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A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic ProblemsIn this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.
Document ID
19970006601
Acquisition Source
Langley Research Center
Document Type
Conference Paper
Authors
Maliassov, Serguei
(Texas A&M Univ. College Station, TX United States)
Date Acquired
August 17, 2013
Publication Date
September 1, 1996
Publication Information
Publication: Seventh Copper Mountain Conference on Multigrid Methods
Subject Category
Numerical Analysis
Accession Number
97N13530
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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