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# 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, TSIJacobianFn *f, PetscCtx 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`)

## 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.

In case `TSSetRHSJacobian()` is also used in conjunction with a fully-implicit solver, multilevel linear solvers, e.g. `PCMG`, will likely not work due to the way `TS` handles rhs matrices.

## See Also

TS: Scalable ODE and DAE Solvers, `TS`, `TSIJacobianFn`, `TSSetIFunction()`, `TSSetRHSJacobian()`, `SNESComputeJacobianDefaultColor()`, `SNESComputeJacobianDefault()`, `TSSetRHSFunction()`

## Level

beginner

## Location

src/ts/interface/ts.c

## Examples

src/ts/tutorials/ex17.c
src/ts/tutorials/ex9.c
src/ts/tutorials/ex19.c
src/ts/tutorials/ex10.c
src/ts/tutorials/ex20.c
src/ts/tutorials/ex16.c
src/ts/tutorials/ex20adj.c
src/ts/tutorials/ex20fwd.c
src/ts/tutorials/ex15.c
src/ts/tutorials/ex14.c

Index of all TS routines
Table of Contents for all manual pages
Index of all manual pages