Numerical solution of scattering problems using a Riemann-Hilbert formulation

TitleNumerical solution of scattering problems using a Riemann-Hilbert formulation
Publication TypeJournal Article
Year of Publication2019
AuthorsSmith S.GLlewell, Luca E.
Volume475
Date Published2019/09
Type of ArticleArticle
ISBN Number1364-5021
Accession NumberWOS:000488551900004
Keywordsboundary-value problem; diffraction; plane; Riemann-Hilbert; scattering; Science & Technology - Other Topics; Sommerfeld; Wiener-Hopf; wiener-hopf factorization
Abstract

A fast and accurate numerical method for the solution of scalar and matrix Wiener-Hopf (WH) problems is presented. The WH 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 WH problems that generalize the classical Sommerfeld problem of diffraction of plane waves by a semi-infinite plane are solved using the approach.

DOI10.1098/rspa.2019.0105
Student Publication: 
No