Fast multipole boundary element method for the simulation of acoustic-structure interaction

A fast multilevel multipole algorithm (FMM) is derived for the Helmholtz equation and adopted to the symmetric Galerkin boundary element method (BEM) for acoustics. The FMM allows to evaluate a matrix-vector product of the BEM with a computational cost of O(N log(2) N), thus leading to a significant reduction of computation time and memory requirements compared to standard BEM formulations. This allows the simulation of large scale acoustic models. A coupling algorithm based on Lagrange Multipliers is proposed for the simulation of structure-acoustic field interaction. Finite plate elements are coupled to a Galerkin boundary element formulation of the acoustic domain. The interface pressure is interpolated as a Lagrange multiplier, thus, allowing the coupling of non-matching grids. The resulting saddle point problem is solved by an approximate Uzawa-type scheme in which the matrix-vector products of the boundary element operators are evaluated efficiently by the fast rnultipole boundary element method. The algorithm is demonstrated on the example of a cavity backed elastic panel.