Preconditioned minimum residual iteration for the h–p version of the coupled FEM/BEM with quasi-uniform meshes

✍ Scribed by Norbert Heuer; Matthias Maischak; Ernst P. Stephan

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 121 KB
• Volume: 6
• Category: Article
• ISSN: 1070-5325
• DOI: 10.1002/(sici)1099-1506(199909)6:6<435::aid-nla174>3.0.co;2-u

✦ Synopsis

We propose and analyze efficient preconditioners for the minimum residual method to solve indefinite, symmetric systems of equations arising from the h-p version of finite element and boundary element coupling. According to the structure of the Galerkin matrix we study two-and three-block preconditioners corresponding to Neumann and Dirichlet problems for the finite element discretization. In the case of exact inversion of the blocks we obtain bounded iteration numbers for the two-block Jacobi solver and O(h -3/4 p 3/2 ) iteration numbers for the three-block Jacobi solver. Here, h denotes the mesh size and p the polynomial degree. For the efficient two-block method we analyze the influence of various preconditioners which are based on further decomposing the trial functions into nodal, edge and interior functions. By further splitting the ansatz space with respect to basis functions associated with the edges we obtain a partially diagonal preconditioner. The penultimate method requires O(log 2 p) iterations whereas the latter method needs O(p log 2 p) iterations. Numerical results are presented which support the theory.