BEM for Helmholtz Equations

Abstract

In this work we study the application of the boundary element method for solving the Helmholtz equation in 3D. Contrary to the finite element method, one does not need to discretize the whole domain and thus the problem dimension is reduced. This advantage is most pronounced when solving an exterior problem, i.e., a problem on an unbounded domain. On the other hand, it should be mentioned that the boundary element discretization leads to dense matrices and is computationally demanding. In this thesis we concentrate on the Galerkin approach known, e.g., from the finite element method. In sections devoted to the discretization of boundary integral equations we describe the combination of analytic and numerical integration used for the computation of matrices generated by boundary integral operators. We also mention the collocation method, which gained its popularity among engineers due to its simplicity.