TSSetIJacobian#

Set the function to compute the matrix dF/dU + a*dF/dU_t where F(t,U,U_t) is the function provided with TSSetIFunction().

Synopsis#

#include "petscts.h"  
PetscErrorCode TSSetIJacobian(TS ts, Mat Amat, Mat Pmat, TSIJacobian f, void *ctx)

Logically Collective

Input Parameters#

ts - the TS context obtained from TSCreate()
Amat - (approximate) matrix to store Jacobian entries computed by f
Pmat - matrix used to compute preconditioner (usually the same as Amat)
f - the Jacobian evaluation routine
ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)

Calling sequence of `f`#

PetscErrorCode f(TS ts, PetscReal t, Vec U, Vec U_t, PetscReal a, Mat Amat, Mat Pmat, 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
a - shift
Amat - (approximate) Jacobian of F(t,U,W+aU), equivalent to dF/dU + adF/dU_t
Pmat - matrix used for constructing preconditioner, usually the same as Amat
ctx - [optional] user-defined context for matrix evaluation routine

Notes#

The matrices Amat and Pmat are exactly the matrices that are used by SNES for the nonlinear solve.

If you know the operator Amat has a null space you can use MatSetNullSpace() and MatSetTransposeNullSpace() to supply the null space to Amat and the KSP solvers will automatically use that null space as needed during the solution process.

The matrix dF/dU + adF/dU_t you provide turns out to be the Jacobian of F(t,U,W+aU) where F(t,U,U_t) = 0 is the DAE to be solved. The time integrator internally approximates U_t by W+aU where the positive “shift” a and vector W depend on the integration method, step size, and past states. For example with the backward Euler method a = 1/dt and W = -aU(previous timestep) so W + aU = a(U - U(previous timestep)) = (U - U(previous timestep))/dt

You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value

The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f You should not assume the values are the same in the next call to f as you set them in the previous call.