On the cost reduction of the fast BEM Hierarchical Matrix approach for partly symmetric surfaces

Sound radiation of vibrating structures is of interest in many engineering disciplines. When considering structures under free field conditions the sound radiation can advantageously be calculated by means of the Boundary Element Method (BEM). Compared to the Finite Element Method (FEM) the standard BEM has the drawback of fully populated system matrices. Fast Boundary Element Methods like the Fast Multipole Method or the Hierarchical Matrix approach effectively reduce this drawback. For the H-Matrix approach rotational symmetric or symmetric structure surfaces can be exploited to further reduce the costs for assembling and storing the approximated system matrix due to its Toeplitz structure. In this paper, it will be outlined how this reduction can also be applied to overall non symmetric surfaces but primarily composed of partly symmetric parts. In order to efficiently solve the linear system of equations while maintaining the advantage of reduced storing costs the usually applied hierarchical LU-decomposition for preconditioning the iterative solver is not recommendable. This is due to the requirement of the total approximated system matrix. Hence an alternative efficient preconditioner will be used for the exterior problem in this paper. The efficiency of the reduced matrix representation will be discussed on numerical examples.

Subjects

H-Matrix

OSRC

Symmetric

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On the cost reduction of the fast BEM Hierarchical Matrix approach for partly symmetric surfaces