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arXiv · 1409.7423

High-order boundary integral equation solution of high frequency wave scattering from obstacles in an unbounded linearly stratified medium

Alex. H. Barnett·Bradley J. Nelson·J. Matthew Mahoney
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Abstract

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber (refractive index) varies linearly in one coordinate, i.e. $(\Delta + E + x_2)u(x_1,x_2) = 0$ where $E$ is a constant; this models quantum particles of fixed energy in a uniform gravitational field, and has broader applications to stratified media in acoustics, optics and seismology. We evaluate the fundamental solution efficiently with exponential accuracy via numerical saddle-point integration, using the truncated trapezoid rule with typically 100 nodes, with an effort that is independent of the frequency parameter $E$. By combining with high-order Nystrom quadrature, we are able to solve the scattering from obstacles 50 wavelengths across to 11 digits of accuracy in under a minute on a desktop or laptop.

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Alex. H. Barnett, Bradley J. Nelson, J. Matthew Mahoney. 2014-09-25. High-order boundary integral equation solution of high frequency wave scattering from obstacles in an unbounded linearly stratified medium. https://doi.org/10.1016/j.jcp.2015.05.034

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