TSSetI2Jacobian#

Set the function to compute the matrix dF/dU + vdF/dU_t + adF/dU_tt where F(t,U,U_t,U_tt) is the function you provided with TSSetI2Function().

Synopsis#

#include "petscts.h"  
PetscErrorCode TSSetI2Jacobian(TS ts, Mat J, Mat P, TSI2Jacobian jac, void *ctx)

Logically Collective

Input Parameters#

ts - the TS context obtained from TSCreate()
J - matrix to hold the Jacobian values
P - matrix for constructing the preconditioner (may be same as J)
jac - the Jacobian evaluation routine
ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)

Calling sequence of `jac`#

PetscErrorCode jac(TS ts, PetscReal t, Vec U, Vec U_t, Vec U_tt, PetscReal v, PetscReal a, Mat J, Mat P, void *ctx)

ts - the TS context obtained from TSCreate()
t - time at step/stage being solved
U - state vector
U_t - time derivative of state vector
U_tt - second time derivative of state vector
v - shift for U_t
a - shift for U_tt
J - Jacobian of G(U) = F(t,U,W+vU,W’+aU), equivalent to dF/dU + vdF/dU_t + adF/dU_tt
P - preconditioning matrix for J, may be same as J
ctx - [optional] user-defined context for matrix evaluation routine

Notes#

The matrices J and P are exactly the matrices that are used by SNES for the nonlinear solve.

The matrix dF/dU + vdF/dU_t + adF/dU_tt you provide turns out to be the Jacobian of G(U) = F(t,U,W+vU,W’+aU) where F(t,U,U_t,U_tt) = 0 is the DAE to be solved. The time integrator internally approximates U_t by W+vU and U_tt by W’+aU where the positive “shift” parameters ‘v’ and ‘a’ and vectors W, W’ depend on the integration method, step size, and past states.