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Multilevel preconditioners for a quadrature Galerkin solution of a biharmonic problem

✍ Scribed by Rakhim Aitbayev

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
169 KB
Volume
22
Category
Article
ISSN
0749-159X

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✦ Synopsis

Efficient multilevel preconditioners are developed and analyzed for the quadrature finite element Galerkin approximation of the biharmonic Dirichlet problem. The quadrature scheme is formulated using the Bogner-Fox-Schmit rectangular element and the product two-point Gaussian quadrature. The proposed additive and multiplicative preconditioners are uniformly spectrally equivalent to the operator of the quadrature scheme. The preconditioners are implemented by optimal algorithms, and they are used to accelerate convergence of the preconditioned conjugate gradient method. Numerical results are presented demonstrating efficiency of the preconditioners.

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