Solution of Exterior Acoustic Problems by the Boundary Element Method at High Wave Number, Error Estimation and Parallel Computation

This paper is concerned with the application of the boundary element method 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 Hl/2-Sobolev space and its approximation can attain a quasi-optimal convergence rate. The Galerkin scheme avoids sensitive properties of hypersingular integration, simplifies the numerical implementation, and improves the quality of the numerical solutions, especially in the range of high wave numbers. An L2-norm residual error estimation technique is also implemented for an adaptive scheme for these problems. The numerical implementation is completed on parallel distributedmemory machines. The validation of the method for high wave numbers is done through tests on a series of numerical examples.