A NEW ALGORITHM FOR STRUCTURAL MODIFICATIONS AND ITS APPLICATIONS

Based on the features of binary tree and fill-in's reducing, the authors proposed a new algorithm for structural modifications, which indicated that in LDL^T factorization, the effect of modification will propagate up to the root along the binary tree. This algorithm is compatible with the standard sparse solver in finite element method, and can be applied to various fields for structural modifications. Compared with traditional Sherman- Morrison-Woodbury formulas or other reanalysis methods, the new algorithm is more efficient if the modications are high-rank. However, if the modications are low-rank, this method might be less efficient. Based on the previous study, the existing procedure of updating triangular factors is improved further in this paper. The alternative formula of recalculating the factors can reduce the amount of calculation significantly and improve the efficiency of reanalysis. Numerical tests show that the improved algorithm can save up to 30% of computation efforts compared with the existing one.