petsc-3.8.4 2018-03-24

TSSetI2Jacobian

Set the function to compute the matrix dF/dU + v*dF/dU_t + a*dF/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 on TS

Input Parameters

	ts	- the TS context obtained from TSCreate()
	J	- Jacobian matrix
	P	- preconditioning matrix for J (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

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

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

Keywords