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

✍ Scribed by Owe Axelsson; Alexander Padiy

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 461 KB
• Volume: 44
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19990228)44:6<801::aid-nme525>3.0.co;2-y

✦ Synopsis

This paper presents a newly developed iterative algorithm for solving problems of linear isotropic elasticity discretized by means of mixed ÿnite 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 ÿeld 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 ÿnite 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 reÿnement steps.

The rate of convergence of the algorithm is bounded uniformly with respect to the problem coe cients, namely the Young's modulus E and the Poisson ratio . This makes it possible to apply the method for a broad class of engineering problems.