BEng - Engineering Physics
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Plane wave sources in electromagnetic FDTD simulations
Plane wave sources are important for electromagnetic simulations across the field, from biomedical imaging via microwaves, to radar cross-section in military applications. We have developed a completely new method for source conditions in Finite-Difference Time-Domain (FDTD) simulations and have proven that the method widely used in the past results in serious computational errors. Our implementation led to orders of magnitude reduction of error (down to machine precision). Effectively this drastically improves the dynamic range that it is possible to model with plane wave simulations in FDTD to the level of 300dB (at double-precision).
The theory behind this implementation is that a plane wave essentially entails projecting all the points in 3D space onto a line parallel to the direction of travel of the wave. This theory should apply to any wave physics simulation problem e.g. seismic or acoustic waves.
Alternative grids for FDTD methods
Tesselation of 3D space for finite-difference methods normally takes on a Cartesian form, mainly because it is familiar to us and also because it mimics the way we think of computer storage i.e. in array-like structures. However, Cartesian grids inherently introduce numerical dispersion errors which result in distorted wavefronts and hence simulation errors. The stability of the method is also intimately tied to the numerical dispersion properties of the method inherited from the grid.
We have recently introduced the idea of using a face-centred cubic (FCC) grid as an alternative to the Cartesian grid, based upon the idea of optimal space filling through close packing of spheres. This grid results in reduced dispersion errors and more relaxed stability bounds for both the acoustic wave equation as well as the electromagnetic vector field equations. The result is a new way of approaching the problem which provides better accuracy for the same amount of storage, or equivalently the same level of accuracy for reduced storage requirements. We have also extended this concept to the so-called Lebedev grid so as to be able to better handle anisotropic material simulations.
Dr. Mike Potter obtained his BEng in engineering physics from the Royal Military College of Canada, Kingston, Ontario, Canada, in 1992. He received his PhD in electrical engineering from the University of Victoria, Victoria, British Columbia, Canada, in 2001. From 1992 to 1997 he served as an officer in the Canadian Navy as a Combat Systems Engineer. After completing his service and attaining the rank of Lieutenant (Navy), he completed his doctoral work in Victoria, British Columbia, Canada. He was in Tucson, Arizona for a post-doctoral fellowship from 2001-2002, and joined the University of Calgary in July 2002.