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Numerical methods for mixed boundary value problems in diffraction and homogenization theory

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CATW03 - Computational complex analysis

In this talk, we present fast and accurate numerical methods for the solution of mixed boundary value problems and of the associated 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 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, as well as problems arising in homogenization theory, are solved using the new approach.

This talk is part of the Isaac Newton Institute Seminar Series series.

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