Computational numerical techniques can overcome the inability to derive closed form solutions of Maxwell's equations under various constitutive relations of media, and boundary conditions.
Also calculating power flow direction (Poynting vector), a waveguide's normal modes, media-generated wave dispersion, and scattering can be computed from the E and H fields.
CEM models may or may not assume symmetry, simplifying real world structures to idealized cylinders, spheres, and other regular geometrical objects.
CEM models extensively make use of symmetry, and solve for reduced dimensionality from 3 spatial dimensions to 2D and even 1D.
Transient response and impulse field effects are more accurately modeled by CEM in time domain, by FDTD.
CEM is application specific, even if different techniques converge to the same field and power distributions in the modeled domain.
Davidson[1] gives two tables comparing the FEM, MoM and FDTD techniques in the way they are normally implemented.
The discrete dipole approximation is a flexible technique for computing scattering and absorption by targets of arbitrary geometry.
[5] The FMM has also applications in computational bioelectromagnetics in the Charge based boundary element fast multipole method.
While the fast multipole method is useful for accelerating MoM solutions of integral equations with static or frequency-domain oscillatory kernels, the plane wave time-domain (PWTD) algorithm employs similar ideas to accelerate the MoM solution of time-domain integral equations involving the retarded potential.
Unlike MoM, PEEC is a full spectrum method valid from dc to the maximum frequency determined by the meshing.
Besides providing a direct current solution, it has several other advantages over a MoM analysis for this class of problems since any type of circuit element can be included in a straightforward way with appropriate matrix stamps.
[7] This model extension, which is consistent with the classical orthogonal formulation, includes the Manhattan representation of the geometries in addition to the more general quadrilateral and hexahedral elements.
[8] The Cagniard-deHoop method of moments (CdH-MoM) is a 3-D full-wave time-domain integral-equation technique that is formulated via the Lorentz reciprocity theorem.
The CdH-MoM has been originally applied to time-domain performance studies of cylindrical and planar antennas[9] and, more recently, to the TD EM scattering analysis of transmission lines in the presence of thin sheets[10] and electromagnetic metasurfaces,[11][12] for example.
Concepts include boundary conditions, linear algebra, injecting sources, representing devices numerically, and post-processing field data to calculate meaningful things.
FDTD is the only technique where one person can realistically implement oneself in a reasonable time frame, but even then, this will be for a quite specific problem.
The basic FDTD algorithm traces back to a seminal 1966 paper by Kane Yee in IEEE Transactions on Antennas and Propagation.
Allen Taflove originated the descriptor "Finite-difference time-domain" and its corresponding "FDTD" acronym in a 1980 paper in IEEE Trans.
Since about 1990, FDTD techniques have emerged as the primary means to model many scientific and engineering problems addressing electromagnetic wave interactions with material structures.
[14] Current FDTD modeling applications range from near-DC (ultralow-frequency geophysics involving the entire Earth-ionosphere waveguide) through microwaves (radar signature technology, antennas, wireless communications devices, digital interconnects, biomedical imaging/treatment) to visible light (photonic crystals, nanoplasmonics, solitons, and biophotonics).
Like FVTD, the numerical flux is used to exchange information between neighboring elements, thus all operations of DGTD are local and easily parallelizable.
With the above merits, DGTD method is widely implemented for the transient analysis of multiscale problems involving large number of unknowns.
[15][16] MRTD is an adaptive alternative to the finite difference time domain method (FDTD) based on wavelet analysis.
The solution approach is based either on eliminating the time derivatives completely (steady state problems), or rendering the PDE into an equivalent ordinary differential equation, which is then solved using standard techniques such as finite differences, etc.
The finite integration technique (FIT) is a spatial discretization scheme to numerically solve electromagnetic field problems in time and frequency domain.
The basic idea of this approach is to apply the Maxwell equations in integral form to a set of staggered grids.
PSTD causes negligible numerical phase velocity anisotropy errors relative to FDTD, and therefore allows problems of much greater electrical size to be modeled.
Because the fields are held as functions of time, this enables arbitrary dispersion in the propagation medium to be rapidly and accurately modelled with minimal effort.
[20] Transmission line matrix (TLM) can be formulated in several means as a direct set of lumped elements solvable directly by a circuit solver (ala SPICE, HSPICE, et al.), as a custom network of elements or via a scattering matrix approach.