petsc-3.5.4 2015-05-23
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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,TSIJacobian f,void *ctx)
```
Logically Collective on TS

### Input Parameters

 ts - the TS context obtained from TSCreate() Amat - (approximate) Jacobian matrix 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

``` f(TS ts,PetscReal t,Vec U,Vec U_t,PetscReal a,Mat Amat,Mat Pmat,void *ctx);
```

 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+a*U), equivalent to dF/dU + a*dF/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.

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

### Keywords

TS, timestep, DAE, Jacobian

### See Also

TSSetIFunction(), TSSetRHSJacobian(), SNESComputeJacobianDefaultColor(), SNESComputeJacobianDefault(), TSSetRHSFunction()

### Examples

src/ts/examples/tutorials/ex6.c.html
src/ts/examples/tutorials/ex8.c.html
src/ts/examples/tutorials/ex9.c.html
src/ts/examples/tutorials/ex10.c.html
src/ts/examples/tutorials/ex14.c.html
src/ts/examples/tutorials/ex15.c.html
src/ts/examples/tutorials/ex16.c.html
src/ts/examples/tutorials/ex17.c.html
src/ts/examples/tutorials/ex19.c.html
src/ts/examples/tutorials/ex20.c.html
src/ts/examples/tutorials/ex22.c.html