Numerical solution and a posteriori error estimation of exterior acoustics problems by a boundary element method at high wave numbers

This paper is concerned with the application of boundary element methods to the exterior acoustical problem at high wave numbers. The major issues here are to establish a strong theoretical foundation for the application of the Burton-Miller integral equation and develop a practical way for its numerical implementation. Unlike many conventional approaches, the problem in this study is formulated by the Galerkin method. Through an analysis on its ellipticity, the Burton-Miller equation is proven to be well-posed in the H-1/2-Sobolev space and its approximation can attain a quasioptimal convergence rate. The Galerkin method avoids sensitive properties of hypersingular integration, simplifies the numerical implementation, and improves the quality of the numerical solutions, especially at high wave numbers. An L(2)-norm residual error estimation technique is also implemented for an adaptive scheme for these problems. The numerical implementation is completed on parallel distributed-memory machines as well as conventional sequential machines. The validation of the method at high wave numbers is done through tests on a series of numerical examples. (C) 1996 Acoustical Society of America.