The Hybrid Boundary Node Method Accelerated by Fast Multipole Expansion Technique for 3D Elasticity
Qiao Wang; Yu Miao; Junjie Zheng

doi:10.3970/cmes.2010.070.123
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 70, No. 2, pp. 123-152, 2010
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Keywords meshless method; hybrid boundary node method; modified variational principle, moving least squares approximation; fast multipole method; 3D elasticity
Abstract In this paper, a fast formulation of the hybrid boundary node method (Hybrid BNM) for solving 3D elasticity is presented. Coupling modified variational principle with the Moving Least Squares (MLS) approximation, the Hybrid BNM only requires discrete nodes constructed on the surface of a domain. The preconditioned GMERS is employed to solve the resulting system of equations. At each iteration step of the GMERS, the matrix-vector multiplication is accelerated by the fast multipole method (FMM). The fundamental solution of three-dimensional elasticity problem is expanded in terms of series. An oct-tree data structure is adopted to subdivide the computational domain into well-separated cells hierarchically and to invoke the multipole expansion approximation. Formulations for the local and multipole expansions and conversion of multipole to local expansion are given. Nearly one million of total unknowns can be computed on a PC with 2.67GHz CPU and 2.0GB RAM. All the formulations are implemented in a computer code written in C++. Numerical examples demonstrate the accuracy and efficiency of the proposed approach.
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