A Galerkin Method for Strongly Singular Volume Integral Equations Arising in Grating Scattering

Details A Galerkin Method for Strongly Singular Volume Integral Equations Arising in Grating Scattering A Galerkin Method for Strongly Singular Volume Integral Equations Arising in Grating Scattering

2012-03-14

arxiv.org/abs/1203.3025v1

Mathematics

Numerical Analysis

17 pages

Scientific paper

Electromagnetic TM scattering from a dielectric diffraction grating can be described by a strongly singular volume integral equation. After periodization, the involved integral operator can be efficiently evaluated on trigonometric polynomials using the fast Fourier transform (FFT), and iterative methods can be used to solve the integral equation. We prove that a trigonometric Galerkin discretization applied to the periodized integral equation converges with optimal order to the solution of the scattering problem. Fully discrete formulas show that the numerical scheme is easy to implement and numerical examples indicate the performance of the method.

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