Coupled FEM-BEM approaches

Abstract

In this chapter we focus on some procedures for solving eddy current problems that are based on a strategy which couples the finite element method (FEM) and the boundary element method (BEM). This kind of coupling allows the numerical approximation of the solution in unbounded domains, a typical situation in electromagnetism. The boundary element method is used for the approximation in the complement of a bounded domain: either the conductor Ω _C or else an artificial computational domain Ω, containing Ω _C but in general not very large. Instead, in the bounded domain the solution is approximated using the finite element method. Compared with the formulations presented in the previous chapters, the coupled FEM—BEM approaches compute the FEM approximation of the solution in a smaller region (say, the conductor), not required to be so large that the use of homogeneous boundary conditions is justified. This can be done because the BEM method takes into account the behaviour of the solution in the external region.