Coupling of Boundary Element and Wave Based Methods for the efficient solution of complex multiple scattering problems

A novel hybrid method for the efficient solution of complex acoustic multiple scattering problems is proposed in this paper. The Wave Based Method and the Boundary Element Method are coupled to benefit from the strengths of both. The former is an indirect Trefftz approach, which has a faster convergence rate and lower computational load compared to element based methods when applied on geometries of moderate complexity. The latter is the state-of-the-art technique for unbounded acoustic problems and can handle very complex geometries. The idea behind the hybrid method is to take advantage of the fast WBM solution for scatterers of moderate complexity and take advantage of the BEMʼs capability for handling scatterers of high complexity. For the BEM part, the indirect variational formulation is used which allows modeling of open boundary problems (zero thickness walls). In addition, the WBM makes it possible to easily add heterogeneities (domain inclusions) to the problem. Therefore, the hybrid method does not only aim for better efficiency but also for extending the variety of configurations that can be tackled by both methods with ease. The accuracy and the performance of the method are demonstrated with three examples, both in 2D and 3D. It is shown that when complex and simple scatterers coexist, the hybrid method is more efficient than the WBM, the BEM and the Fast-Multipole BEM while it is able to provide accuracy of similar level.