Finite-difference Time-domain Method - Popularity

Popularity

Interest in FDTD Maxwell’s equations solvers has increased nearly exponentially over the past 20 years. Increasingly, engineers and scientists in nontraditional electromagnetics-related areas such as photonics and nanotechnology have become aware of the power of FDTD techniques. As shown in the figure on the right, an estimated 2,000 FDTD-related publications appeared in the science and engineering literature in 2006, as opposed to fewer than 10 as recently as 1985. The current rate of growth (based upon a study of ISI Web of Science data) is approximately 5:1 over the period 1995 to 2006. Furthermore, the descriptor "finite difference time domain" has become widely used, having appeared in this exact form in 43,900 articles as of August 7, 2011, according to Google Scholar.

Notwithstanding both the general increase in academic publication throughput during the same period and the overall expansion of interest in all Computational electromagnetics (CEM) techniques, there are seven primary reasons for the tremendous expansion of interest in FDTD computational solution approaches for Maxwell’s equations:

1. FDTD uses no linear algebra. Being a fully explicit computation, FDTD avoids the difficulties with linear algebra that limit the size of frequency-domain integral-equation and finite-element electromagnetics models to generally fewer than 109 electromagnetic field unknowns. FDTD models with as many as 109 field unknowns have been run; there is no intrinsic upper bound to this number.
2. FDTD is accurate and robust. The sources of error in FDTD calculations are well understood, and can be bounded to permit accurate models for a very large variety of electromagnetic wave interaction problems.
3. FDTD treats impulsive behavior naturally. Being a time-domain technique, FDTD directly calculates the impulse response of an electromagnetic system. Therefore, a single FDTD simulation can provide either ultrawideband temporal waveforms or the sinusoidal steady-state response at any frequency within the excitation spectrum.
4. FDTD treats nonlinear behavior naturally. Being a time-domain technique, FDTD directly calculates the nonlinear response of an electromagnetic system. This allows natural hybriding of FDTD with sets of auxiliary differential equations that describe nonlinearities from either the classical or semi-classical standpoint. One research frontier is the development of hybrid algorithms which join FDTD classical electrodynamics models with phenomena arising from quantum electrodynamics, especially vacuum fluctuations, such as the Casimir effect.
5. FDTD is a systematic approach. With FDTD, specifying a new structure to be modeled is reduced to a problem of mesh generation rather than the potentially complex reformulation of an integral equation. For example, FDTD requires no calculation of structure-dependent Green functions.
6. Parallel-processing computer architectures have come to dominate supercomputing. FDTD scales with high efficiency on parallel-processing CPU-based computers, and extremely well on recently developed GPU-based accelerator technology.
7. Computer visualization capabilities are increasing rapidly. While this trend positively influences all numerical techniques, it is of particular advantage to FDTD methods, which generate time-marched arrays of field quantities suitable for use in color videos to illustrate the field dynamics.

Taflove has argued that these factors combine to suggest that FDTD will remain one of the dominant computational electrodynamics techniques (as well as potentially other multiphysics problems).