A Two-Level Overlapping Hybrid Domain Decomposition Method for Eigenvalue Problems

Research paper by Wei Wang, Xuejun Xu

Indexed on: 01 Jun '18Published on: 23 Jan '18Published in: SIAM journal on numerical analysis

Abstract

SIAM Journal on Numerical Analysis, Volume 56, Issue 1, Page 344-368, January 2018. In this paper, we present a two-level overlapping hybrid domain decomposition method for solving the large scale discrete elliptic eigenvalue problems. In order to eliminate the components in the orthogonal complement space of the eigenspace, we construct a parallel preconditioner for the eigenvalue problem in fine space. After one coarse space correction in each iteration, we get the error reduction as $\gamma=c(1-C\frac{\delta}{H})$, where $C$ is a constant independent of the mesh size $h$ and the diameter of subdomains $H$, $\delta$ is the overlapping size among the subdomains, and $c\rightarrow1$ decreasingly as $H\rightarrow0$, which means the greater the number of subdomains, the better the convergence rate. Different from other numerical algorithms in the literature, we do not need any assumptions between $H$ and $h$. Numerical results supporting our theory are given.