March 2014
Intermediate
876 pages
28h 17m
English
Content preview from The Finite Element Method in Electromagnetics, 3rd Edition
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CHAPTER 9ABSORBING BOUNDARY CONDITIONS
When solving open-region scattering/radiation problems using the finite element method, the infinite region exterior to the scatterer/radiator must be truncated with an artificial boundary to limit the size of the computational domain. Consequently, a boundary condition must be introduced at this artificial boundary for a unique finite element solution. Such a condition should make the boundary appear as transparent as possible to the scattered/radiated field, or in other words, it should minimize the nonphysical reflections from that boundary. A class of boundary conditions designed for this purpose is called absorbing boundary conditions or radiation boundary conditions, which, unlike the boundary integral equations or eigenfunction expansions discussed in Chapters 10 and 11, lead to localized relations between the boundary fields. Consequently, the highly sparse and banded nature of the finite element system matrices—a distinct advantage of the finite element method—is retained. Some of these absorbing boundary conditions were employed, without derivation, in Section 4.7.2 for two-dimensional scattering computations.
In this chapter we discuss the derivation of the absorbing boundary conditions for two-and three-dimensional scattering and antenna applications and examine their performance in terms of the plane-wave reflection coefficient. Then we describe an adaptive approach to systematically improve the accuracy of the absorbing boundary ...
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