Computational aspects of a spatial-spectral domain integral equation for scattering by objects of large longitudinal extent

Abstract

-With a 3D spatial spectral integralequation method for EM scattering from finite objects, a significant part of the computation time is spent on a middle region around the origin of the spectral domain. Especially when the scatterer extends to more than a wavelength in the stratification direction, a fine discretization on this region is required, consuming much computation time in the transformation to the spatial domain. Numerical evidence is shown that the information in the middle region of the spectral domain is largely linearly dependent. Therefore, a truncated singular-value decomposition is proposed to make the computation time largely independent of the discretization on this middle region. For a practical example the increased computational efficiency and the approximation error of the singular-value decomposition are shown.

A Hermite-Interpolation Discretization and a Uniform Path Deformation for the Spatial Spectral Domain Integral Equation Method in Multilayered Media for Te Polarization

“…This method is not very optimized, but since the M-part is small, not much computation time is used. A more optimized method for this part was presented in [22].…”

A Parallel 3D Spatial Spectral Volume Integral Equation Method for Electromagnetic Scattering from Finite Scatterers

“…According to [9], the most time-consuming components of this Maxwell solver [6] are the computation of the Gabor-frame expansion coefficients of the scatterers and iteratively solving the VIE, which take 146 seconds (12.7%) and 962 seconds (84.1%) for a 3D simulation domain of 60 cubic wavelengths with 36 scatterers as in [10], respectively. The extension of this solver to scatterometry applications is challenging: a simulation domain quickly becomes larger than 1000λ 3 , with λ the wavelength, since the illumination areas can range up to several micrometers [11,Ch.…”