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AN APPROXIMATE BOUNDARY INTEGRAL METHOD FOR ACOUSTIC SCATTERING IN SHALLOW OCEANS

Department of Mathematics, Georgetown University, Washington, DC20057, USA

This author's research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation, the Minnesota Supercomputer Institute and the Alliant Techsystem Co.

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YI YAN

Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, USA

This author's work was supported in part by the National Science Foundation Grant RII-8610671 and the Commonwealth of Kentucky through the University of Kentucky's Center for Computational Sciences. AMS(MOS) subject classifications: Primary 35A40, 35J05; Secondary 65N99, 65R20, 76Q05, 76–08.

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https://doi.org/10.1142/S0218396X93000044Cited by:4 (Source: Crossref)

Abstract

The problem of a time-harmonic acoustic wave scattering from a cylindrical object in shallow oceans is solved by an approximate boundary integral method. In the method we employ a Green's function of the Helmholtz equation with sound soft sea level and sound hard sea bottom conditions, and reformulate the problem into a boundary integral equation on the surface of the scattering object. The kernel of the integral equation is given by an infinite series, and is approximated by an appropriate truncation. The integral equation is then fully discretized by applying a quadrature rule. The method has an O(N⁻³) rate of convergence. Various numerical examples are presented.