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Zbl 1204.65140
Hu, Qiya; Shu, Shi; Wang, Junxian
Nonoverlapping domain decomposition methods with a simple coarse space for elliptic problems. (English)
[J] Math. Comput. 79, No. 272, 2059-2078 (2010). ISSN 0025-5718; ISSN 1088-6842/e

The authors 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 {\it J. H. Bramble, J. E. Pasciak} and {\it A. H. Schatz} [Math. Comput. 53, No.~187, 1--24 (1989; Zbl 0668.65082)], but with much simpler coarse solvers. It is shown that the preconditioned conjugate gradient method with such substructuring preconditioner has a nearly optimal convergence rate, although the condition numbers of the preconditioned systems are not quasi-optimal yet.
[Srinivasan Natesan (Assam)]

MSC 2000:: *65N55 Multigrid methods; domain decomposition (BVP of PDE)
65F10 Iterative methods for linear systems
65N30 Finite numerical methods (BVP of PDE)
65N12 Stability and convergence of numerical methods (BVP of PDE)
65F08
35J25 Second order elliptic equations, boundary value problems
35R05 PDE with discontinuous coefficients or data

Keywords: domain decomposition; coarse subspace; substructuring preconditioner; inexcat solver; condition number; elliptic equations; strongly discontinuous coefficients; preconditioned conjugate gradient method; convergence

Citations: Zbl 0668.65082

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