An exact reanalysis algorithm for local non-topological high-rank structural modifications in finite element analysis

•A novel reanalysis algorithm DIFFERING from Woodbury formula is proposed.•The new algorithm UPDATES the triangular factors of the original stiffness matrix.•The new algorithm makes use of binary partition tree in sparse matrix scheme.•Compared to Woodbury formula, it is more suitable for high-rank modification.•Numerical tests indicate that this algorithm is superior for larger problems.

This paper proposes a novel direct reanalysis algorithm based on finding updated triangular factorization in sparse matrix solution. The key concept lies on the binary tree characteristics of the global stiffness matrix derived by a graph partitioner as fill-ins’ reducer. Accommodating a local modification, the update of the triangular factor happens only through a particular path of the binary tree, which traces back from modified nodes to the root node. Numerical examples show that the proposed algorithm improves reanalysis efficiency significantly, especially for high-rank structural modification. In terms of implementation, little additional storage is needed to perform the proposed algorithm. This method can be applied to a wide range of engineering problems and can be the foundation of a lot of subsequent analyses.