There has been much research in the last decade into the topic of accelerated methods for solving the matrix equations associated with a method of moments solution of surface integral equations. Our own interest has mainly been in the application of such methods to two-dimensional terrain profile propagation problems. We have also been active in developing algorithms for application to three-dimensional scattering problems. The figures below shows electric fields calculated above metallic plates using a three dimensional version of the fast far-field algorithm.
Another area of our research is in the area of hybridised solutions where results from asymptotic analysis are incorporated into the exact numerical solutions and vice versa. A related topic is on the development of efficient iterative methods. This slide show outlines work performed in collaboration with the radio propagation group in TCD in extending the 'forward/ backward' iterative method to the three dimensional electric field integral equation.