Journal of Computational Physics
A fast, higher-order solver for scattering by penetrable bodies in three dimensions
Journal of Computational Physics
The efficient solution of electromagnetic scattering for inhomogeneous media
Journal of Computational and Applied Mathematics
Preconditioning techniques for the iterative solution of scattering problems
Journal of Computational and Applied Mathematics
Fast convolution with the free space Helmholtz Green's function
Journal of Computational Physics
Generation of smooth grids with line control for scattering from multiple obstacles
Mathematics and Computers in Simulation
| Hi-index | 0.02 |
This paper provides a theoretical analysis of a higher-order, FFT-based integral equation method introduced recently [IEEE Trans. Antennas and Propagation, 48 (2000), pp. 1862--1864] for the evaluation of transverse electric--polarized electromagnetic scattering from a bounded, penetrable inhomogeneity in two-dimensional space. Roughly speaking, this method is based on Fourier smoothing of the integral operator and the refractive index n(x). Here we prove that the solution of the resulting integral equation approximates the solution of the exact integral equation with higher-order accuracy, even when n(x) is a discontinuous function---as suggested by the numerical experiments contained in the paper mentioned above. In detail, we relate the convergence rates of the computed interior and exterior fields to the regularity of the scatterer, and we demonstrate, with a few numerical examples, that the predicted convergence rates are achieved in practice.