| 三维Helmholtz方程外边值问题的虚边界元法 |
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| 引用本文： | 马健军,祝家麟,贾丽君.三维Helmholtz方程外边值问题的虚边界元法[J].西南师范大学学报(自然科学版),2009,34(6). |
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| 作者姓名： | 马健军 祝家麟 贾丽君 |
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| 作者单位： | 1. 四川外语学院,国际商学院,重庆,400031
2. 重庆大学,数理学院,重庆,400045 |
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| 摘 要： | 基于位势的延拓,推导出三维虚边界积分方程.通过选择不同的虚边界,避免相应内问题的特征值与波数重合,从而保证解的唯一性.数值算例验证了该方法求解任意波数三维Helmholtz方程外边值问题的有效性.
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| 关 键 词： | Helmholtz方程外边值问题 双层位势 单层位势 虚边界元 |
The Virtual Boundary Element Method for Exterior Problems of the 3-D Helmholtz Equation |
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| MA Jian-jun,ZHU Jia-lin,JIA Li-jun.The Virtual Boundary Element Method for Exterior Problems of the 3-D Helmholtz Equation[J].Journal of Southwest China Normal University(Natural Science),2009,34(6). |
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| Authors: | MA Jian-jun ZHU Jia-lin JIA Li-jun |
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| Abstract: | A virtual boundary method for solving the Dirichlet and Neumann exterior problems of the 3-D Helmholtz equation,which is valid for all wave number is presented in this paper.When wave number is an eigenvalue of the interior Dirichlet or Neumann problem for the Laplacian,the solution of the boundary integral equation correspond to eigenvalue is not unique.Based on the extension of potential function,Virtual boundary integral equation is deduced.The uniqueness problem is granted by choosing different virtual boundary,with which the wave number do not coincide with the eigenvalue of the original interior Dirichlet or Neumann problem for the Laplacian.The results of numerical examples demonstrate that the scheme presented is practical and effective for the exterior problems of the 3-D Helmholtz equation with any wave numbers. |
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| Keywords: | exterior problems of the Helmholtz equation double layer potential function single layer potential the virtual boundary element method |
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