The solution of the scalar wave equation in the exterior of a sphere

JOURNAL OF COMPUTATIONAL PHYSICS

卷:274

Article

Greengard, Leslie¹  Hagstrom, Thomas²  Jiang, Shidong³ 

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[2] So Methodist Univ, Dept Math, Dallas, TX 75275 USA

[3] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA

关键词: Wave equation;    Scattering;    Time-domain;    Separation of variables;    Numerical stability;   

DOI  :  10.1016/j.jcp.2014.05.031

来源: Elsevier

【 摘 要 】

We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that permits the evaluation of the solution at an arbitrary target, without the use of a spatial grid and without numerical dispersion error. In the process, we correct some errors in the analytic literature concerning the asymptotic behavior of the logarithmic derivative of the spherical modified Hankel function. We illustrate the performance of the method with several numerical examples. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free