Preconditioning Higher Order Finite Element Systems by Algebraic Multigrid Method of Linear Elements
Year: 2006
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 5 : pp. 657–664
Abstract
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-JCM-8781
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 5 : pp. 657–664
Published online: 2006-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Finite element Algebraic multigrid methods Preconditioned Conjugate Gradient Condition number.