The generalization of a two-dimensional spatial spectral volume integral equation to a three-dimensional spatial spectral integral equation formulation for electromagnetic scattering from dielectric objects in a stratified dielectric medium is explained. In the spectral domain, the Green function, contrast current density, and scattered electric field are represented on a complex integration manifold that evades the poles and branch cuts that are present in the Green function. In the spatial domain, the field-material interactions are reformulated by a normal-vector field approach, which obeys the Li factorization rules. Numerical evidence is shown that the computation time of this method scales as O(Nlog N) on the number of unknowns. The accuracy of the method for three numerical examples is compared to a finite element method reference.
Bibliographical notePart of the following topical collections:•2017 - Optical Wave and Waveguide Theory and Numerical Modelling
- Electromagnetic scattering
- Gabor frames
- Integral equations
- Spectral methods