Review of large scale computing in electromagnetics with fast integral equation solvers

Abstract

This paper reviews recent advances in large-scale computational electromagnetics using frequency domain integral equations. It gives a brief history of methods to solve Maxwell's equations, followed by a description of various historical ages in solution technique developments. Then it describes computational electromagnetics followed by a brief description of how fast integral equation solvers such as the multilevel fast multipole algorithm (MLFMA) is constructed using the tree network. Some examples of large scale computing using MLFMA are given. Ray physics used to further accelerate the speed of MLFMA. The parallel implementation of MLFMA in a code called ScaleME is reviewed, and some example calculations and scaling studies are given. Finally, we review the recent development of the fast inhomogeneous plane wave algorithm (FIPWA) for layered media for large scale computing.