Fast Multipole Boundary Element Method For
The Simulation Of Acoustic-structure Interaction
Author(s)
L. Gaul & M. Fischer
Abstract
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 log2 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 multipole
boundary element method. The algorithm is demonstrated on the example of a
cavity backed elastic panel.
Keywords: fast multipole Galerkin BEM, acoustic-structure interaction, mortar
BEM-FEM coupling.
1 Introduction
The application of the fast multipole BEM for the simulation of acoustic fieldstructure
interaction problems poses new demands on the solver for the coupled
systems: direct approaches are not applicable and iterative schemes suffer from illconditioning.
An approximate Uzawa-type algorithm is proposed for the solution
of saddle point systems arising from mortar coupling. The efficiency of the nested
Keywords
fast multipole Galerkin BEM, acoustic-structure interaction, mortar
BEM-FEM coupling.
Related Book
Other papers in this volume
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