Nonoverlapping domain decomposition methods with a simple coarse space for elliptic problems
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- by Qiya Hu, Shi Shu and Junxian Wang PDF
- Math. Comp. 79 (2010), 2059-2078 Request permission
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.References
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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
- 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. - © Copyright 2010 American Mathematical Society
- Journal: Math. Comp. 79 (2010), 2059-2078
- MSC (2010): Primary 65F10, 65N30
- DOI: https://doi.org/10.1090/S0025-5718-10-02361-6
- MathSciNet review: 2684355