On updating the structure of sparse matrix factors

Abstract

AbstractStructural analysis often involves the solution of a sparse system of linear equations using matrix factorization. For structural reanalysis problems, the system of equations is progressively changing and matrix factorization is required at each iteration step. In this paper, we study the problem of updating the structure of sparse matrix factors using an ordered‐tree model. The ordered‐tree model provides the information needed to symbolically compute the non‐zero structure of the matrix factor of a sparse matrix. Furthermore, for matrix factor modification problems, this tree model can be used to determine the numerically modified entries in the matrix factor. Examples for modification of a structure and h‐adaptive refinement of a finite element model are given to illustrate the potential application of the procedures developed in this study.