# 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, void *ctx)
```

Logically Collective

## Input Parameters#

(approximate) matrix to store Jacobian entries computed by**Amat -**`f`

matrix used to compute preconditioner (usually the same as**Pmat -**`Amat`

)the Jacobian evaluation routine**f -**user-defined context for private data for the Jacobian evaluation routine (may be**ctx -**`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 + a*dF/dU_t you provide turns out to be
the Jacobian of F(t,U,W+a*U) where F(t,U,U_t) = 0 is the DAE to be solved.
The time integrator internally approximates U_t by W+a*U 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 = -a*U(previous timestep) so
W + a*U = 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 conjuction 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#

## Examples#

src/ts/tutorials/ex34.c

src/ts/tutorials/ex3.c

src/ts/utils/dmplexlandau/tutorials/ex2.c

src/ts/utils/dmplexlandau/tutorials/ex1f90.F90

src/ts/tutorials/ex9.c

src/ts/tutorials/ex41.c

src/ts/tutorials/ex17.c

src/ts/tutorials/ex19.c

src/ts/tutorials/ex15.c

src/ts/utils/dmplexlandau/tutorials/ex1.c

Index of all TS routines

Table of Contents for all manual pages

Index of all manual pages