[petsc-users] Penalization vs. setting interior points for Laplace eqn

[Barry Smith]

  I think you can just set the values there. The advantage is simplicity plus it won’t mess up the convergence of the iterative methods as a penalization likely would.

   Barry

On Oct 3, 2014, at 10:22 AM, Åsmund Ervik <asmund.ervik at ntnu.no> wrote:

> Dear PETSc users,
> 
> (This may not be very PETSc-specific, but here goes.)
> 
> I'm using KSP for solving two equations of Poisson/Laplace type. First I solve a Laplace equation in a box with Dirichlet BCs on the top/bottom and Neumann on the sides, and discontinuous coefficients inside the box. This gives me an electric potential. I then use this as one input in a two-phase incompressible Navier-Stokes solver in the same box domain, again with discontinuous coefficients, where the electric potential contributes to part of the pressure jump across the phase boundaries. Here I solve a pressure Poisson equation. This code gives good results which agree with theoretical results and experiments.
> 
> Now I want to do simulations in a complex domain. I have already implemented L2 penalization for the flow part, without an electric field, and this works well. Now I want to be able to set a constant potential in the part of the domain where I apply penalization. Does it make sense to do penalization for the Laplace equation somehow, or should I just set the potential values on the grid points where I want to?
> 
> Regards,
> Åsmund