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fast multilevel multipole (FMM) algorithm
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A fast multilevel multipole (FMM) algorithm 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 the 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 with computational cost of O(N 2) . This allows the simulation of large scale acoustic models. The performance of the algorithm is demonstrated on the example of sound radiation from an L-shaped domain with BE discretizations of up to 105 elements. A coupling algorithm based on Lagrange multipliers is proposed for the simulation of structure-acoustic field interaction. Finite plate elements are coupled to the 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 multipole boundary element method. The algorithm is demonstrated on the example of a cavity-backed elastic panel.

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