Fast evaluation of electro-static interactions in multi-phase dielectric media

A method is presented for the rapid evaluation of electro-static interactions in a dielectric medium containing inclusions with different dielectric properties. The principal observation is that in environments where several potential evaluations are required for a fixed geometry, it is advantageous to precompute compressed representations of the inverses of certain operators. Numerical examples in two dimensions show a speed-up of a factor of 10–100 when compared to the fastest existing methods. Moreover, the method presented is based on direct (as opposed to iterative) techniques, making it preferable to existing methods in environments involving ill-conditioned problems.