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Numerical solution of matrix Wiener–Hopf problems via a Riemann–Hilbert formulation

Presented by: 
Elena Luca University of California, San Diego
Date: 
Thursday 15th August 2019 - 10:30 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
In this talk, we present a fast and accurate numerical method for the solution of scalar and matrix Wiener–Hopf problems. The Wiener–Hopf problems are formulated as Riemann–Hilbert problems on the real line, and the numerical approach for such problems of e.g. Trogdon & Olver (2015) is employed. It is shown that the known far-field behaviour of the solutions can be exploited to construct tailor-made numerical schemes providing 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 new approach.

This is joint work with Prof. Stefan G. Llewellyn Smith (UCSD).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons