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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:297

Article

Barnett, Alex H.¹  Nelson, Bradley J.²  Mahoney, J. Matthew³ 

[1] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

[2] Stanford Univ, Inst Computat & Math Engn, Stanford, CA 94305 USA

[3] Univ Vermont, Dept Neurol Sci, Burlington, VT 05405 USA

关键词: Scattering;    Acoustic;    Helmholtz;    Graded-index;    Refraction;    Gravity;    Quantum;    Integral equation;   

DOI  :  10.1016/j.jcp.2015.05.034

来源: Elsevier

【 摘 要 】

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 10(2) nodes, with an effort that is independent of the frequency parameter E. By combining with a 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free