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PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS 被引量：2

PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS
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摘要 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. 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.
作者 Yun-qing Huang Shi Shu Xi-jun Yu
机构地区 Hunan Key Laboratory for Computation and Simulation in Science and Engineering Laboratory of Computational Physics
出处 《Journal of Computational Mathematics》 SCIE EI CSCD 2006年第5期657-664,共8页 计算数学（英文）
关键词 Finite element Algebraic multigrid methods Preconditioned Conjugate Gradient Condition number. Finite element, Algebraic multigrid methods, Preconditioned Conjugate Gradient, Condition number.
分类号 O24 [理学—计算数学]
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参考文献11

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同被引文献11

  • 1孙杜杜,舒适.求解三维高次拉格朗日有限元方程的代数多重网格法[J].计算数学,2005,27(1):101-112. 被引量：17
  • 2肖映雄,张平,舒适,阳莺.等代数结构面网格剖分下三维弹性问题的代数多重网格法[J].工程力学,2005,22(6):76-81. 被引量：4
  • 3Braess D. Finite elements: theory, fast solvers, and applications in solid mechanics [M]. England: Cambridge University Press, 2001.
  • 4Griebel M, Oeltz D, Schweitzer M A. An algebraic multigrid method for linear elasticity [J]. SIAM Journal of Scientific Computing, 2003, 25(2): 385-407.
  • 5Brezina M, Cleary A J, Falgout R D, Henson V E, Jones J E, Manteuffel T A, McCormick S F, Ruge J W. Algebraic multigfid based on element interpolation (AMGe)[J].Journal of Scientific Computing, 2000, 22(5): 1570- 1592.
  • 6Jones J, Vassilevski P. AMGe based on element agglomeration [J]. SIAM Journal of Scientific Computing, 2001, 23(1): 109- 133.
  • 7Sumant P S, Cangellaris A C, Aluru N R. A node-based agglomeration AMG solver for linear elasticity in thin bodies [J]. Communications in Numerical Methods in Engineering, 2009, 25: 219-236.
  • 8Mandel J, Brezina M, Vanek P. Energy optimization of algebraic multigrid bases [J]. Computing, 1999, 62(3): 205-228.
  • 9Xiao Y X, Shu S, Zhao T Y. A geometric-based algebraic multigrid for higher-order finite element equations in two dimensional linear elasticity [J]. Numerical Linear Algebra with Applications, 2009, 16(7): 535- 559.
  • 10Saad Y. Iterative methods for sparse linear systems [M]. 2nd ed. Philadelphia, PA: Society for Industrial and Applied Mathematies, 2003.

引证文献2

Journal of Computational Mathematics
2006年 第5期

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