Acta Mechanica Slovaca 2011, 15(3):30-37 | DOI: 10.21496/ams.2011.025
Application of Fast Multipole Boundary Method in Elastostatic Problems
- University of ®ilina, Faculty of Mechanical Engineering , Department of Applied Mechanics, Univerzitná 1, 01026 ®ilina
The boundary element method (BEM) is a numerical method for solving boundary-value or initial-value problems formulated by use of boundary integral equations. In the BEM, only the boundaries - that is, surfaces for three-dimensional problems or curves for two dimensional (2D) problems - of a problem domain need to be discretized. However the boundary element method (BEM) has been limited to solving problems with a few thousand degrees of freedom (DOFs) on a personal computer. This is because the conventional BEM, in general, produces dense and nonsymmetric matrices. The main idea of the fast multipole (FM) BEM is to employ iterative solvers to solve the BEM system of equations. Using this method we can solve models with more than one million equations on a laptop computer. In this paper, the governing equations for elasticity problems are reviewed first. Numerical examples are provided to demonstrate the accuracy and efficiencies of fast multipole method (FMM) for solving 2D elasticity problems.
Keywords: Boundary Element Method, Fast Multipole Method, Reciprocity Based FEM
Received: March 28, 2011; Accepted: May 24, 2011; Published: October 31, 2011 Show citation
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