Huge An Optimal Parallel Robin-Robin Iterative Method for the Mixed Finite Element Discretization of the Second Order Elliptic Problems

WANG Feng; ZENG Yu-Ping

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Huge An Optimal Parallel Robin-Robin Iterative Method for the Mixed Finite Element Discretization of the Second Order Elliptic Problems

WANG Feng 1, ZENG Yu-Ping 2

1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023

2. School of Mathematics, Jiaying University, Meizhou 514015

*Correspondence author

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Funding: the Doctoralfund of Ministry of Education of China （No.20123207120001）, the opening fund of Jiangsu Key Lab forNSLSCS （No.201402）

Opened online:20 November 2015

Accepted by: none

Citation: WANG Feng, ZENG Yu-Ping.Huge An Optimal Parallel Robin-Robin Iterative Method for the Mixed Finite Element Discretization of the Second Order Elliptic Problems[OL]. [20 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4661919

The Robin-Robin iterative method is a kind of nonoverlapping domain decomposition method, in which the information is exchanged by the Robin boundary condition on the interface. The purpose of this paper is to introduce a parallel Robin-Robin iterative method for the mixed finite element approximation of the second order elliptic problems, and give a condition for choosing Robin parameters and relaxation parameter. Based on the spectral theory of the block operator matrices and eigenvalue estimates of the Neumann to Dirichlet operator for the mixed finite element methods, it is proved that the convergence rate of the algorithm is independent of the mesh size and the jump in the coefficient. Some numerical experiments are presented to confirm our results.

Keywords:Computational Mathematics, Robin-Robin iterative methods, domain decomposition, mixed finite elements

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