Fast solution of electromagnetic boundary value problems by the characteristic basis functions/FEM approach

The finite element method (FEM) is a powerful approach to the numerical solution of electromagnetic scattering and/or radiation problems. The method described in this paper resembles the domain decomposition method, but it exhibits some distinctive differences in the implementation. The computational domain (composed of the FEM mesh) is subdivided into a number of subdomains and a hierarchical class of characteristic basis functions (CBFs) are evaluated. The computation of the CBFs is based on the physics of the problem, since they are computed via the couplings of the subdomains. The hierarchical structure is based on the order of the couplings, as is seen in the derivation of the algorithm.