Application of Sherman-Morrison formula in adaptive analysis by BEM

Abstract

Mesh refinement may give rise to variable dimension system of linear equations in adaptive analysis. In each adaptive step, the matrix decomposition methods are adopted to solve linear algebraic equations, which is obviously time-consuming and computationally expensive for large-scale problems. A new algorithm for solving a variable dimension system of linear equations is proposed in this paper, which combines matrix deformation with the Sherman-Morrison formula. This method not only retains the advantages of the Sherman-Morrison formula, but also is particularly suitable for adaptive analysis. Compared with the matrix decomposition method, our method has outstanding performance in promoting computational efficiency. Several numerical examples are used to illustrate the superiority of the proposed method when applying to solve 2D elasticity problems.