A system of boundary integral equations for the transmission problem in acoustics

Authors:
George C. Hsiao;Liwei Xu
Affiliations:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716-2553, United States;Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, United States
Venue:
Applied Numerical Mathematics
Year:
2011

Citing 8
Cited 1

A fast algorithm for particle simulations

Journal of Computational Physics
On single integral equations for the transmission problem of acoustics

SIAM Journal on Applied Mathematics
Rapid solution of integral equations of scattering theory in two dimensions

Journal of Computational Physics
The resistive and conductive problems for the Exterior Helmholtz Equation

SIAM Journal on Applied Mathematics
Fast and Efficient Algorithms in Computational Electromagnetics

Fast and Efficient Algorithms in Computational Electromagnetics
Stabilized FEM-BEM Coupling for Helmholtz Transmission Problems

SIAM Journal on Numerical Analysis
Mixed boundary integral methods for Helmholtz transmission problems

Journal of Computational and Applied Mathematics
Symmetric boundary integral formulations for Helmholtz transmission problems

Applied Numerical Mathematics

A fast and high-order method for the three-dimensional elastic wave scattering problem

Journal of Computational Physics

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper, we reduce the classical two-dimensional transmission problem in acoustic scattering to a system of coupled boundary integral equations (BIEs), and consider the weak formulation of the resulting equations. Uniqueness and existence results for the weak solution of corresponding variational equations are established. In contrast to the coupled system in Costabel and Stephan (1985) [4], we need to take into account exceptional frequencies to obtain the unique solvability. Boundary element methods (BEM) based on both the standard and a two-level fast multipole Galerkin schemes are employed to compute the solution of the variational equation. Numerical results are presented to verify the efficiency and accuracy of the numerical methods.