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Nonoverlapping domain decomposition methods with a simple coarse space for elliptic problems


Authors: Qiya Hu, Shi Shu and Junxian Wang
Journal: Math. Comp. 79 (2010), 2059-2078
MSC (2010): Primary 65F10, 65N30
DOI: https://doi.org/10.1090/S0025-5718-10-02361-6
Published electronically: April 26, 2010
MathSciNet review: 2684355
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Abstract: We propose a substructuring preconditioner for solving three-dimensional elliptic equations with strongly discontinuous coefficients. The new preconditioner can be viewed as a variant of the classical substructuring preconditioner proposed by Bramble, Pasiack and Schatz (1989), but with much simpler coarse solvers. Though the condition number of the preconditioned system may not have a good bound, we are able to show that the convergence rate of the PCG method with such substructuring preconditioner is nearly optimal, and also robust with respect to the (possibly large) jumps of the coefficient in the elliptic equation.


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Additional Information

Qiya Hu
Affiliation: LSEC, Institute of Computational Mathematics and Scientific Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Email: hqy@lsec.cc.ac.cn

Shi Shu
Affiliation: Department of Mathematics, Xiangtan University, Hunan 411105, People’s Republic of China
Email: shushi@xtu.edu.cn

Junxian Wang
Affiliation: Department of Mathematics, Xiangtan University, Hunan 411105, People’s Republic of China
Email: xianxian.student@sina.com

DOI: https://doi.org/10.1090/S0025-5718-10-02361-6
Keywords: Domain decomposition, coarse subspace, substructuring preconditioner, inexact solver, condition number
Received by editor(s): October 9, 2008
Received by editor(s) in revised form: June 7, 2009
Published electronically: April 26, 2010
Additional Notes: The first author was supported by Natural Science Foundation of China G10771178, The Key Project of Natural Science Foundation of China G10531080, and National Basic Research Program of China G2005CB321702.
The second author was supported by Natural Science Foundation of China (10676031, 10771178), the Basic Research Program of China under grant 2005CB321702.
Article copyright: © Copyright 2010 American Mathematical Society

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