The Method of Moments (MOM) and Related Codes

Integral equation methods have proved to be powerful tools for the numerical computation of electromagnetic fields. Among the integral equation methods the method of moments (MOM) is frequently used for the analysis of EMC problems. In this contribution the mathematical basis and the principle of the MOM are introduced. Meanwhile many MOM variants exist, concerning e.g. the formulation of the integral equation (EFIE, MFIE, CFIE, ...) or concerning modeling by means of thin-wire structures using line-current sources or with surface structures applying surface currents and discretization by quadrangular or triangular surface patches. The tutorial lesson will treat some of these variants. It is also shown how to analyze dielectric materials. In the MOM it is required to solve an equation system with a fully occupied matrix, and problems of industrial applications can lead to many thousands of unknowns. Therefore it can be advantageous to choose an iterative method instead of Gauss elimination or LU decomposition to solve the equation system. The contribution gives some recommendations for modeling and computation, concerning computer storage and frequency-dependent segmentation. The conditions for thin-wire simulations are shown as well as some modeling requirements when conductors are simulated by surface patches. Some remarks on possible checks concerning the validity of the solution follow. A comparison of the MOM with differential equation approaches shows that the MOM offers a lot of advantages. Particularly favorable is the MOM when exterior problems (open geometries) have to be treated, and when only few different, linear and homogeneous media are considered. In the EMC practice there are many applications of this type, for instance radiation from short-wave antennas, far-field evaluations like radiation diagrams, or coupling through apertures out of or into enclosures. As will be shown in the contribution the MOM is very suitable for hybridizing with analytical and numerical procedures like GTD/UTD. When combining with analytical methods, e.g. transmission line theory, a lot of sophisticated tasks can be solved, e.g. precise and reliable computation of high values of shielding effectiveness or coupling into shielded cables. In contrast to the FDTD method or the FEM, the MOM requires only a surface gridding, therefore the expenditure for gridding is relatively low. In the tutorial lecture some codes which are based on the MOM are quoted. Finally, some examples which have been treated by means of the MOM illustrate the applicability of this method.