On the nature of discrete plan wave and huygens' source for a perfectly matched tfsf implementation in the fdtd scheme
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2010
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Abstract
Scattered wave problems resulting from objects exhibiting complex geometries and high heterogeneities which often occur in applied science or engineering applications can only be solved by numerical means. An important class of these problems comes from scatterers being radiated by a far-field source such as a plane wave. In the FDTD (Finite-Difference Time-Domain) numerical method, the Total-Field
Scattered-Field (TFSF) technique is a Huygens' source algorithm that can source this far-field problem efficiently. For most applications the time-domain IFA (Incident Field Array) method has been successfully used for a number of years. Other applications such as radar-cross-section (RCS) evaluation, backscattered field from biomedical cells, or buried objects where the material contrast against the uniform
background is small, can all have a scattered field well below the incident wave, i.e. a dynamic range smaller than -100 dB. An accurate frequency domain known as the AFP ( Analytic Field Propagator) method was recently developed to address such a small scattering analysis. However, the preprocessing stage necessitates prodigious
data storage, therefore limiting t his accurate technique to 2D and a special case of 3D problems.
This thesis first introduces a one-to-many mapping technique to reduce a general 3D plane wave source into a 1D representation. Hence, the memory storage problem of the AFP method is mitigated significantly. It is also demonstrated that an FDTD plane wave propagation direction can be expressed in terms of a discrete angle called the rational angle. The one-to-many mapping and rational angle are then used to construct a true time-domain numerical plane wave source valid for any scheme where partial derivative operators are approximated with finite differencing counterparts; the technique developed here is not unique to FDTD algorithms. When used as the Huygens' source for a 1D / 2D / 3D TFSF formulation, the proposed algorithm completely removes the spurious scattered field associated with existing formulations. This solution has never before available to the FDTD community. Because
of the recursive algorithm, the large memory issue is also avoided. Numerical examples confirm the leakage error is at the finite precision limit (-300 dB for double precision).
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Bibliography: p. 129-142
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Citation
Tan, T. M. (2010). On the nature of discrete plan wave and huygens' source for a perfectly matched tfsf implementation in the fdtd scheme (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/3506