Numerical Analysis in Electromagnetics

EM modeling and simulation (EM-MODSIM) necessitates a good understanding and use of numerical analysis. Built-in MATLAB functions such as roots(), diff(), gradient(), trapz(), and inv() can be used for most of numerical analysis jobs. Although MATLAB makes life easy for engineers, EM-MODSIM people should always depend on their own codes; at least aware of and well understand what is going on behind these built-in commands. This chapter reviews briefly some numerical analysis fundamentals which are essential for EM-MODSIM studies. Taylor's expansion is one of a few important methods for the numerical solution of ordinary differential equations (ODEs). An important topic in numerical analysis is the root finding of a given nonlinear function. Method of moments (MoM) is used to solve linear systems of equations. Multiloop circuits are also solved using linear systems of equations.