Computing and compression of the boundary element matrices for the Helmholtz equation

Abstract

The boundary integral formulation for the Dirichlet boundary value problem is considered and the collocation boundary element method for the discretisation of the problem is used. In order to compute the entries of the matrices for several wave numbers, the inverse Fourier transform with respect to the wave number is applied to them. The analytical forms and some important properties of the transformed matrices are deduced. After applying the Fourier transform, new matrices depending on the wave number are obtained and the associated linear systems are treated. Further, the adaptive cross approximation (ACA) algorithm is applied to the matrices solving efficiently the linear systems. Finally, some numerical examples for the solution are presented.