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THE GABOR FRAME AS A DISCRETIZATION FOR THE 2D TRANSVERSE-ELECTRIC SCATTERING-PROBLEM DOMAIN INTEGRAL EQUATION

By R. J. Dilz and M. C. van Beurden

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Abstract:
We apply the Gabor frame as a projection method to numerically solve a 2D transverse electric-polarized domain-integral equation for a homogeneous medium. Since the Gabor frame is spatially as well as spectrally very well convergent, it is convenient to use for solving a domain integral equation. The mixed spatial and spectral nature of the Gabor frame creates a natural and fast way to Fourier transform a function. In the spectral domain we employ a coordinate scaling to smoothen the branchcut found in the Green function. We have developed algorithms to perform multiplication and convolution efficiently, scaling as O(NlogN) on the number of Gabor coefficients, yielding an overall algorithm that also scales as O(NlogN).

Citation:
R. J. Dilz and M. C. van Beurden, "The gabor frame as a discretization for the 2D transverse-electric scattering-problem domain integral equation," Progress In Electromagnetics Research B, Vol. 69, 117-136, 2016.
doi:10.2528/PIERB16061406
http://www.jpier.org/pierb/pier.php?paper=16061406

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