研究目的
To numerically solve a 2D transverse-electric-polarized domain-integral equation for a homogeneous medium using the Gabor frame as a projection method.
研究成果
The study demonstrates that the Gabor frame can be effectively used as a discretization method for solving domain integral equations in electromagnetic scattering problems, with the algorithm scaling efficiently as O(N log N). The method shows promise for larger structures but is limited by the accuracy of piecewise-linear discretization in one direction.
研究不足
The Gabor frame is not very suitable for discretizing discontinuous functions, and the method requires a relatively large minimum number of Gabor frames for small simulation regions.
1：Experimental Design and Method Selection:
The study employs the Gabor frame as a discretization method for solving the domain integral equation, leveraging its spatial and spectral convergence properties.
2：Sample Selection and Data Sources:
The method is applied to simulate electromagnetic scattering from dielectric objects in a homogeneous background medium.
3：List of Experimental Equipment and Materials:
The study is computational, focusing on algorithm development rather than physical equipment.
4：Experimental Procedures and Operational Workflow:
The algorithm involves discretizing the problem using the Gabor frame, applying Fourier transforms, and performing multiplications and convolutions efficiently.
5：Data Analysis Methods:
The accuracy and efficiency of the method are evaluated through simulations of scattering from various dielectric objects.
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