Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Multilevel Preconditioners for a Quadrature Galerkin Solution of a Biharmonic Problem
 

Summary: Multilevel Preconditioners for a Quadrature
Galerkin Solution of a Biharmonic Problem
Rakhim Aitbayev
Department of Mathematics, New Mexico Institute of Mining and Technology,
Socorro, New Mexico 87801
Received 1 April 2005; accepted 15 August 2005
Published online in Wiley InterScience (www.interscience.wiley.com).
DOI 10.1002/num.20122
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
Fox­Schmit 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. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 22: 000­000, 2006
Keywords: biharmonic problem; multilevel method; preconditioner; finite element method; Gaussian
quadrature; orthogonal spline collocation
I. INTRODUCTION
The purpose of this article is to develop and analyze multilevel preconditioners for the quadrature
finite element Galerkin approximation of a biharmonic problem. Efficient algorithms for the

  

Source: Aitbayev, Rakhim - Department of Mathematics, New Mexico Institute of Mining and Technology

 

Collections: Mathematics