Fast algorithms applied to the acoustical energy boundary element method
The Energy Boundary Element Method (EBEM) aims at the solution of acoustic high frequency problems, where the classic BEM becomes inefficient due to the large number of degrees of freedom (DOF) required. A transition to non-phased energetic state variables removes the correlation between the investigated frequency range and the element size. In the EBEM the number of DOF is thus determined primarily by the complexity of the geometry. In order to speed up the computation and to handle structures of very high geometric complexity, a fast multipole algorithm for the EBEM is investigated. It has a great potential to reduce the numerical effort in the Boundary Element Method (BEM). Helmholtz and Laplace problems have been solved very efficiently applying this algorithm. However, the kernels used in the EBEM require an adaptation of the algorithm. In this paper the development of a fast multipole formulation of the EBEM is presented.