| 利用边界元法求解一类重调和方程 |
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| 引用本文： | 崔玉环,屈静国,陈一鸣,杨爱民.利用边界元法求解一类重调和方程[J].计算数学,2012,34(1):49-56. |
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| 作者姓名： | 崔玉环 屈静国 陈一鸣 杨爱民 |
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| 作者单位： | 1. 河北联合大学轻工学院, 河北唐山 063000;
2. 燕山大学理学院, 河北秦皇岛 066004 |
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| 摘 要： | 边界元法(BEM)和多重互易法(MRM)相结合求解一类重调和方程.通过重调和基本解序列给出的MRM-方法和BEM, 推导出该类问题的MRM-边界变分方程, 用边界元法求解该变分方程, 从而得到重调和方程的近似解, 并给出了解的存在唯一性证明.通过数值算例说明了MRM-方法具有收敛速度快、计算精度高, 易编程等优点, 为使用边界元法数值求解重调和方程提供了方法和理论依据.适合于工程中的实际运算.
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| 关 键 词： | 边界元法 MRM 边界积分方程 边界变分方程 |
| 收稿时间： | 2011-04-25; |
BOUNDARY ELEMENT METHOD FOR SOLVING A KIND OF BIHARMONIC EQUATION |
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| Cui Yuhuan
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Qu Jingguo
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Chen Yiming
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Yang Aimin.BOUNDARY ELEMENT METHOD FOR SOLVING A KIND OF BIHARMONIC EQUATION[J].Mathematica Numerica Sinica,2012,34(1):49-56. |
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| Authors: | Cui Yuhuan Qu Jingguo Chen Yiming Yang Aimin |
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| Institution: | 1. Qinggong College, Hebei United University, Tangshan 063000, Hebei, China;
2. College of Sciences, Yanshan University, Qinhuangdao 066004, Hebei, China |
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| Abstract: | Boundary element method(BEM) and multiple reciprocity method(MRM) are used to solve a kind of biharmonic equation.Apply MRM which is derived from the sequence of fundamental solutions for biharmonic operator and BEM,to educe the MRM boundary variational equation of this problem.Solve this variational equation by BEM to obtain the approximation solution of the biharmonic equation,and the existence and uniqueness of the corresponding solution are given.Finally the numerical example shows that this method has faster convergence,higher precision and easier programming.It provides approach and theoretical basis to solve biharmonic equation by BEM and is suitable for the practical computation of engineering. |
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| Keywords: | BEM MRM boundary integral equation boundary variational equation |
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