A fast direct solver for high frequency scattering from a large cavity   in two dimensions
  We present a fast direct solver for the simulation of electromagnetic scattering from an arbitrarily-shaped, large, empty cavity embedded in an infinite perfectly conducting half space. The governing Maxwell equations are reformulated as a well-conditioned second kind integral equation and the resulting linear system is solved in nearly linear time using a hierarchical matrix factorization technique. We illustrate the performance of the scheme with several numerical examples for complex cavity shapes over a wide range of frequencies. 
Jun Lai, Sivaram Ambikasaran, Leslie F. Greengard
math.NA cs.NA