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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 85
PROCEEDINGS OF THE FIFTEENTH UK CONFERENCE OF THE ASSOCIATION OF COMPUTATIONAL MECHANICS IN ENGINEERING Edited by: B.H.V. Topping
Paper 46
Adaptive Space-Time Boundary Element Method for Three-Dimensional Scalar Wave Propagation J.X. Zhou, T. Koziara and T.G. Davies
Department of Civil Engineering, Glasgow University, United Kingdom Full Bibliographic Reference for this paper
J.X. Zhou, T. Koziara, T.G. Davies, "Adaptive Space-Time Boundary Element Method for Three-Dimensional Scalar Wave Propagation", in B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 46, 2007. doi:10.4203/ccp.85.46
Keywords: boundary element method, adaptive scheme, space-time, time-dependent, impulse wave.
Summary
The wave propagation and its interactions with natural or man-made
bodies are important problems in civil engineering. A general boundary
element scheme to solve the two-dimensional transient elastodynamics problem was
derived by Mansur & Brebbia [2]. The three-dimensional elastodynamic
time-domain BEM formulation and implementation were studied by Manolis
& Beskos [1] in the context of three-dimensional dynamic soil-structure
interaction problems. However, this early research lacked systematic
analysis of the error estimation, convergence and stability. The instability
was observed even for uniform meshes when the space-time ratio
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Further difficulties are met when impulse wave propagations are solved
by the BEM. Zienkiewicz [3] put impulse wave propagation problems
in the list of unsolved problems, because a reasonable accuracy cannot
be achieved unless the element size is less than 1/10th of the minimum
wavelength. When the incident wavelength becomes small, the number of nodes
will increase dramatically, which is beyond the capacity of the largest
computer used today. Thus, a completely new method of approximation
is required to deal with the short-wave propagation.
Therefore, the conventional BEM modeling of wave problems encounters
many difficulties despite its popularity. Firstly, solving an impulse
wave problem in a large and complex domain is expensive. Secondly,
it is still difficult for time domain BEM solvers to produce stable
results, specially for impulsive loads. Thirdly, the space-time ratio
The new idea in this paper is to introduce adaptive schemes to improve the computational efficiency of dynamic BEM, which includes error estimation, automatic mesh refinements and a new BEM solver for refined meshes. The development of such adaptive BEM schemes is vital for BEM to model impulsive wave problems efficiently. Surface elements in the space are indexed, like books in a library, to accelerate the spatial search to decide which part of the boundary mesh should be integrated in different time step. Then gradient-based and two-solution-based error indicators are used to locate moving high-gradient areas in the wave propagation, a triangular element refinement based on longest edge propagation path (LEPP) is employed to improve solution accuracy while retaining the computational efficiency. Local time stepping is designed to fully employing space-time adaptivity. We apply the method to solve problems of wave propagation in a three-dimensional bar and a three-dimensional spherical cavity under various explosion loading. Compared with traditional dynamic BEM, the solution is more accurate, less artificial-damped and more stable. References
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