Efficient Method to Avoid Fictitious Eigenvalues for Indirect BEM

One potential shortcoming of the Boundary Element Method in acoustics is that the solution to an exterior Neumann problem is polluted by fictitious resonances at certain frequencies corresponding to internal problem eigenfrequencies. In Indirect BEM, an efficient approach for the mitigation of this issue consists in to apply a prescribed value of internal impedance creating a discontinuity between the conditions across the boundary. This method allows to avoid the problem on the entire frequency range but, on the other hand, the computational cost drastically increases because of the larger number of unknown. Imposing the impedance only on a certain percentage of elements, fictitious resonances are mitigated, obtaining an accurate solution with reduced computational requirements. The percentage of elements needed to obtain an accurate solution is strictly dependent on the analyzed frequency and the geometry of the model. In this paper we provide some guidelines to overcome the problem and reduce the computational cost yielding an accurate solution. Academic and real industrial cases, which are solved with standard IBEM and Fast Multipole BEM, are proposed in order to illustrate the robustness of this method and the correlation of the required percentage of elements with the frequency and the geometry of the model. Finally, we investigate the effect of the application of discontinuous types of boundary conditions on an Indirect boundary element problem.