|Title||Numerical solution of scattering problems using a Riemann-Hilbert formulation|
|Publication Type||Journal Article|
|Year of Publication||2019|
|Authors||Smith S.GLlewell, Luca E.|
|Type of Article||Article|
|Keywords||boundary-value problem; diffraction; plane; Riemann-Hilbert; scattering; Science & Technology - Other Topics; Sommerfeld; Wiener-Hopf; wiener-hopf factorization|
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.