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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 367802, 8 pages
http://dx.doi.org/10.1155/2014/367802
Research Article

A New Iterative Method for Linear Systems from XFEM

1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
2School of Mathematics and Statistics, Center for Computational Geosciences, Xi’an Jiaotong University, Xi’an 710049, China
3School of Mathematics and Computer, Hubei University of Arts and Science, Xiangyang, Hubei 441053, China

Received 12 September 2013; Accepted 16 December 2013; Published 14 January 2014

Academic Editor: Trung Nguyen Thoi

Copyright © 2014 Jianping Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The extend finite element method (XFEM) is popular in structural mechanics when dealing with the problem of the cracked domains. XFEM ends up with a linear system. However, XFEM usually leads to nonsymmetric and ill-conditioned stiff matrix. In this paper, we take the linear elastostatics governing equations as the model problem. We propose a new iterative method to solve the linear equations. Here we separate two variables and Enr, so that we change the problems into solving the smaller scale equations iteratively. The new program can be easily applied. Finally, numerical examples show that the proposed method is more efficient than common methods; we compare the -error and the CPU time in whole process. Furthermore, the new XFEM can be applied and optimized in many other problems.