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*/