This can make long-time simulations and high frequency propagation challenging to compute with FDTD, as the initial error (and thus the grid size) have to be really small to compensate the effect of this error accumulation. This is called numerical dispersion error, and it can quickly become one of the main accuracy limitations of the FDTD.Ĭonsequently, in FDTD the error accumulates over time, especially for high frequencies. As with any finite difference method, the propagation of a wave in the discrete grid doesn’t obey the exact dispersion relations of Maxwell’s equations, but rather an approximate version of them. The flexibility of time-domain discretization comes at a certain price, tough. Some of the main advantages of the FDTD is that, being based on the time domain, the FDTD method supports a wide range of frequencies, and additionally, the incorporation of non-linear materials is straightforward. The FDTD acronym, in turn, was coined later by Taflove in the 1980’s. The method was first proposed in a seminal 1966 paper by Kane Yee. Method of Moments (MoM), or equivalently, Boundary Element Method (BEM)īefore digging deeper into each one of these options, lets give a short summary of this three alternatives: MethodįDTD is the application of finite differences to Maxwell’s equations, in a second order, stable, staggered-grid approach for electric and magnetic fields.There are three basic numerical approaches for electromagnetic simulation, namely: In this post we discuss the basic trade-offs between these families of methods, and we give some references to some of the best open-source implementations out there. Each of these approaches is best suited for certain cases, and has advantages and disadvantages. There are three major family of numerical methods for Electromagnetic simulations: FDTD, FEM and MoM. There are also many ways to approach the computations required in these various areas. Computational Electromagnetics encompasses a wide range of application areas, including antennas, nano-photonics, solar cells, metamaterials, lasers, and many more.
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