Non-uniform sources in the total/scattered finite difference time domain (FDTD) method
Date
2018-11-01
Authors
Potter, Michael E.
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Abstract
The Finite-Difference Time-Domain (FDTD) method has been used extensively in
electromagnetic field modeling because of its ability to robustly handle interactions of fields
with complex heterogeneous structures. In particular, the total/scattered field formulation
has allowed for efficient implementation of arbitrarily directed uniform plane waves, consequently
facilitating efficient modeling of far-field scattering problems. The total/scattered
approach is not restricted to plane waves and can be expanded to any waveforms that can
be described in analytical or semi-analytical form.
While existing formulations of FDTD have been immensely successful, they are
not well suited to problems that involve near field scattering/interaction problems, where
both the source and object are in the same domain but at a substantial distance from each
other. This is due to the exceedingly high demands for computational resources that may
result from the domain size, and/or dramatically different requirements for the mesh density
in the source and object areas. One solution to this problem is to separate the domain into
source and scatterer regions coupled by surface boundary radiation conditions. However,
this method can incur large storage requirements for calculation of the radiation conditions.
A specific near-field situation of interest to the utility industry is the case of workers
near high voltage powerlines. In this instance, the field pattern takes on a cylindrical,
transverse electromagnetic character. More general radiating sources can be accurately
represented in the near-field by using spherical wave expansions, which are often used to
represent antennas measured on test ranges. Successful implementation of these analytic
solutions is feasible within the FDTD framework, and would allow for the illumination of
the scatterer modeled at a considerably lower cost than in the standard approach. This
thesis presents a method where these non-uniform, near-field, sources can be implemented
implicitly as source conditions in an existing FDTD method. The specific case of powerline
fields is described first, followed by the more general case of spherical waves.
The analytic solution for powerline fields is implemented to show that near-field
source configuration can be successfully modeled implicitly with accurate and efficient results.
The method is validated by comparing with known analytic solutions, with very good
accuracy being achieved. Then, a specific example of a human under a powerline close by is
modeled to examine predictions made earlier under the assumption of a plane wave source
condition. For a similar powerline source configuration, results of organ dosimetry predict
that induced fields are from ten to sixty percent greater than predicted with the plane wave
source.
This same approach is applied to model a more general and difficult problem,
namely spherical waves as sources in the total/scattered FDTD, called the SW-FDTD.
Since transverse properties of spherical modes are known, the behavior of a mode can be
represented on a one-dimensional radial grid. Thus, much like the plane wave sources in the
FDTD method, the spherical wave modes are time-stepped on one-dimensional staggered
electric/magnetic field source grids in the radial direction, representing mode propagation
in free space. Spherical wave modes can then be interpolated and summed on the Huygens’
surface to represent the total field of the source, thus providing the coupling between the
complex source and a scatterer using one-dimensional grids. It is assumed that the object of
interest is beyond the reactive near-field of the source, and therefore there is no significant
coupling between source and object.
The SW-FDTD method is validated by comparing simulations with several analytic
solutions that increase in complexity, demonstrating very good accuracy. Issues
relating to the numerical implementation are discussed, including the effects of numerical
dispersion, stability, and simple Mur first order boundary conditions. Incorporation of the
method as a source condition in an existing FDTD program, and validation of this synthesis,
show that the SW-FDTD method can implictly model sources as accurately as explicit
models do. The efficiency, and the reduction of errors remain issues for further research to
improve the overall utility of the SW-FDTD method.
Description
Keywords
Finite differences, Time-domain analysis, Electromagnetism