Theory and Computation of Electromagnetic Fields, 2nd Edition

Chapter 10The Method of Moments

The method of moments (MoM), also known as the moment method, is another powerful numerical technique developed to rise up to the challenge of solving increasingly complex problems in electromagnetics. Similar to the finite element method, the moment method transforms the governing equation of a boundary-value problem into a matrix equation to enable its solution on digital computers. Although the basic mathematical concepts of the moment method were in existence during the early twentieth century, true interest in it did not arise until the mid-1960s, with the publication of pioneering work by Mei and Van Bladel [1], Andreasen [2], Oshiro [3], Richmond [4], and others. The unified formulation of the method was presented by Harrington in his seminal book [5] in 1968. Since then, the method has been developed further and applied to a variety of important electromagnetic problems [6–10]. Today, it has become one of the predominant methods in computational electromagnetics. The moment method is particularly well suited to open-region electromagnetic problems such as wave scattering and antenna radiation. It is very efficient for problems involving either impenetrable or homogeneous objects. Its capability has been further enhanced by the development of a variety of fast algorithms that can deal with very large moment-method matrix equations.

In this chapter, we first describe the basic principle of the moment method using a simple electrostatic problem. ...