The field of applied
electromagnetics that uses high-performance
computers and
numerical algorithms to solve electromagnetic problems that generally have no
analytic solution.
The Computational EM (or CEM) area has been at the forefront of advanced algorithms for solving large boundary-value problems. These problems range between those of EM radiation, inverse imaging, scattering, and EM compatibility/interference (to name a few). These types of problems have direct applications in such fields as radar systems, antenna design, and medical imaging.
In CEM there are a host of well-developed techniques for solving Maxwell's Equations. In the time domain, the most widely used are finite-differencing techniques such as the Finite Difference Time Domain method (FDTD). In the frequency domain, there are the Finite Element Method (FEM), Method of Moments (MoM), and Physical Theory of Diffraction (PTD) (among others).
There are several very good graduate schools in CEM in the United States. Among these are at the University of Missouri-Rolla, Ohio State University, the University of Michigan, and The Center for Computational Electromagnetics at the University of Illinois at Urbana-Champaign (where I had my brain bent into many strange but amusing shapes).