[1]王泽文,吴红利,胡彬.一类混合边界条件的裂缝散射问题及数值模拟[J].江西师范大学学报(自然科学版),2015,(06):592-598.
　WANG Zewen,WU Hongli,HU Bin.A Scattering Problem of a Crack with Mixed Boundary Conditions and Its Numerical Simulations[J].Journal of Jiangxi Normal University:Natural Science Edition,2015,(06):592-598.
点击复制

一类混合边界条件的裂缝散射问题及数值模拟()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2015年06期
页码:
592-598
栏目:
出版日期:
2015-12-31

文章信息/Info

Title:
A Scattering Problem of a Crack with Mixed Boundary Conditions and Its Numerical Simulations
作者:
王泽文;吴红利;胡彬
东华理工大学理学院,江西 南昌 330013
Author(s):
WANG Zewen; WU Hongli; HU Bin
School of Science,East China University of Technology,Nanchang Jiangxi 330013,China
关键词:
Helmholtz方程;  散射问题;  裂缝;  混合边界条件;  积分方程
Keywords:
Helmholtz equation;  scattering problem;  crack;  mixed boundary conditions;  integral equation
分类号:
O 241.8; O 241.6
文献标志码:
A
摘要:
考虑时谐电磁波对非常薄的无限长圆柱理想导体的散射问题,该散射体在水平截面上抽象为平面上的曲线段(即裂缝).假设曲线段是光滑的,且其2侧赋予不同的边界条件(混合边界条件),首先证明了散射问题解的唯一性; 然后通过位势理论与积分方程方法,将问题转化为等价的奇异积分方程组并证明了解的存在性; 最后,通过求解奇异积分方程组给出了混合边界裂缝散射问题的数值模拟.
Abstract:
Consider a scattering problem of time-harmonic electromagnetic plane waves from a thin infinitely long cylindrical obstacle.The thin obstacle is a curve segment referred to as crack.Assuming that the crack is smooth,and both sides of the crack have different boundary conditions(mixed boundary conditions),the uniqueness of the solution is firstly given for the scattering problem.Then the scattering problem is transformed into an equivalent system of hypersingular integral equations by the potential theory and the integral equation method,and the existence of the solution is also proved.Finally,numerical simulations of the scattering problem for the mixed boundary crack are presented by solving the system of hypersingular integral equations.

参考文献/References:

[1] Kress R.Inverse scattering from an open arc [J].Mathematical Methods in the Applied Sciences,1995,18(4):267-293.
[2] Monch L.On the numerical solution of the direct scattering problem for an open sound-hard arc [J].Journal of Computational and Applied Mathematics,1996,71(2):343-356.
[3] Wendland W L,Stephan E P.A hypersingular boundary integral method for two-dimensional screen and crack problems [J].Archive for Rational Mechanics and Analysis,1990,112(4):363-390.
[4] Kress R,Lee K M.Integral equation methods for scattering from an impedance crack [J].Journal of Computational and Applied Mathematics,2003,161(1):161-177.
[5] Liu Jijun,Krutitskii P A,Sini M.Numerical solution of the scattering problem for acoustic waves by a two-sided crack in 2-dimensional space[J].Journal of Computational Mathematics,2011,29(2):141-166.
[6] 严国政.具有混合裂缝散射问题的边界积分方程方法 [J].数学物理学报,2011,31A(5):1167-1175.
[7] Wang H,Liu J.Numerical solution for the Helmholtz equation with mixed boundary condition [J].Numerical Mathematics(English Serers),2007,16(3):203.
[8] Monch L.On the inverse acoustic scattering problem by an open arc:the sound-hard case [J].Inverse Problems,1997,13(5):1379.
[9] Cakoni F,Colton D.The linear sampling method for cracks [J].Inverse Problems,2003,19(2):279.
[10] Liu Jijun,Sini M.Reconstruction of cracks of different types from far-field measurements [J].Mathematical Methods in the Applied Sciences,2010,33(8):950-973.
[11] Colton D,Kress R.Inverse acoustic and electromagnetic scattering theory [M].New York:Springer,2013.
[12] Colton D,Kress R.Integral equation methods in scattering theory [M].New York:Springer-Verlag,Wiley,1983.
[13] McLean W.Strongly elliptic systems and boundary integral equations [M].Cambridge:Cambridge University Press,2000.

备注/Memo

备注/Memo:
基金项目:国家自然科学基金(11161002),江西省自然科学基金(20142BAB201008),江西省青年科学基金(20132BAB211014)和江西省青年科学家培养计划(20122BCB23024)资助项目.
更新日期/Last Update: 1900-01-01