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

[Jonathan Backs]

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