STRONG COUPLING OF THE FAST MULTILEVEL MULTIPOLE BOUNDARY ELEMENT METHOD WITH THE FINITE ELEMENT METHOD FOR VIBRO-ACOUSTIC PROBLEMS

摘要

Nowadays, the sound quality has an ever-growing influence on the overall impression of a product. To predict the sound radiation of structures, both a structural and an acoustic problem have to be solved. In this work, the structural part is modelled by the finite element (FE) method, whereas the exterior acoustic problem is efficiently simulated with the boundary element (BE) method. To overcome the well known bottleneck of fully populated boundary element matrices, the fast multilevel multipole method is applied. In case of thin structures and dense fluids, a strong coupling between the two problems is essential, since the effect of the acoustic pressure onto the surface of the structure is not negligible. Two different methods are investigated: First, the structural displacements are eliminated yielding a Schur complement formulation. Secondly, the problem is formulated with a Lagrangian multiplier and an Uzawa-type algorithm with nested inner-outer iterations is applied. In both cases, iterative solvers with different preconditioners are used.