Exponential decay of errors of a fundamental solution method applied to a reduced wave problem in the exterior region of a disc

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:231

Article

Chiba, Fumihiro¹ 

[1] Univ Electrocommun, Fac Electrocommun, Dept Comp Sci, Chofu, Tokyo 1828585, Japan

关键词: Reduced wave problem;    Helmholtz equation;    Fundamental solution method;    Collocation method for integral equations of convolution type;    Dirichlet boundary value problem;    Normalized wave number;    Shadow;   

DOI  :  10.1016/j.cam.2009.05.026

来源: Elsevier

【 摘 要 】

This paper concerns a fundamental solution method (FSM, in abbreviation) applied to a reduced wave problem in the exterior region of a disc. The convergent rate of approximate solutions to the exact one is proven to be asymptotically exponentially decreasing with respect to the number N of collocation points employed in an approximate problem. Using obtained FSM solutions we add two numerical tests: numerical estimate of errors including cases of high wave numbers; and visualization of total waves appeared in the scattering phenomena around a circular obstacle in the cases of kappa = 50 and kappa = 100. where kappa is a normalized wave number, defined through kappa = length of wave number vector x radius of the disc. In the second test, the total waves almost vanish behind the disc, seemingly corresponding to the phenomenon of shadowing in the classical literature of physics. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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