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

Abstract

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.

Accuracy control in the optimization of microwave devices by finite-element methods

“…Over the years, finite elements were pioneered to suit the needs of electromagnetic problems [19][20][21][22]. Today, finite elements are a mainstay in electrical engineering and are a well-developed electromagnetic analysis CAO tool [23][24][25].…”

Enhancement of the intrinsic gamma-ray stopping efficiency of Geiger–Müller counters

“…It was thought that the most suitable way to investigate the potential effects of the electrically insulating disks on the electric field of the counter would be through the use of the finite element analysis method which also is applied to calculations of electromagnetic fields in arbitrary geometries [18].…”

A 2-D model that accounts for 3-D fringing in MEMS devices

“…As is well known, when FEA is used for modeling open-space problems, one must address the problem of boundary conditions at infinity. Many well-known techniques exist [25], and we have chosen the simplest, that of creating a large bounding box and setting the boundary conditions on the surface of this box to zero.…”