Virtual Boundary Element Collocation Method with RBF Interpolation on Virtual Boundary and Diagonalization Feature in Fast Multipole Method

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The algorithm idea of virtual boundary element collocation method with RBF interpolation on virtual boundary and diagonalization feature in fast multipole method is presented to study 2-D elasticity problems in this paper. In other words, the new fast multipole method (FMM) adopting diagonalization and the generalized minimal residual (GMRES) algorithm are jointly employed to solve the equations related to virtual boundary element collocation method (VBEM) with RBF interpolation on virtual boundary. In this paper, the numerical scheme suitable for original FMM with respect to two-dimensional problem of elasticity is optimized, through the introduction of concept of diagonalization, in terms of the radial basis function to express the unknown virtual load functions, in order to further improve the efficiency of the problem to be solved. Then large-scale numerical simulations of elastostatics might be achieved by the method. Numerical examples in the paper have proved the feasibility, efficiency and calculating precision of the method.

Info:

Periodical:

Advanced Materials Research (Volumes 378-379)

Edited by:

Brendan Gan, Yu Gan and Y. Yu

Pages:

166-170

DOI:

10.4028/www.scientific.net/AMR.378-379.166

Citation:

W. Si and Q. Xu, "Virtual Boundary Element Collocation Method with RBF Interpolation on Virtual Boundary and Diagonalization Feature in Fast Multipole Method", Advanced Materials Research, Vols. 378-379, pp. 166-170, 2012

Online since:

October 2011

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$35.00

[1] Sun Huanchun, Zhang Lizhou, Xu Qiang, et al. Non-singularity boundary element methods [M] . Dalian Universit y of Technology Press, (1999).

[2] Q. Xu, H.C. Sun, Virtual boundary element least-square collocation method, chinese journal of computationalal mechanics, vol. 14, pp.166-173, (1997).

[3] Zhang Zhijia,Xu Qiang. Application of Fast Multipole VBEM to Two-Dimensional Potential Problems. [J]. 2009 International Conference on Engineering Computation,ICEC 2009 (217-220).

DOI: 10.1109/icec.2009.40

[4] L. Greengard,V. Rokhlin. A Fast Algorithm for Particle Simulations. [J]. Comput. Phys. 1985,60: 187-207.

[5] Hrycak T,Rokhlin V.An improved fast multipole algorithm for potential fields. SIA M J Sci Comput, 1998.19:l804—1826.

[6] Liu, G.R. Gu, Y.T., An Introduction to Meshfree Methods and Their Programming. Springer press, Dordrecht, (2005).

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