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What is FDTD and how is it used for antennas?

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The finite-difference time-domain (FDTD) method, introduced by Kane Yee in 1966, discretizes Maxwell’s curl equations on a staggered grid where electric and magnetic field components are offset by half a cell and updated alternately in time.[1][2] A single run excited by a broadband pulse yields the antenna’s response over a wide band via Fourier transform, making FDTD efficient for wideband antennas and complex inhomogeneous environments such as phones next to heads.

What sets the time step and cell size?

Stability requires the Courant condition Δt ≤ 1/(c√(1/Δx² + 1/Δy² + 1/Δz²)). Cells are usually no larger than λ/10 at the highest frequency, often λ/20 or finer, and much finer around small features; non-uniform grids and sub-gridding help.[2]

How are open boundaries handled?

Perfectly matched layers (PML), introduced by Berenger in 1994, absorb outgoing waves with very low reflection over wide angles and bandwidths; they are placed a fraction of a wavelength from the antenna. Far fields come from a near-to-far-field transformation on a surface enclosing the structure.[3][2]

What are FDTD’s weaknesses?

Staircased curved surfaces (mitigated by conformal methods), long run times for high-Q resonant antennas whose fields ring for many periods, and memory scaling with volume. The finite integration technique (FIT) used in CST’s time-domain solver is closely related.[2][4]

Frequently asked questions

Why use a Gaussian pulse?

Its spectrum covers the band of interest in one simulation.

Why do high-Q antennas take long in FDTD?

Energy decays slowly, so many time steps are needed for accurate spectra.

Is openEMS FDTD?

Yes; it uses an equivalent-circuit FDTD formulation.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

  1. “Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media”. K. S. Yee, IEEE Transactions on Antennas and Propagation, vol. 14, no. 3, pp. 302-307. May 1966.
  2. “Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed.”. A. Taflove and S. C. Hagness, Artech House. 2005.
  3. “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves”. J.-P. Berenger, Journal of Computational Physics, vol. 114, no. 2, pp. 185-200. October 1994.
  4. “CST Studio Suite (time-domain FIT and frequency-domain solvers)”. Dassault Systèmes. product documentation.
Categories: Simulation