关于Helmholtz外问题的边界积分方程解的唯一性问题

王清; 徐博侯

关于Helmholtz外问题的边界积分方程解的唯一性问题

王清¹,
徐博侯²

浙江大学力学系

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出版历程
- 收稿日期: 1989-02-01
- 刊出日期: 1990-10-15

On the Uniqueness of Boundary Integral Equation for the Exterior Helmholtz Problem

Wang Qing¹,
Xu Bo-hou²

Department of Mechanics, Zhejiang University, Hangzhou

摘要

摘要: 本文用能量分析的观点探讨了用边界积分方程描述Helmholtz外问题时,解的唯一性不能保持的原因.文中证明了,当利用积分方程来描述问题时,实际上将无穷远处的Sommerfeld条件改成了既适合于外向波(辐射波),又适合于内向波(吸收波),即整个系统的能量保持守恒.并根据此观点解释了保持唯一性的算法.
- Helmholtz外问题 /
- 边界积分方程 /
- 唯一性
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.
- exterior Helmholtz problem /
- boundary integral equation /
- uniqueness

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参考文献(13)

[1]	Sommerfeld,A.,Partial Differential Equation in Physics,Academic Press(1949).
[2]	Schenck,H.A.,Improved integral formulation for acoustics radiation problems,J.Acoust.Soc.Am.,44(1968),41-58.
[3]	Burton.A.J.and G.F.Miller,The application of integral equation methods to the numerical solution of some exterior boundary value problems,Proc.R.Soc.London.,Ser.A.,323(1971),201-210.
[4]	Waterman,P.C.,New formulation of acoustic scattering,J.Acoust.Soc.Am.,45(1969),1417-1429.
[5]	Kleinman,R.E.and G.F.Roach,Boundary integral equations for the three-dimensional Helmholtz equation,SIAM,Review,16(1974),214-236.
[6]	Piaszczyk,C.M.,Acoustic radiation from vibrating surface at characteristic frequencies,J.Acoust.Soc.Am.,75(1984),363-375.
[7]	Martin,P.A.,On the null-field equations for the exterior problems of acoustics,Q.J.Mech Appl.Math.,33(1980),385-396.
[8]	Brod,K.,On the uniqueness of solution for all wave numbers in acoustic radiation,J.Acoust.Soc.Am.,76(1984),1238-1243.
[9]	Filippi,P.J.T.,.Integral equations in acoustics,Theoretical Acoustics and Numerical Techniques,Ed.by P.Filippi,Springer-Verlag(1983),1-49.
[10]	Meyer,W.L,W.A.Bell,B.T.Zinn and M.P.Stallybrass,Boundary integral solution of three dimensional acoustic radiation problems,J.Sound and Vib.,59,2(1978),242-262.
[11]	Amini,S.and D.T.Wilton,An investigation of boundary element methods for the exterior acoustic problem,Compu.Meth.in Appl.Mech.and Eng.,54(1986),49-65.
[12]	斯米尔诺夫,В,И.,<高等数学教程》,谷超豪、金福临译,第4卷,第2分册,人民教育出版社(1958).
[13]	柯朗、希尔伯脱,数学物理方法》,能振翔、杨应辰译,Ⅰ卷,科学出版社(1981).