Applied Mathematics and Mechanics (English Edition) ›› 1990, Vol. 11 ›› Issue (10): 965-971.

• 论文 • 上一篇    下一篇

ON THE UNIQUENESS OF BOUNDARY INTEGRAL EQUATION FOR THE EXTERIOR HELMHOLTZ PROBLEM

王清1, 徐博侯2   

  1. 1. Department of Civil Engineering, Zhejiang University, Hangzhou;
    2. Department of Mechanics, Zhejiang University, Hangzhou
  • 收稿日期:1989-02-01 出版日期:1990-10-18 发布日期:1990-10-18

ON THE UNIQUENESS OF BOUNDARY INTEGRAL EQUATION FOR THE EXTERIOR HELMHOLTZ PROBLEM

Wang Qing1, Xu Bo-hou2   

  1. 1. Department of Civil Engineering, Zhejiang University, Hangzhou;
    2. Department of Mechanics, Zhejiang University, Hangzhou
  • Received:1989-02-01 Online:1990-10-18 Published:1990-10-18

摘要: From the point of view of energy analysis, the cause that the uniqueness of the boundary integral equation induced from the exterior Helmholtz problem does not hold is investigated in this paper. It is proved that the Sommerfeld’s condition at the infinity is changed so that it is suitable not only for the radiative wave but also for the absorptive wave when we use the boundary integral equation to describe the exterior Helmholtz problem. There fore, the total energy of the system is conservative. The mathematical dealings to guarantee the uniqueness are discussed based upon this explanation.

关键词: exterior Helmholtz problem, boundary integral equation, uniqueness

Abstract: From the point of view of energy analysis, the cause that the uniqueness of the boundary integral equation induced from the exterior Helmholtz problem does not hold is investigated in this paper. It is proved that the Sommerfeld’s condition at the infinity is changed so that it is suitable not only for the radiative wave but also for the absorptive wave when we use the boundary integral equation to describe the exterior Helmholtz problem. There fore, the total energy of the system is conservative. The mathematical dealings to guarantee the uniqueness are discussed based upon this explanation.

Key words: exterior Helmholtz problem, boundary integral equation, uniqueness

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