Numerical solution of scattering problems using a Riemann--Hilbert formulation
Numerical Analysis
2019-04-09 v1 Complex Variables
Abstract
A fast and accurate numerical method for the solution of scalar and matrix Wiener--Hopf problems is presented. The Wiener--Hopf problems are formulated as Riemann--Hilbert problems on the real line, and a numerical approach developed for these problems is used. It is shown that the known far-field behaviour of the solutions can be exploited to construct numerical schemes providing spectrally accurate results. A number of scalar and matrix Wiener--Hopf problems that generalize the classical Sommerfeld problem of diffraction of plane waves by a semi-infinite plane are solved using the approach.
Cite
@article{arxiv.1904.03762,
title = {Numerical solution of scattering problems using a Riemann--Hilbert formulation},
author = {Stefan G. Llewellyn Smith and Elena Luca},
journal= {arXiv preprint arXiv:1904.03762},
year = {2019}
}