A Review of the Extended Finite Element Method and its Applications

The extended finite element method(XFEM) is a numerical method for modeling discontinuity such as cracks,holes,inclusions etc within a standard finite element framework.In the XFEM,special functions which can reflect the problem's solution characteristics are added to the finite element approximation using the framework of partition of unity.The geometry and extended process of discontinuous interface is described by level sets method(LSM).Compared to the standard finite element method,it can obtain more accuracy without remeshing.An overview and recent progress of the extended finite element method are presented.The theory basis of XFEM is introduced from section 1 to 4.Tow critical problems in XFEM are discussed in section 5.The implementation and application of XFEM are outlined in Section 6 and Section 7,and finally some recommendations of future work are presented in section 8.