Block iterative solvers for higher order finite volume methods

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Recently, new higher order finite volume methods (FVM) were introduced in [JZ. Cai, J. Douglas, M. Park, Development and analysis of higher order finite volume methods over rectangles for elliptic equations, Adv. Comput. Math. 19 (2003) 3-33], where the linear system derived by the hybridization with Lagrange multiplier satisfying rile flux consistency condition is reduced to a linear system for a pressure variable by all appropriate quadrature rule. We study the convergence of an iterative solver for this linear system. The conjugate gradient (CC) method is a natural choice to solve the system, but it seems slow, possibly due to the non-diagonal dominance of the system. In this paper, we propose block iterative methods with a reordering scheme to solve the linear system derived by the higher order FVM and prove their convergence. With a proper ordering. each block subproblem can be solved by fast methods Such as the multigrid (MG) method. The numerical experiments show that these block iterative methods are much faster than CC. (C) 2009 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2009-10
Language
English
Article Type
Article
Citation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.232, no.2, pp.378 - 387

ISSN
0377-0427
DOI
10.1016/j.cam.2009.06.018
URI
http://hdl.handle.net/10203/20482
Appears in Collection
MA-Journal Papers(저널논문)
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