International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 11, Pages 687-694
doi:10.1155/S0161171202110027

Solving the Dirichlet acoustic scattering problem for a surface with added bumps using the Green's function for the original surface

Maxim J. Goldberg1,2 and Seonja Kim3

1Physical Sciences Department, York College of Pennsylvania, York 17405, PA, USA
2School of Theoretical and Applied Science, Ramapo College of New Jersey, 505 Ramapo Valley Road, Mahwah 07430, NJ, USA
3School of Computer Science and Information Systems, Fairleigh Dickinson University, 1000 River Road, Mail Code T-BE2-01, Teaneck 07666, NJ, USA

Received 1 October 2001

Copyright © 2002 Maxim J. Goldberg and Seonja Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We solve the Dirichlet problem for acoustic scattering from a surface which has been perturbed by the addition of one or more bumps. We build the solution for the bumpy case using the Green's function for the unperturbed surface, and the solution of a local integral equation in which the integration is carried out only over the added bumps. We conclude by giving an alternative formulation of our method for the special case of a bump on a plane.