Method of moments (electromagnetics)

The method of moments (MoM), also known as the moment method and method of weighted residuals, is a numerical method in computational electromagnetics. It is used in computer programs that simulate the interaction of electromagnetic fields such as radio waves with matter, for example antenna simulation programs like NEC that calculate the radiation pattern of an antenna. Generally being a frequency-domain method, it involves the projection of an integral equation into a system of linear equations by the application of appropriate boundary conditions. This is done by using discrete meshes as in finite difference and finite element methods, often for the surface. The solutions are represented with the linear combination of pre-defined basis functions; generally, the coefficients of these basis functions are the sought unknowns. Green's functions and Galerkin method play a central role in the method of moments. For many applications, the method of moments is identical to the boundary element method. It is one of the most common methods in microwave and antenna engineering. Development of boundary element method and other similar methods for different engineering applications is associated with the advent of digital computing in the 1960s. Prior to this, variational methods were applied to engineering problems at microwave frequencies by the time of World War II. While Julian Schwinger and Nathan Marcuvitz have respectively compiled these works into lecture notes and textbooks, Victor H. Rumsey has formulated these methods into the "reaction concept" in 1954. The concept was later shown to be equivalent to the Galerkin method. In the late 1950s, an early version of the method of moments was introduced by Yuen Tze Lo at a course on mathematical methods in electromagnetic theory at University of Illinois. In the 1960s, early research work on the method was published by K. Mei and J. Van Bladel. and J. H. Richmond. In the same decade, the systematic theory for the method of moments in electromagnetics was largely formalized by Roger F.