Domain decomposition preconditioners for elliptic equations with jump coefficients
Domain decomposition preconditioners for elliptic equations with jump coefficients
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DOI：
10.1002/nla.566
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发表时间：
2008-03
影响因子：
4.3
通讯作者：
Yunrong Zhu
中科院分区：
文献类型：
--
作者：
Yunrong Zhu
本文证明了二阶强不连续系数椭圆型边值问题线性有限元逼近的重叠区域分解预条件的鲁棒性。通过分析域分解预条件系统的特征值分布，我们证明了只有少数特征值会随不连续跳跃或网格大小而退化，所有其他特征值在跳跃和网格大小方面几乎均匀地上下有界。结果证明，对于大跳跃和网格尺寸，预条件共轭梯度方法的收敛速度几乎是一致的。版权所有©2008 John Wiley & Sons， Ltd
This paper provides a proof of the robustness of the overlapping domain decomposition preconditioners for the linear finite element approximation of second‐order elliptic boundary value problems with strongly discontinuous coefficients. By analyzing the eigenvalue distribution of the domain decomposition preconditioned system, we prove that only a small number of eigenvalues may deteriorate with respect to the discontinuous jump or mesh size, and all the other eigenvalues are bounded below and above nearly uniformly with respect to the jump and mesh size. As a result, we prove that the convergence rate of the preconditioned conjugate gradient methods is nearly uniform with respect to the large jump and mesh size. Copyright © 2008 John Wiley & Sons, Ltd.