Recent developments in fast-multipole based frequency and time domain solvers

This paper reviews the state of the art in fast integral equation techniques for solving large scale electromagnetic scattering and radiation problems. The Multilevel Fast Multipole Algorithm and its frequency and time domain derivatives are discussed. These techniques permit the rapid evaluation of fields due to known sources and hence accelerate the solution of boundary value problems arising in the analysis of a wide variety of electromagnetic phenomena. Specifically, the application of the Steepest Descent: Fast Multipole Method to the frequency domain analysis of radiation from quasi planar structures, e.g., rough surfaces and finite microstrip structures, is described. In addition, the extension of the fast multipole concept to the Plane Wave Time Domain algorithm that permits the efficient analysis of transient phenomena is outlined.