Multilevel methods for Wilson element approximation of elasticity problem

In this paper, a multilevel preconditioner and a V-cycle multigrid algorithm are presented for Wilson nonconforming element approximation of elasticity problem. The condition number of the multilevel preconditioner is shown to be bounded by a constant independent of mesh size and mesh level. Moreove...

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Vydáno v:Computer methods in applied mechanics and engineering Ročník 174; číslo 1; s. 191 - 201
Hlavní autor: Xu, Xuejun
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 04.05.1999
Elsevier
Témata:
Computational techniques
Exact sciences and technology
Finite-element and galerkin methods
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Physics
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Conjugate gradient method
Finite element method
Multigrid
Non conforming finite element
Elasticity
Numerical method
Preconditioning
Structural analysis
ISSN:0045-7825, 1879-2138
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Abstract In this paper, a multilevel preconditioner and a V-cycle multigrid algorithm are presented for Wilson nonconforming element approximation of elasticity problem. The condition number of the multilevel preconditioner is shown to be bounded by a constant independent of mesh size and mesh level. Moreover, optimal convergence rate of the V-cycle multigrid algorithm is obtained. A numerical example is given to illustrate the efficiency of our methods.
AbstractList In this paper, a multilevel preconditioner and a V-cycle multigrid algorithm are presented for Wilson nonconforming element approximation of elasticity problem. The condition number of the multilevel preconditioner is shown to be bounded by a constant independent of mesh size and mesh level. Moreover, optimal convergence rate of the V-cycle multigrid algorithm is obtained. A numerical example is given to illustrate the efficiency of our methods.
Author Xu, Xuejun
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  organization: Institute of Computational Mathematics, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, PR China
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Cites_doi 10.1016/0045-7825(76)90002-5
10.1090/S0025-5718-1981-0595040-2
10.1016/0045-7825(76)90059-1
10.1016/S0045-7825(96)01130-9
10.1137/0731089
10.1007/s002110050084
10.1137/1034116
10.1137/0732008
10.1002/nme.1620100602
10.1007/BF01405567
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Issue 1
Keywords Conjugate gradient method
Finite element method
Multigrid
Non conforming finite element
Elasticity
Numerical method
Preconditioning
Structural analysis
Language English
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SubjectTerms Computational techniques
Exact sciences and technology
Finite-element and galerkin methods
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Physics
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Title Multilevel methods for Wilson element approximation of elasticity problem
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