| 三维Helmholtz方程边值问题的新型边界积分-微分方程及其边界元解法 |
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| 引用本文： | 张新红,同登科.三维Helmholtz方程边值问题的新型边界积分-微分方程及其边界元解法[J].纯粹数学与应用数学,2009,25(1):176-182. |
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| 作者姓名： | 张新红 同登科 |
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| 作者单位： | 中国石油大学(华东)数学与计算科学学院,山东,东营,257061 |
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| 摘 要： | 用双层位势表示的二维Neumann边值问题的边界归化方法,将原始问题归化为新型边界积分-微分方程,由此导出一种新的既能保持原始问题的自伴性,又具有可积弱奇性积分核的边界变分方程.本文将此法推广到三维Helmholtz方程Neumann边值问题,并给出最优能量模误差估计和内部最大模超收敛估计.
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| 关 键 词： | 边界元法 积分-微分方程 变分方程 范数 误差估计 |
A new boundary integral-differential equation for three dimensional Helmholtz equation and its boundary element methods |
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| ZHANG Xin-hong,TONG Deng-ke.A new boundary integral-differential equation for three dimensional Helmholtz equation and its boundary element methods[J].Pure and Applied Mathematics,2009,25(1):176-182. |
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| Authors: | ZHANG Xin-hong TONG Deng-ke |
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| Institution: | School of Mathematics and Computational Science;China University of Petroleum;Dongying 257061;China |
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| Abstract: | The boundary element method for the Neumann boundary value problems by using double-layer potential is to reduce the original problems to boundary integral-differential equations,and to get the new boundary variational equations equivalent to them. This method keeps the self-adjointness of the original problem while avoiding complicated calculation of the finite of the divergent integral.In this paper,this method is deduced to Neumann boundary value problem of three-dimensional Helmhotlz equation,and the es... |
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| Keywords: | boundary element method integral-differential equations variational formulas norm error estimates |
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