Acceleration of Fast Multipole Method for Large-Scale Periodic Structures With Finite Sizes Using Sub-Entire-Domain Basis Functions

2007 ◽  
Vol 55 (2) ◽  
pp. 414-421 ◽  
Author(s):  
Wei Bing Lu ◽  
Tie Jun Cui ◽  
Hui Zhao
Keyword(s):  
Large Scale ◽  
Periodic Structures ◽  
Fast Multipole Method ◽  
Basis Functions ◽  
Fast Multipole ◽  
Entire Domain ◽  
Multipole Method

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

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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