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) { PetscFunctionBegin; * U = 0.4*PetscSinReal(200*PETSC_PI*t); PetscFunctionReturn(0); } /* Defines the DAE passed to the time solver */ static PetscErrorCode IFunctionImplicit(TS ts,PetscReal t,Vec Y,Vec Ydot,Vec F,void *ctx) { PetscErrorCode ierr; const PetscScalar *y,*ydot; PetscScalar *f; PetscFunctionBegin; /* The next three lines allow us to access the entries of the vectors directly */ ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr); ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr); ierr = VecGetArrayWrite(F,&f);CHKERRQ(ierr); 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.; ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr); ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr); ierr = VecRestoreArrayWrite(F,&f);CHKERRQ(ierr); PetscFunctionReturn(0); } /* 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,void *ctx) { PetscErrorCode ierr; PetscInt rowcol[] = {0,1,2,3,4}; const PetscScalar *y,*ydot; PetscScalar J[5][5]; PetscFunctionBegin; ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr); ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr); ierr = PetscMemzero(J,sizeof(J));CHKERRQ(ierr); 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 ; ierr = MatSetValues(B,5,rowcol,5,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr); ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr); ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr); ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); if (A != B) { ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); } PetscFunctionReturn(0); } int main(int argc,char **argv) { TS ts; /* ODE integrator */ Vec Y; /* solution will be stored here */ Mat A; /* Jacobian matrix */ PetscErrorCode ierr; PetscMPIInt size; PetscInt n = 5; PetscScalar *y; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Initialize program - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRMPI(ierr); if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create necessary matrix and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); ierr = MatSetFromOptions(A);CHKERRQ(ierr); ierr = MatSetUp(A);CHKERRQ(ierr); ierr = MatCreateVecs(A,&Y,NULL);CHKERRQ(ierr); ierr = VecGetArray(Y,&y);CHKERRQ(ierr); y[0] = 0.0; y[1] = 3.0; y[2] = y[1]; y[3] = 6.0; y[4] = 0.0; ierr = VecRestoreArray(Y,&y);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr); /* Must use ARKIMEX with fully implicit stages since mass matrix is not the indentity */ ierr = TSARKIMEXSetType(ts,TSARKIMEXPRSSP2);CHKERRQ(ierr); ierr = TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);CHKERRQ(ierr); /*ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);*/ ierr = TSSetIFunction(ts,NULL,IFunctionImplicit,NULL);CHKERRQ(ierr); ierr = TSSetIJacobian(ts,A,A,IJacobianImplicit,NULL);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetSolution(ts,Y);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set solver options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetMaxTime(ts,0.15);CHKERRQ(ierr); ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); ierr = TSSetTimeStep(ts,.001);CHKERRQ(ierr); ierr = TSSetFromOptions(ts);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Do time stepping - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSolve(ts,Y);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatDestroy(&A);CHKERRQ(ierr); ierr = VecDestroy(&Y);CHKERRQ(ierr); ierr = TSDestroy(&ts);CHKERRQ(ierr); ierr = PetscFinalize(); return ierr; } /*TEST build: requires: !single !complex test: args: -ts_monitor TEST*/