摘要
对由Ｈｅｌｍｈｏｌｔｚ方程Ｎｅｕｍａｎｎ外问题化归的各种边界积分方程进行了讨论。在用Ｈｅｌｍｈｏｌｔｚ表达式导出这些积分方程的过程中，分析了其中一些方程当波数ｋ是内问题的特征值时没有唯一解这一著名难题产生的原因，并提出了克服这一难题的方法，即给出了一个既与原边值问题等价、又对所有波数ｋ都具有唯一解的直接边界积分方程。同时，分别对各种边界积分方程的优点及不足之处进行了评述。
This paper presents a discussion on various boundary integral equations reduced from the exterior Neumann problem of Helmholtz equation.The author analyses how the famous difficulty that some equations have no unique solution when the wave number k is an eigenvalue of an interior problem is arised in the course of reducing these equations from Helmholtz representations,and proposes a method of overcoming the difficulty,that is,introducing a direct boundary integral equation which has unique solution for all wave numbers k and is equivalent to the original boundary value problem.Besides,advantages and shortcomings for these integral equations are estimated respectively.
出处
《重庆建筑大学学报》
CSCD
1998年第2期35-40,46,共7页
Journal of Chongqing Jianzhu University
关键词
位势
边值问题
边界
积分方程法
potential, boundary value problems of Helmholtz equation, boundary elements
