On a robust and scalable linear elasticity solver based on a saddle point formulation

This paper presents a newly developed iterative algorithm for solving problems of linear isotropic elasticity discretized by means of mixed nite elements. It continues work started in References 1{5. The proposed method uses a pressure Schur complement approach to solve a saddle-point system arising in the mixed formulation. As an inner solver for the displacement eld variables it uses an extension to the robust black-box multilevel procedure suggested in Reference 4. The proposed method works on a hierarchical sequence of nite element meshes to solve the problem with an arithmetic cost, nearly proportional to the dimension of the arising algebraic system. The coarsest mesh in the above sequence of meshes can consist of almost arbitrary triangular patches, which allows in practice to capture the solution even using a moderate number of successive re nement steps. The rate of convergence of the algorithm is bounded uniformly with respect to the problem coe cients, namely the Youngʹs modulus E and the Poisson ratio . This makes it possible to apply the method for a broad class of engineering problems. Copyright