The Finite Element Method in Electromagnetics, 3rd Edition

CHAPTER 10FINITE ELEMENT–BOUNDARY INTEGRAL METHODS

In electromagnetics and particularly in the area of electromagnetic scattering and radiation, many problems involve an open, infinite domain. Their numerical analysis is often carried out using integral equation methods and the finite element method. As we have seen in the preceding chapters, the finite element method has a relatively simple formulation and is particularly suited for modeling complex penetrable structures. More important, it produces sparse or banded matrices, which can be stored and solved efficiently using a variety of well-developed sparse or banded matrix solvers. However, when used alone, the finite element method cannot incorporate the Sommerfeld radiation condition in an exact manner because the radiation condition is valid only at infinity. One approach to alleviating this difficulty is to extend the finite element computational domain far from the source region so that the radiation condition is reasonably accurate and can be imposed at its boundary. This is a major shortcoming of the finite element method, and much effort in the past was concentrated on the development of various asymptotic or absorbing boundary conditions that are more accurate at a truncation boundary close to the source so that they can be used to reduce the computational domain (see Section 4.7.2 and Chapter 9). The major advantage of the absorbing boundary conditions, which include those derived from perfectly matched layers (PMLs), ...