Universität Stuttgart
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Item Open Access The fast multipole boundary element method and its application to structure acoustic field interaction(2004) Fischer, Matthias; Gaul, Lothar (Prof. Dr.-Ing. habil.)The goal of the thesis is to provide an efficient simulation tool for the prediction of sound radiation from vibrating structures. Acoustic simulations are an important step to optimize the properties of a new product early in the design phase rather than curing mistakes afterwards. The boundary element method (BEM) is widely used in acoustics, since it allows the simulation of fields in unbounded domains. Only the surface of the sound radiating structure must be discretized with a very low cost for mesh generation and preprocessing. The limiting factor for the application of the BEM to large-scale simulations is its fully populated system matrix. It implies that computing time and memory requirements increase quadratically with the number of elements which cannot be handled even for moderately sized problems. The fast multipole BEM allows the computation of the BEM matrix-vector products at a quasi-linear numerical cost. The reduction is achieved by multilevel clustering of the boundary elements and the use of the multipole series expansion for the evaluation of the fundamental solution. In combination with an efficient iterative solver, multipole BEM simulations can be performed on large models consisting of more than 100,000 boundary elements. The generalized minimal residual method (GMRES) and multigrid solvers are most suitable for the solution of the BEM systems of equations. An approximate inverse preconditioner is developed for both approaches that restricts the number of required iterations and thus allows efficient multipole BEM simulations on fine discretizations and high frequencies. For the simulation of structure-acoustic field interaction problems, the coupled field equations must be solved. The structure is commonly discretized using finite elements, whereas for the acoustic field the BEM is favorable. A mortar FEM-BEM coupling algorithm is developed that allows the combination of non-conforming meshes. The high flexibility for the choice of discretizations offers a high efficiency, since specialized shape functions and adaptive mesh refinement can be used in the subdomains. The mortar coupling algorithm yields a saddle point problem that is solved using an inexact Uzawa algorithm. The iterative solver enables the use of the multipole BEM and thus coupled simulations on large boundary element models.