​​​Electromagnetics and Multiphysics
​Modeling and Simulation

CEM Methods

There are many numerical methods that have been developed to solve

Maxwell’s equations. The three most-widely used methods are:

◆ Method of Moments (MoM) / Boundary Element Method (BEM)

◆ Finite Element Method (FEM)

◆ Finite-Difference Time-Domain (FDTD) Method​

​Many commercial CEM codes have been developed around particular methods, and, of course, each method has its strengths and weaknesses. Historically,

the codes themselves had their strengths and weaknesses that were

associated with the strengths and weaknesses of underlying numerical


Recognizing these differences, software developers have been addressing the shortcomings of their numerical techniques of choice. This work has led to an effective blurring of the differences between various commercial simulation packages. Furthermore, many companies started to apply multiple methods

in their packages, sometimes combining two or more methods into hybrid methods. In addition, complementary simulation techniques have been

developed to address the weaknesses of some methods, most notably,

effective formulation of unbounded (open) problems.

​As a result, detailed comparison of the various methods, which used to be an important factor in selecting software packages, is much less important now. Below is a reference list of various numerical methods used for solving

Maxwell’s equations. 

​​Method of Moments (MoM) & Boundary Element Method (BEM) 

​Generalized Multipole Technique (GMT)
Similar to MOM/BEM, but the basis functions are chosen to satisfy Maxwell's equations at some distance away from the boundaries, rather than on the boundaries.

​​Time-Domain Method of Moments (TD-MoM)
Essentially, MoM formulated in time domain rather than in frequency domain.

Finite Element Method (FEM)

Finite-Difference Time-Domain (FDTD) Method

Finite Integration Technique (FIT)

Partial Element Equivalent Circuit (PEEC) Method

Transmission Line Matrix (TLM) Method

Finite-Volume Time-Domain (FVTD) Technique 
The FVTD technique is based on the integral form of Maxwell's curl equations.

The FVTD method solves the equations numerically by integrating them over

a volume that has been meshed into arbitrarily-shaped elements;

consequently, the resulting meshes can be unstructured. FVTD combines the strengths of both FDTD and FEA methods. Unbounded problems can be

handled with the use of perfectly-matched layer (PML) absorbing boundaries.

Finite-Element Time-Domain (FETD) Technique or TDFEM 
The FETD technique takes advantage of both FDTD and FEA methods. There

are two main varieties of this technique: (1) the time-dependent Maxwell’s equations are discretized which leads to a generalization for FDTD method for unstructured meshes, (2) one of the field variables is eliminated from the Maxwell’s equations which leads to second-order (curl-curl) equations which

in turn are discretized.

Finite-Difference Frequency-Domain (FDFD) Technique

Physical Optics (PO)

Uniform Theory of Diffraction (UTD)

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