Finite Difference Time Domain (FDTD)
- Finite Difference Time Domain (FDTD)
FDTD Yee cell Voxel mesh of a Cessna aircraft for FDTD solution
General Applicability of the Technique
The finite difference time domain (FDTD) solution technique has gained popularity in computational electromagnetics (CEM) over the past decade due to its relatively straightforward and efficient formulation.
The FDTD method is well suited to modelling inhomogeneous materials and simulation of wideband antennas.
Technical FoundationElectric and magnetic fields are computed on two offset rectilinear grids and marched in time. This approach allows for the use of central differencing to approximate Maxwell’s equations, achieving second order accuracy using first order numeric differentiation. Fourier techniques are applied to convert the native time domain results into the frequency domain: a single FDTD simulation with a pulsed excitation can be used to characterise a wideband frequency response of an antenna.The FDTD method uses a volume meshing technique that employs voxels to accurately mesh the computational space. Voxels are calculated on a non-uniform rectilinear mesh: the mesh can be locally refined in regions of geometric detail or in areas where high field gradients are expected.The method is conditionally stable and the time step must be calculated from the smallest mesh cell to guarantee stability. Including small geometrical features will reduce the time step, resulting in longer computational time.Non-conformal alignment or curvatures in the model can also result in a staircase approximation of a model, which can be improved by further refinement of the mesh or (when possible) rotating the geometry to be conformally aligned in the FDTD grid.The FDTD method also lends itself well to various parallelisation techniques. Currently, FEKO supports the use of GPU accelerations to obtain significant speedups.
Typical Application of the FDTD
Possible applications of the FDTD span a wide range of problems. It is best suited to problems that include highly inhomogeneous materials and therefore a popular choice in biomedical applications for the modelling of human phantoms. The FDTD is a very efficient solution for wideband problems, and is well-suited to analyse broadband antennas.
FDTD voxel mesh of a GSM antenna
FDTD voxel mesh of a human head, with FDTD boundaries