CSR STORAGE METHOD OF EXTENDED FINITE ELEMENT STIFFNESS MATRIX

Abstract

The extended finite element method（ XFEM） is one of the most widely used numerical methods to deal with cracks,holes and inclusions. Based on the partition of unity method（ PUM）,the additional function terms are introduced to the displacement approximation function of the standard finite element method（ FEM） to reflect the discontinuous characteristics and singular characteristics of the displacement field in XFEM. The introduce of the additional function terms leads to the uncertainty of the element stiffness matrix（ ESM） of XFEM. Hence,the assembly algorithm of standard FEM global stiffness matrix（ GSM）is no longer applicable to XFEM. A new assembly algorithm based on the‘Generalized adjacent node pairs’ is proposed. In this algorithm,we use the one-to-one corresponding relationship between‘Generalized adjacent node pairs’ and the non-zero terms in GSM,And with the compressed sparse row storage format（ CSR） of large sparse matrix,the GSM of compressed storage is formed directly from the ESM. In this paper,the implementation process of the algorithm is detailed,and the program is successfully implemented in the XFEM program developed by Fortran,and the effectiveness of the algorithm is verified.

Keywords

• XFEM;Global stiffness matrix;Compressed sparse row（CSR） storage;Assembly algorithm of stiffness matrix