An exact reanalysis algorithm using incremental Cholesky factorization and its application to crack growth modeling

作者：Pais Matthew J; Yeralan Sencer N; Davis Timothy A; Kim Nam H^*

来源：International Journal for Numerical Methods in Engineering, 2012, 91(12): 1358-1364.

DOI：10.1002/nme.4333

• Cholesky update
• downdate
• crack propagation
• optimization
• reanalysis
• X-FEM

In this paper, an exact reanalysis algorithm based on an incremental Cholesky factorization is presented, which can solve a linear system of equations when a small portion of the coefficient matrix is modified. The efficiency of the proposed algorithm is demonstrated by modeling quasi-static crack growth in the extended finite element method. The example presented shows that a 60% to 70% reduction in computational time is achievable by using the reanalysis approach for solving crack growth problems. It is shown that the reanalysis approach has increasing benefits as the mesh density increases.

• 出版日期2012-9-21