CMES-Vol. 58, No. 2, 2010

Open Access

ARTICLE

On a Reformulated Convolution Quadrature Based Boundary Element Method
M. Schanz¹
CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 109-130, 2010, DOI:10.3970/cmes.2010.058.109
Abstract Boundary Element formulations in time domain suffer from two problems. First, for hyperbolic problems not too much fundamental solutions are available and, second, the time stepping procedure is expensive in storage and has stability problems for badly chosen time step sizes. The first problem can be overcome by using the Convolution Quadrature Method (CQM) for time discretisation. This as well improves the stability. However, still the storage requirements are large. A recently published reformulation of the CQM by Banjai and Sauter [Rapid solution of the wave equation in unbounded domains, SIAM J. Numer. Anal., 47,… More >

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ARTICLE

Comparison of the Fast Multipole Method with Hierarchical Matrices for the Helmholtz-BEM
D. Brunner¹, M. Junge¹, P. Rapp¹, M. Bebendorf², L. Gaul¹
CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 131-160, 2010, DOI:10.3970/cmes.2010.058.131
Abstract The simulation of the hydroacoustic sound radiation of ship-like structures has an ever-growing importance due to legal regulations. Using the boundary element method, the overall dimension of the problem is reduced and only integrals over surfaces have to be considered. Additionally, the Sommerfeld radiation condition is automatically satisfied by proper choice of the fundamental solution. However, the resulting matrices are fully populated and the set-up time and memory consumption scale quadratically with respect to the degrees of freedom. Different fast boundary element methods have been introduced for the Helmholtz equation, resulting in a quasilinear complexity.… More >

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A New Adaptive Algorithm for the Fast Multipole Boundary Element Method
M. S. Bapat¹, Y. J. Liu^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 161-184, 2010, DOI:10.3970/cmes.2010.058.161
Abstract A new definition of the interaction list in the fast multipole method (FMM) is introduced in this paper, which can reduce the moment-to-local (M2L) translations by about 30-40% and therefore improve the efficiency for the FMM. In addition, an adaptive tree structure is investigated, which is potentially more efficient than the oct-tree structure for thin and slender domains as in the case of micro-electro-mechanical systems (MEMS). A combination of the modified interaction list (termed L2 modification in the adaptive fast multipole BEM) and the adaptive tree structure in the fast multipole BEM has been implemented… More >

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Energetic Galerkin BEM for wave propagationNeumann exterior problems
A. Aimi¹, M. Diligenti¹, S. Panizzi¹
CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 185-220, 2010, DOI:10.3970/cmes.2010.058.185
Abstract In this paper we consider 2D wave propagation Neumann exterior problems reformulated in terms of a hypersingular boundary integral equation with retarded potential. Starting from a natural energy identity satisfied by the solution of the differential problem, the related integral equation is set in a suitable space-time weak form. Then, a theoretical analysis of the introduced formulation is proposed, pointing out the novelties with respect to existing literature results. At last, various numerical simulations will be presented and discussed, showing accuracy and stability of the space-time Galerkin boundary element method applied to the energetic weak More >

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