Fast multipole boundary element approaches for acoustic attenuation prediction of reactive silencers

The fast multipole boundary element method (FMBEM) is applied to predict the acoustic attenuation performance of reactive silencers. In order to overcome the difficulty of singular boundaries for the acoustic computation of reactive silencers with internal thin wall structure or/and perforated components, two approaches, the substructure FMBEM (Sub-FMBEM) and mixed-body FMBEM (MB-FMBEM) are proposed, and the theoretical foundations and numerical processes of the both approaches are introduced. The studies demonstrated that the ordering of column vectors and numbering of nodes in the Sub-FMBEM have great influence on the convergence of iteration, and the MB-FMBEM may reduce the number of elements and the computational complexity since it only needs to discretize one side boundary of the thin wall and perforated components and it is not necessary to create the interfaces. The Sub-FMBEM, MB-FMBEM and Sub-BEM are then employed to calculate the transmission loss of reactive silencers with thin wall components and perforated tubes, the computational accuracy and efficiency of the approaches are validated. The data of precomputing time and total iterative computational time demonstrated that, the computational efficiency of Sub-FMBEM will descend as the frequency arising, and the Sub-FMBEM may reveal higher computational efficiency than Sub-BEM only when the number of nodes is big enough.