Electromagnetic field modeling and simulation have become increasingly popular for accurate designs in modern electrical and electronic engineering, thanks to the drastic advances in computer technology. They have been applied in many areas, in particular in industrial designs where the reduction in the number of design cycles or product's time-to-market has become very critical in a global competitive environment. For instance, in antennas, most of the practical designs are now done with simulations using commercially available software packages before actual prototyping and testing. In high-frequency electronic circuits, due to the fact that analyses based on simple circuit theory are no longer adequate, electromagnetic simulators are increasingly being used to improve design accuracy. In biomedical engineering, numerical simulations are often required to compute dosimetry in a biological body since an actual measurement is either difficult or impossible.
Many numerical methods have been developed so far for electromagnetic modeling and simulation. They present different approaches to the approximate solutions of the electromagnetic field governing equations, namely, Maxwell's equations. They include frequency-domain methods such as the finite-difference frequency-domain (FDFD) method, finite-element (FEM) method and the conventional method of moments (MoM), and the time domain methods such as finite-difference time-domain (FDTD) method, transmission-line-matrix (TLM) method, time-domain finite-element (TD-FEM) method, and time-domain integral formulations. On one hand, these methods have been proven to be effective in solving electromagnetic structure problems with their respective advantages and disadvantages. On the other hand, they appear to have been derived on different mathematical bases and their solution procedures also appear to be different from each other, presenting challenges and difficulty for students, beginners and even practitioners in understanding and applying them.
This lecture is intended to show otherwise: all the numerical methods can be generalized or derived with the method of the weighted residuals, or method of moments; As the result, an easy way to understand and apply numerical methods is presented and a new perspective on numerical methods and a new way to develop innovative numerical methods are shown. In particular, unifying concepts among numerical methods are described and based on the concepts emerging numerical methods such as meshless, hybrid and multilevel techniques are demonstrated.