A new iterative method for linear systems from XFEM

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 U 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 L 2 -error and the CPU time in whole process. Furthermore, the new XFEM can be applied and optimized in many other problems. © 2014 Jianping Zhao et al.