What is the "best" computational method?
The answer to this question depends to a great extent on the particular
problem that is to be analyzed. Analytical methods are very good at
analyzing certain problems with a high degree of symmetry and they can
provide a great deal of insight into the behavior of many configurations.
However, an accurate evaluation of most realistic electromagnetic
configurations requires a numerical approach.
Method of Moments
Numerical techniques based on the method of weighted residuals are called
moment methods. EM modelers have come to use the term "moment method"
synonymously with "boundary element method". The boundary element method is
a moment method applied to the solution of surface integral equations.
Most commercial moment method codes are boundary element codes, however
the method of
weighted residuals can be applied to differential equations as well as
integral equations. In general, moment method techniques do an excellent
job of analyzing unbounded radiation problems and they excel at analyzing
PEC (perfect electric conductor) configurations and homogeneous dielectrics.
They are not well-suited to the analysis of complex inhomogeneous
geometries.
Finite Element Method
Finite element techniques require the entire volume of the configuration to
be meshed as opposed to surface integral techniques, which only require the
surfaces to be meshed. However each mesh element may have completely
different material properties from those of neighboring elements. In
general, finite element techniques excel at modeling complex inhomogeneous
configurations. However, they do not model unbounded radiation problems as
effectively as moment method techniques.
Finite Difference Time Domain
Finite difference time domain (FDTD) techniques also require the entire
volume to be meshed. Normally, this mesh must be uniform, so that the mesh
density is determined by the smallest detail of the configuration. Unlike
most finite element and moment method techniques, FDTD techniques work in
the time domain. This makes them very well-suited to transient analysis
problems. Like the finite element method, FDTD methods are very good at
modeling complex inhomogeneous configurations. Also, many FDTD
implementations do a better job of modeling unbounded problems than finite
element modeling codes. As a result, FDTD techniques are often the method
of choice for modeling unbounded complex inhomogeneous geometries.
Other Techniques
There are numerous other electromagnetic modeling techniques. Methods such
as the Transmission Line Matrix Method (TLM), Generalized Multipole Technique
(GMT), and others each have their own set of advantages for particular
applications.
Reference
Survey of Numerical Electromagnetic Modeling
Techniques
UMR EMC LAB Technical Report: TR91-1-001.2