[petsc-users] Coupled multi-component problems with TS

[Barry Smith]

   Jonathan,

   You need to switch to PETSc-dev http://www.mcs.anl.gov/petsc/petsc-as/developers/index.html to access the DAE solvers that Jed Brown has developed. 

    For that you use TSSetIFunction() and TSSetIJacobian() .

    Examples in src/ts/examples/tutorials

 ex14.c:  ierr = TSSetIFunction(ts,THIFunction,thi);CHKERRQ(ierr);
ex15.c:  ierr = TSSetIFunction(ts,FormIFunction,&user);CHKERRQ(ierr);
ex17.c:  ierr = TSSetIFunction(ts,FormIFunction,&user);CHKERRQ(ierr);
ex18.c:  ierr = TSSetIFunction(ts,FormResidual,&user);CHKERRQ(ierr);
ex8.c:  ierr = TSSetIFunction(ts,problem->function,problem->data);CHKERRQ(ierr);

all use this functionality.

   Good luck and feel free to send more questions once you are going, but I suspect it will be easy for you with this hint.


    Barry

On Jun 29, 2011, at 6:23 PM, Jonathan Backs wrote:

> Hi,
> 
> I am developing my first application with PETSc in an attempt to solve two coupled non-linear PDEs: (1) Poisson's equation for electric potential with a temperature-dependent electrical conductivity, and (2) the heat diffusion equation with a voltage-dependent thermal conductivity and a voltage-and-temperature-dependent source term (ohmic heating from the electric potential and the temperature-dependent electrical conductivity).
> 
> So far I have solved the two problems separately without problems: Poisson's equation with a voltage-dependent electric conductivity (no timestepping), and the heat equation with a temperature-dependent thermal conductivity (timestepping, but no source term; the heat came from the boundary conditions in this case). However, I am not sure how to set up PETSc for solving these non-linear equations simultaneously. For example, when setting up a non-linear problem with time stepping, I understand I have to set the RHSFunction and RHSJacobian, assuming the left hand side provided by PETSc is the time-derivative of the independent variable; When setting up a non-linear problem without time stepping, I understand I have to set the Function assuming a zero left hand side (and then set the Jacobian according to the Function).
> 
> I have tried to implement the coupled problem using a three-dimensional DA with two degrees of freedom (V and T). While PETSc seems to facilitate the use of multiple degrees of freedom in the same RHSFunction (and RHSJacobian), I cannot assign an RHSFunction for the Poisson's equation since the Poisson's equation does not include a time derivative. I have not been able to find any examples in the documentation or on this mailing list that illustrated this particular type of problem.
> 
> Could anyone offer a hint as to the proper strategy for implementing this coupled system of PDEs?
> 
> Thank you for your time,
> 
> Jon