Parallel multilevel fast multipole method for solving large-scale problems

2005 ◽  
Vol 47 (4) ◽  
pp. 110-118 ◽  
Author(s):  
Fang Wu ◽  
Yaojiang Zhang ◽  
Zaw Zaw Oo ◽  
Erping Li
Keyword(s):  
Large Scale ◽  
Fast Multipole Method ◽  
Fast Multipole ◽  
Large Scale Problems ◽  
Multipole Method

Fast Multipole Virtual Boundary Element - Least Square Method for Solving 2-D Elastic Problems

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.

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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