static char help[] = "Transistor amplifier.\n"; /*F ` This example illustrates the implementation of an implicit DAE index-1 of form M y'=f(t,y) with singular mass matrix, where [ -C1 C1 ] [ C1 -C1 ] M =[ -C2 ]; Ck = k * 1e-06 [ -C3 C3] [ C3 -C3] [ -(U(t) - y[0])/1000 ] [ -6/R + y[1]/4500 + 0.01 * h(y[1]-y[2]) ] f(t,y)= [ y[2]/R - h(y[1]-y[2]) ] [ (y[3]-6)/9000 + 0.99 * h([y1]-y[2]) ] [ y[4]/9000 ] U(t) = 0.4 * Sin(200 Pi t); h[V] = 1e-06 * Exp(V/0.026 - 1) ` Useful options: -ts_monitor_lg_solution -ts_monitor_lg_timestep -lg_indicate_data_points 0 F*/ /* Include "petscts.h" so that we can use TS solvers. Note that this file automatically includes: petscsys.h - base PETSc routines petscvec.h - vectors petscmat.h - matrices petscis.h - index sets petscksp.h - Krylov subspace methods petscviewer.h - viewers petscpc.h - preconditioners petscksp.h - linear solvers */ #include FILE *gfilepointer_data, *gfilepointer_info; /* Defines the source */ PetscErrorCode Ue(PetscScalar t, PetscScalar *U) { PetscFunctionBeginUser; *U = 0.4 * PetscSinReal(200 * PETSC_PI * t); PetscFunctionReturn(PETSC_SUCCESS); } /* Defines the DAE passed to the time solver */ static PetscErrorCode IFunctionImplicit(TS ts, PetscReal t, Vec Y, Vec Ydot, Vec F, PetscCtx ctx) { const PetscScalar *y, *ydot; PetscScalar *f; PetscFunctionBeginUser; /* The next three lines allow us to access the entries of the vectors directly */ PetscCall(VecGetArrayRead(Y, &y)); PetscCall(VecGetArrayRead(Ydot, &ydot)); PetscCall(VecGetArrayWrite(F, &f)); f[0] = ydot[0] / 1.e6 - ydot[1] / 1.e6 - PetscSinReal(200 * PETSC_PI * t) / 2500. + y[0] / 1000.; f[1] = -ydot[0] / 1.e6 + ydot[1] / 1.e6 - 0.0006666766666666667 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 1.e8 + y[1] / 4500.; f[2] = ydot[2] / 500000. + 1.e-6 - PetscExpReal((500 * (y[1] - y[2])) / 13.) / 1.e6 + y[2] / 9000.; 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.; f[4] = (3 * ydot[4]) / 1.e6 - (3 * ydot[3]) / 1.e6 + y[4] / 9000.; PetscCall(VecRestoreArrayRead(Y, &y)); PetscCall(VecRestoreArrayRead(Ydot, &ydot)); PetscCall(VecRestoreArrayWrite(F, &f)); PetscFunctionReturn(PETSC_SUCCESS); } /* Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. */ static PetscErrorCode IJacobianImplicit(TS ts, PetscReal t, Vec Y, Vec Ydot, PetscReal a, Mat A, Mat B, PetscCtx ctx) { PetscInt rowcol[] = {0, 1, 2, 3, 4}; const PetscScalar *y, *ydot; PetscScalar J[5][5]; PetscFunctionBeginUser; PetscCall(VecGetArrayRead(Y, &y)); PetscCall(VecGetArrayRead(Ydot, &ydot)); PetscCall(PetscMemzero(J, sizeof(J))); J[0][0] = a / 1.e6 + 0.001; J[0][1] = -a / 1.e6; J[1][0] = -a / 1.e6; J[1][1] = a / 1.e6 + 0.00022222222222222223 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 2.6e6; J[1][2] = -PetscExpReal((500 * (y[1] - y[2])) / 13.) / 2.6e6; J[2][1] = -PetscExpReal((500 * (y[1] - y[2])) / 13.) / 26000.; J[2][2] = a / 500000 + 0.00011111111111111112 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 26000.; J[3][1] = (99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 2.6e6; J[3][2] = (-99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 2.6e6; J[3][3] = (3 * a) / 1.e6 + 0.00011111111111111112; J[3][4] = -(3 * a) / 1.e6; J[4][3] = -(3 * a) / 1.e6; J[4][4] = (3 * a) / 1.e6 + 0.00011111111111111112; PetscCall(MatSetValues(B, 5, rowcol, 5, rowcol, &J[0][0], INSERT_VALUES)); PetscCall(VecRestoreArrayRead(Y, &y)); PetscCall(VecRestoreArrayRead(Ydot, &ydot)); PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); if (A != B) { PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); } PetscFunctionReturn(PETSC_SUCCESS); } int main(int argc, char **argv) { TS ts; /* ODE integrator */ Vec Y; /* solution will be stored here */ Mat A; /* Jacobian matrix */ PetscMPIInt size; PetscInt n = 5; PetscScalar *y; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Initialize program - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscFunctionBeginUser; PetscCall(PetscInitialize(&argc, &argv, NULL, help)); PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create necessary matrix and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); PetscCall(MatSetFromOptions(A)); PetscCall(MatSetUp(A)); PetscCall(MatCreateVecs(A, &Y, NULL)); PetscCall(VecGetArray(Y, &y)); y[0] = 0.0; y[1] = 3.0; y[2] = y[1]; y[3] = 6.0; y[4] = 0.0; PetscCall(VecRestoreArray(Y, &y)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); PetscCall(TSSetType(ts, TSARKIMEX)); /* Must use ARKIMEX with fully implicit stages since mass matrix is not the identity */ PetscCall(TSARKIMEXSetType(ts, TSARKIMEXPRSSP2)); PetscCall(TSSetEquationType(ts, TS_EQ_DAE_IMPLICIT_INDEX1)); /*PetscCall(TSSetType(ts,TSROSW));*/ PetscCall(TSSetIFunction(ts, NULL, IFunctionImplicit, NULL)); PetscCall(TSSetIJacobian(ts, A, A, IJacobianImplicit, NULL)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetSolution(ts, Y)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set solver options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetMaxTime(ts, 0.15)); PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); PetscCall(TSSetTimeStep(ts, .001)); PetscCall(TSSetFromOptions(ts)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Do time stepping - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSolve(ts, Y)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatDestroy(&A)); PetscCall(VecDestroy(&Y)); PetscCall(TSDestroy(&ts)); PetscCall(PetscFinalize()); return 0; } /*TEST build: requires: !single !complex test: args: -ts_monitor TEST*/