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Volume 24, Issue 5
Preconditioning Higher Order Finite Element Systems by Algebraic Multigrid Method of Linear Elements

Yun-qing Huang, Shi Shu & Xi-jun Yu

J. Comp. Math., 24 (2006), pp. 657-664.

Published online: 2006-10

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  • 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.

  • Keywords

Finite element, Algebraic multigrid methods, Preconditioned Conjugate Gradient, Condition number.

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COPYRIGHT: © Global Science Press

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@Article{JCM-24-657, author = {Yun-qing Huang, Shi Shu and Xi-jun Yu}, title = {Preconditioning Higher Order Finite Element Systems by Algebraic Multigrid Method of Linear Elements}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8781.html} }
TY - JOUR T1 - Preconditioning Higher Order Finite Element Systems by Algebraic Multigrid Method of Linear Elements AU - Yun-qing Huang, Shi Shu & Xi-jun Yu JO - Journal of Computational Mathematics VL - 5 SP - 657 EP - 664 PY - 2006 DA - 2006/10 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8781.html KW - Finite element, Algebraic multigrid methods, Preconditioned Conjugate Gradient, Condition number. AB -

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.

Yun-qing Huang, Shi Shu and Xi-jun Yu. (2006). Preconditioning Higher Order Finite Element Systems by Algebraic Multigrid Method of Linear Elements. Journal of Computational Mathematics. 24 (5). 657-664. doi:
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