Numerical solution of scattering problems using a Riemann–Hilbert formulation-Reference-Cited by-同舟云学术

Numerical solution of scattering problems using a Riemann–Hilbert formulation

Published:2019-09 Issue:2229 Volume:475 Page:20190105
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Llewellyn Smith Stefan G.¹²^ORCID,Luca Elena¹^ORCID

Affiliation:

1. Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, La Jolla, CA 92093-0411, USA

2. Scripps Institution of Oceanography, UCSD, La Jolla, CA 92039-0213, USA

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.

Funder

Division of Mathematical Sciences

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2019.0105

Reference43 articles.

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