What is the "best" computational method to analyze EM interactions with
objects?
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 "surface integral technique" even though 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. A more complete overview of the various
computational electromagnetic modeling techniques is presented in the document
Survey of Numerical
Electromagnetic Modeling Techniques by Prof. Todd Hubing.