| 四阶微分方程Hermite有限元的预处理共轭梯度法 |
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| 引用本文： | 赵国忠.四阶微分方程Hermite有限元的预处理共轭梯度法[J].大学数学,2010,26(2). |
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| 作者姓名： | 赵国忠 |
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| 作者单位： | 包头师范学院,数学科学学院,包头,014030 |
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| 摘 要： | 对一类四阶微分方程两点边值问题的Hermite有限元方法进行了研究.首先讨论了该方程通常意义下的Galerkin有限元离散,考虑到有限元离散得到的线性方程组的对称正定性,文中采用了预处理最速下降法和共轭梯度方法求解线性方程组,通过选择不同的预处理器,使得求解该方程组的迭代次数有了很大的改观.
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| 关 键 词： | Hermite有限元 四阶微分方程 最速下降法 共轭梯度法 预处理器 |
Preconditioned Conjugate Gradient Method of Hermite Finite Element Approximations for Two Point Boundary Value Problem of Fourth Order Differential Equations |
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| ZHAO Guo-zhong.Preconditioned Conjugate Gradient Method of Hermite Finite Element Approximations for Two Point Boundary Value Problem of Fourth Order Differential Equations[J].College Mathematics,2010,26(2). |
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| Authors: | ZHAO Guo-zhong |
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| Abstract: | Hermite finite element approximation for two-point boundary value problem of fourth-order differential equations is discussed.Considering the symmetric and positive of the discrete matrix,steepest decent method and preconditioned conjugate gradient method are used to solve the equation.Different preconditioned matrixes are used to reduce the iterative number. |
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| Keywords: | Hermite finite element fourth order differential equation steepest decent method preconditioned conjugate gradient method preconditioner |
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