Describing discontinuous finite 3D scattering objects in Gabor coefficients: fast and accurate methods

Area of Science:

• Computational electromagnetics
• Applied mathematics
• Wave scattering theory

Background:

• Accurate computation of Gabor coefficients is crucial for Gabor-frame-based spatial spectral Maxwell solvers.
• Traditional discrete Gabor transform methods often require heavy oversampling for discontinuous functions, impacting efficiency.
• Electromagnetic scattering in layered media presents computational challenges.

Purpose of the Study:

• To present two novel, accurate, and efficient methods for computing Gabor coefficients.
• To address the limitations of traditional discrete Gabor transform methods for scattering object cross sections.
• To improve the analysis of three-dimensional scattering objects in layered media.

Main Methods:

• Method 1: Combines analytically obtained 2D Fourier transform of object cross sections (described by 2D characteristic functions) with the discrete Gabor transform.
• Method 2: Utilizes the divergence theorem and expansion of the dual window function for Gabor coefficient computation.
• Both methods employ semi-analytical approaches to mitigate oversampling requirements.

Main Results:

• Significant improvements in accuracy and computation time demonstrated for both proposed methods compared to the traditional discrete Gabor transform.
• Effective handling of discontinuous functions in scattering object cross sections.
• Enhanced performance for Gabor-frame-based spatial spectral Maxwell solvers.

Conclusions:

• The presented methods offer substantial advancements in computing Gabor coefficients for electromagnetic scattering.
• These techniques provide more efficient and accurate analysis of scattering objects, particularly those with discontinuous cross sections.
• The findings contribute to the development of more powerful computational electromagnetics tools.