A hybrid virtual–boundary element formulation for heterogeneous materials

2011 ◽

Vol 204-210 ◽

pp. 2196-2201

Author(s):

Yan Tao Jiang ◽

Si Tian Chen ◽

Cheng Hua Li

Keyword(s):

Boundary Element ◽

Large Scale ◽

Fast Multipole Method ◽

Main Idea ◽

Least Square Method ◽

Least Square ◽

Fast Multipole ◽

Large Scale Problems ◽

Virtual Boundary ◽

Virtual Boundary Element

In this paper, the fast multipole virtual boundary element - least square method (Fast Multipole VBE - LSM) is proposed and used to simulate 2-D elastic problems, which is based on the fast multipole method (FMM) and virtual boundary element - least square method (VBE - LSM).The main idea of the method is to change computational model by applying the FMM to conventional VBE - LSM. The memory and operations could be reduced to be of linear proportion to the degree of freedom (DOF) and large scale problems could be effectively solved on a common desktop with this method. Numerical results show that this method holds virtues of high feasibility, accuracy and efficiency. Moreover, the idea of this method can be generalized and extended in application.

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Virtual boundary element integral method for 2-D piezoelectric media

Finite Elements in Analysis and Design ◽

10.1016/j.finel.2004.10.007 ◽

2005 ◽

Vol 41 (9-10) ◽

pp. 875-891 ◽

Cited By ~ 12

Author(s):

Yao Weian ◽

Hui Wang

Keyword(s):

Boundary Element ◽

Integral Method ◽

Piezoelectric Media ◽

Virtual Boundary ◽

Virtual Boundary Element

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.378-379.166 ◽

2011 ◽

Vol 378-379 ◽

pp. 166-170

Author(s):

Wei Si ◽

Qiang Xu

Keyword(s):

Boundary Element ◽

Collocation Method ◽

Large Scale ◽

Fast Multipole Method ◽

Fast Multipole ◽

Multipole Method ◽

Elasticity Problems ◽

Virtual Boundary ◽

Minimal Residual ◽

Virtual Boundary Element

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.

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Theory of Fast Multipole Virtual Boundary Element Method and Discussion on Key Issues

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.152-154.1828 ◽

2012 ◽

Vol 152-154 ◽

pp. 1828-1833

Author(s):

Yan Tao Jiang ◽

Hong Yuan Bai

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Computing Time ◽

Engineering Application ◽

Reference Value ◽

Fast Multipole ◽

Key Issues ◽

Virtual Boundary ◽

Virtual Boundary Element ◽

Element Method

The basic theory of fast multipole virtual boundary element method (VBEM) is discussed through expanding the fundamental solution, and the algorithm can make the complexities of operation and memory about solution of the equations to be of linear proportion to the freedoms of the problem. Numerical examples are presented to demonstrate the feasibility, accuracy and efficiency of the method. At the same time, the relationships between the order for expansion and the storage capacity, computing time, precision are analyzed, and the influence of boundary points in the leaf to the calculation efficiency is discussed. The corresponding reference value is put forward for the convenience of engineering application.

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