec Y, Vec Ydot, PetscReal a, Mat A, Mat B, void *ctx)
 75: {
 76:   PetscInt           rowcol[] = {0, 1, 2, 3, 4};
 77:   const PetscScalar *y, *ydot;
 78:   PetscScalar        J[5][5];

 81:   VecGetArrayRead(Y, &y);
 82:   VecGetArrayRead(Ydot, &ydot);

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

 86:   J[0][0] = a / 1.e6 + 0.001;
 87:   J[0][1] = -a / 1.e6;
 88:   J[1][0] = -a / 1.e6;
 89:   J[1][1] = a / 1.e6 + 0.00022222222222222223 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 2.6e6;
 90:   J[1][2] = -PetscExpReal((500 * (y[1] - y[2])) / 13.) / 2.6e6;
 91:   J[2][1] = -PetscExpReal((500 * (y[1] - y[2])) / 13.) / 26000.;
 92:   J[2][2] = a / 500000 + 0.00011111111111111112 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 26000.;
 93:   J[3][1] = (99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 2.6e6;
 94:   J[3][2] = (-99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 2.6e6;
 95:   J[3][3] = (3 * a) / 1.e6 + 0.00011111111111111112;
 96:   J[3][4] = -(3 * a) / 1.e6;
 97:   J[4][3] = -(3 * a) / 1.e6;
 98:   J[4][4] = (3 * a) / 1.e6 + 0.00011111111111111112;

100:   MatSetValues(B, 5, rowcol, 5, rowcol, &J[0][0], INSERT_VALUES);

102:   VecRestoreArrayRead(Y, &y);
103:   VecRestoreArrayRead(Ydot, &ydot);

105:   MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
106:   MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
107:   if (A != B) {
108:     MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
109:     MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
110:   }
111:   return 0;
112: }

114: int main(int argc, char **argv)
115: {
116:   TS           ts; /* ODE integrator */
117:   Vec          Y;  /* solution will be stored here */
118:   Mat          A;  /* Jacobian matrix */
119:   PetscMPIInt  size;
120:   PetscInt     n = 5;
121:   PetscScalar *y;

123:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124:      Initialize program
125:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127:   PetscInitialize(&argc, &argv, (char *)0, help);
128:   MPI_Comm_size(PETSC_COMM_WORLD, &size);

131:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132:     Create necessary matrix and vectors
133:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
134:   MatCreate(PETSC_COMM_WORLD, &A);
135:   MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE);
136:   MatSetFromOptions(A);
137:   MatSetUp(A);

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

141:   VecGetArray(Y, &y);
142:   y[0] = 0.0;
143:   y[1] = 3.0;
144:   y[2] = y[1];
145:   y[3] = 6.0;
146:   y[4] = 0.0;
147:   VecRestoreArray(Y, &y);

149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150:      Create timestepping solver context
151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152:   TSCreate(PETSC_COMM_WORLD, &ts);
153:   TSSetProblemType(ts, TS_NONLINEAR);
154:   TSSetType(ts, TSARKIMEX);
155:   /* Must use ARKIMEX with fully implicit stages since mass matrix is not the identity */
156:   TSARKIMEXSetType(ts, TSARKIMEXPRSSP2);
157:   TSSetEquationType(ts, TS_EQ_DAE_IMPLICIT_INDEX1);
158:   /*TSSetType(ts,TSROSW);*/
159:   TSSetIFunction(ts, NULL, IFunctionImplicit, NULL);
160:   TSSetIJacobian(ts, A, A, IJacobianImplicit, NULL);

162:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163:      Set initial conditions
164:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
165:   TSSetSolution(ts, Y);

167:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168:      Set solver options
169:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
170:   TSSetMaxTime(ts, 0.15);
171:   TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER);
172:   TSSetTimeStep(ts, .001);
173:   TSSetFromOptions(ts);

175:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176:      Do time stepping
177:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
178:   TSSolve(ts, Y);

180:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
182:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183:   MatDestroy(&A);
184:   VecDestroy(&Y);
185:   TSDestroy(&ts);
186:   PetscFinalize();
187:   return 0;
188: }

190: /*TEST
191:     build:
192:       requires: !single !complex
193:     test:
194:       args: -ts_monitor

196: TEST*/