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Restricted Additive Schwarz Preconditioner for Elliptic Equations with Jump Coefficients

Part of: Numerical linear algebra Partial differential equations, boundary value problems

Published online by Cambridge University Press:  19 September 2016

Zhiyong Liu  and
Yinnian He
Zhiyong Liu*
Affiliation:
School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China
Yinnian He*
Affiliation:
Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
*
*Corresponding author. Email:zhiyongliu1983@163.com (Z. Y. Liu), heyn@mail.xjtu.edu.cn (Y. N. He)
*Corresponding author. Email:zhiyongliu1983@163.com (Z. Y. Liu), heyn@mail.xjtu.edu.cn (Y. N. He)
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Abstract

This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap (RASHO) for the second order elliptic problems with jump coefficients. By analyzing the eigenvalue distribution of the RASHO preconditioner, we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and meshsize.

Keywords

Jump coefficientsconjugate gradienteffective condition numberdomain decompositionrestricted additive Schwarz

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N55: Multigrid methods; domain decomposition 65F10: Iterative methods for linear systems
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016 , pp. 1072 - 1083
Copyright
Copyright © Global-Science Press 2016 

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