| 二维Helmholtz方程Dirichlet问题的边界元解法 |
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| 引用本文： | 金朝嵩. 二维Helmholtz方程Dirichlet问题的边界元解法[J]. 土木建筑与环境工程, 1988, 10(3) |
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| 作者姓名： | 金朝嵩 |
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| 摘 要： | 本文首先讨论了二维Helmho1tz方程Diricblet边值问题广义解的存在唯一性,然后得到了同时适合内问题和外问题的解的解积分表达式,并导出了与边值问題对应的第一类Fredholm边界积分方程.最后给出了与边界积分方程等价的变分方程的一种有限元近似解法.
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| 关 键 词： | 边界元方法 Sobolev空间 拟微分子算子 有限元 边界积分方程 |
A BOUNDARY ELEMENT METHOD FOR SOLVING DIRICHLET PROBLEM OF THE HELMHOLTZ EQUATION IN R~2 |
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| Jin Chaosong. A BOUNDARY ELEMENT METHOD FOR SOLVING DIRICHLET PROBLEM OF THE HELMHOLTZ EQUATION IN R~2[J]. Journal of Civil,Architectrual & Environment Engineering, 1988, 10(3) |
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| Authors: | Jin Chaosong |
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| Affiliation: | Jin Chaosong |
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| Abstract: | This paper presents a boundary element method for solving Dirichlet bou-ndary value problem of the Helmholtz equation in R~2.First,the existence andthe uniqueness of an extended solution for the problem are obtained.Then,thesolution is expressed in terms of simple layer potentials,and this expression,which is suitable to the interior as well as the exterior problem,leads to aboundary integral equation of the first kind.Finally,a finite element approachis applied to solve a variational form which is equivalent to the boundaryintegral equation. |
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| Keywords: | boundary element method Sobolev spaces pseudo-differential operators finite element boundary integral equation. |
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