Improving the Convergence of the Fast Multipole BEM for the Exterior Sound Radiation of a Truck Muffler

In the last few years, some of the computational limitations imposed by the classical Boundary Element Methods (BEM) have been overtaken thanks to the Fast Multipole BEM (FMBEM) which allows solving large acoustic models much faster. Nevertheless, as the BEM, the FMBEM suffers from non-uniqueness of the solution and the exterior prediction is polluted by fictitious resonances. Since the FMBEM is based on an iterative solver, not only the accuracy is degraded. In fact, the number of iterations to the convergence, in correspondence of a fictitious resonance, is larger and the total computational time increases. Applying the impedance condition over the whole inner boundary allows to completely damp fictitious resonances with a drastic increase of computational cost. Nevertheless, when the condition is applied on a well-chosen percentage of elements, the accurate solution is obtained even faster. The efficiency of this approach and its applicability to industrial-size problems is proved in this paper. Numerical predictions of the exterior noise emitted by a truck muffler are compared with experimental data. After a comparison between classical BEM and FMBEM solutions, the improvement obtained by properly applying the internal absorption is illustrated both in terms of solution accuracy and computational efforts.