... small part needs to be updated. A Woodbury formula-based algorithm is developed to reduce the solution scale of the inverse heat conduction matrix. Highlights The crack is assumed to be within a known local region, but without any geometric information, which needs to be determined by solving...

... mathematical Woodbury formula. Findings Consequently, the updating and factorization of the global tangent stiffness matrix are avoided, and the computational effort of structural nonlinear analyses only focuses on the updating and factorization of a small-dimensional matrix representing the local...

...Gang Li; Shuo Jia; Hong-Nan Li Purpose The purpose of this paper is to make a theoretical comprehensive efficiency evaluation of a nonlinear analysis method based on the Woodbury formula from the efficiency of the solution of linear equations in each incremental step and the selected iterative...