March 2014
Intermediate
876 pages
28h 17m
English
Content preview from The Finite Element Method in Electromagnetics, 3rd Edition
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CHAPTER 4TWO-DIMENSIONAL FINITE ELEMENT ANALYSIS
In Chapter 3 we developed the finite element method and demonstrated its application in one-dimensional space. Although the method has not been widely used for one-dimensional problems, it has been popular in two-dimensional spaces, where the mathematical models of most physical problems are so complicated that an analytical or closed-form solution is often not available. Today, the finite element method has been very well developed for two-dimensional problems and plays a significant role in many science and engineering fields, including electromagnetics. In this chapter we first formulate the finite element solution for a general two-dimensional boundary-value problem using simple linear triangular elements. Then we illustrate its application to electromagnetic problems, including computation of electrostatic and magnetostatic potentials and fields, quasistatic analysis of multiconductor transmission lines, characterization of parallel-plate waveguide discontinuities, and computation of wave scattering by cylindrical structures. We conclude the chapter with an introduction to more sophisticated higher-order and isoparametric elements.
4.1 BOUNDARY-VALUE PROBLEM
The boundary-value problem under consideration is defined by the second-order partial differential equation
where ϕ is the unknown function; αx, αy, and β are ...
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