BIT Numerical Mathematics

, Volume 49, Issue 3, pp 509–526 | Cite as

Matrix decomposition algorithms for the C0-quadratic finite element Galerkin method

  • Kui Du
  • Graeme Fairweather
  • Que N. Nguyen
  • Weiwei Sun
Article

Abstract

Explicit expressions for the eigensystems of one-dimensional finite element Galerkin (FEG) matrices based on C0 piecewise quadratic polynomials are determined. These eigensystems are then used in the formulation of fast direct methods, matrix decomposition algorithms (MDAs), for the solution of the FEG equations arising from the discretization of Poisson’s equation on the unit square subject to several standard boundary conditions. The MDAs employ fast Fourier transforms and require O(N2log N) operations on an N×N uniform partition. Numerical results are presented to demonstrate the efficacy of these algorithms.

Keywords

Poisson’s equation Finite element Galerkin method Piecewise quadratic functions Generalized eigenvalue problem Matrix decomposition algorithms 

Mathematics Subject Classification (2000)

65F05 65N22 65N30 

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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  • Kui Du
    • 1
  • Graeme Fairweather
    • 2
  • Que N. Nguyen
    • 4
  • Weiwei Sun
    • 1
  1. 1.Department of MathematicsCity University of Hong KongKowloonHong Kong
  2. 2.Department of Mathematical and Computer SciencesColorado School of MinesGoldenUSA
  3. 3.Mathematical ReviewsAmerican Mathematical SocietyAnn ArborUSA
  4. 4.Avanade Inc.SeattleUSA

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