Numerical solution of scattering problems using a Riemann-Hilbert formulation.
| Autor: | Llewellyn Smith SG; Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, La Jolla, CA 92093-0411, USA.; Scripps Institution of Oceanography, UCSD, La Jolla, CA 92039-0213, USA., Luca E; Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, La Jolla, CA 92093-0411, USA. |
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| Jazyk: | angličtina |
| Zdroj: | Proceedings. Mathematical, physical, and engineering sciences [Proc Math Phys Eng Sci] 2019 Sep; Vol. 475 (2229), pp. 20190105. Date of Electronic Publication: 2019 Sep 04. |
| DOI: | 10.1098/rspa.2019.0105 |
| Abstrakt: | 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. Competing Interests: The authors declare that they have no competing interests. (© 2019 The Author(s).) |
| Databáze: | MEDLINE |
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