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

Roeland J. Dilz | Zendy; Martijn C. van Beurden | Zendy

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

Author(s) -

Roeland J. Dilz,

Martijn C. van Beurden

Publication year - 2016

Publication title -

progress in electromagnetics research b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.208

H-Index - 47

ISSN - 1937-6472

DOI - 10.2528/pierb16061406

Subject(s) - discretization , domain (mathematical analysis) , transverse plane , scattering , mathematical analysis , frame (networking) , mathematics , physics , computer science , optics , telecommunications , medicine , anatomy

We apply the Gabor frame as a projection method to numerically solve a 2D ransverse-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(N log N ) on the number of Gabor coefficients, yielding an overall algorithm that also scales as O(N log N ).

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