Numerical solution of scattering problems using a Riemann--Hilbert\n formulation

2019/04/07 by Stefan G. Llewellyn Smith, Elena Luca, Smith, Stefan G. Llewellyn +1
Mathematics · Engineering · #Algebraic and Geometric Analysis #Numerical methods in inverse problems #Geophysics and Sensor Technology

paper · pdf · doi:10.48550/arxiv.1904.03762

Abstract

A fast and accurate numerical method for the solution of scalar and matrix\nWiener--Hopf problems is presented. The Wiener--Hopf problems are formulated as\nRiemann--Hilbert problems on the real line, and a numerical approach developed\nfor these problems is used. It is shown that the known far-field behaviour of\nthe solutions can be exploited to construct numerical schemes providing\nspectrally accurate results. A number of scalar and matrix Wiener--Hopf\nproblems that generalize the classical Sommerfeld problem of diffraction of\nplane waves by a semi-infinite plane are solved using the approach.\n

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