Application of the finite-element method to electromagnetic and electrical topics

The application of the finite element method in electromagnetics is reviewed. The emphasis is on formulations of 3D electromagnetic problems that are suitable for finite-element analysis and difficulties that have been encountered, such as spurious modes and gauging of vector potentials. Following an introduction to scalar and vector finite elements and a discussion of techniques for handling unbounded domains, the three main areas of application are covered: magnetic fields, electric fields, and electromagnetic waves. In the analysis of magnetic fields, the various possible potential formulations are explained and compared; magnetic material models are reviewed; and force calculation techniques are summarized. For electric fields complications arise when the relationship between electric field and charge movement is not simple: several different cases are considered. Electromagnetic wave problems are of two types: eigenvalue (resonant cavities and waveguides) and deterministic (radiation and scattering). The principle difficulty here is the occurence of spurious (non physical) modes, which can affect both types of problem. The reasons for spurious modes and the available remedies are outlined.