On the construction of a vertex space preconditioner for Morley element

Abstract

Abstract In this paper, based on a specially chosen domain decomposition, we construct an overlapping additive Schwarz preconditioner according to the framework of [Brenner, Numer. Math. 72: 419–447, 1996] for the Morley element and show that its condition number is optimal; we analyze in details the structure of this preconditioner, and after proper choices of inexact solvers, we obtain a vertex space preconditioner for the Morley element. Compared with the preconditioners constructed in [Huang, J. Comp. Math. 17: 615–628, 1999, Shi and Xie, J. Comp. Math. 16: 289–304, 1998, Xie, Domain Decomposition and Multigrid Methods for Nonconforming Plate Elements, Chinese Academy of Sciences, 1998], this preconditioner has some advantages, i.e., the computational cost adds little, but the condition number improves greatly.