Open AccessFast multipole boundary element analysis of two‐dimensional elastoplastic problems
Author(s) -
Wang P. B.,
Yao Z. H.
Publication year - 2007
Publication title -
communications in numerical methods in engineering
Language(s) - English
Resource type - Journals
eISSN - 1099-0887
pISSN - 1069-8299
DOI - 10.1002/cnm.930
Subject(s) - fast multipole method , multipole expansion , boundary element method , degrees of freedom (physics and chemistry) , mathematics , matrix (chemical analysis) , boundary (topology) , nonlinear system , mathematical analysis , coefficient matrix , finite element method , algorithm , physics , materials science , quantum mechanics , composite material , thermodynamics , eigenvalues and eigenvectors
This paper presents a fast multipole boundary element method (BEM) for the analysis of two‐dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run‐time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad‐tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix–vector multiplication are both reduced to O ( N ), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd.