Fast Boundary Element Methods in Acoustics

Wave propagation problems play an important role, not only in the scientific community, but also in industry. Think of acoustic scattering, sound radiation and other related problems. A common feature of these problems is the large or even infinite extension of the acoustic domain compared to the rather limited extension of the surface of the embedded scatterer. The appropriateness of solving such problems is inherent to the boundary element method: The solution in the domain (large or even infinite extension) is available, once the solution on the boundary (limited extension) is computed. But, standard boundary element formulations lead to fully populated system matrices and the computation of their entries is very expensive. This issue has been remedied by the introduction of fast boundary element formulations, the topic of the thesis at hand. Our objective is twofold. In the first place, we construct two efficient numerical schemes, theH-matrix and the directional fast multipole scheme. Both enable an efficient treatment of fully populated matrices of oscillatory nature. In the second place, we apply these schemes to acoustic boundary element formulations and reduce their quadratic complexity to an almost linear one. We validate our approaches by means of numerical examples. We solve a time-domain problem by means ofH-matrices and several time-harmonic problems by means of the directional fast multipole method. We emphasize on the fact that both presented approaches are kernel independent, up to a certain extend.