阻尼边界条件散射问题的数值解法 |
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引用本文: | 王连堂,杨阿莉,管金友,王青云,张梅东.阻尼边界条件散射问题的数值解法[J].数学物理学报(A辑),2009,29(6):1704-1713. |
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作者姓名: | 王连堂 杨阿莉 管金友 王青云 张梅东 |
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作者单位: | 王连堂,王青云,张梅东(西北大学数学系,西安,710069);杨阿莉(西安工程大学理学院,西安,710048);管金友(铜陵学院基础教育系,安徽铜陵,244000) |
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基金项目: | 西安工程大学博士启动基金 |
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摘 要: | 该文研究了光滑区域上二维Helmholtz方程阻尼边界条件外问题的数值解法, 应用单双层位势组合来逼近散射场, 因此积分方程中含有超奇异算子. 给出了超奇异算子的离散化方法, 在Holder空间中给出了误差估计和解析边界的收敛性分析. 最后针对该方法给出数值实例, 以表明该方法的有效性.
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关 键 词: | Helmholtz方程 阻尼边界条件 积分方程 超奇异算子 |
收稿时间: | 2007-12-02 |
修稿时间: | 2009-01-09 |
On the Numerical Solution of the Direct Acoustic Scattering Problem for an Impedance Boundary |
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Institution: | Department of Mathematics, Northwest University, Xi'an 710069 |
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Abstract: | In this paper, the authors describe a fully discrete method for the numerical solution of the hyper-singular integral equation arising from the combined single and double layer potential approach for the solution of the exterior impedance boundary problem to the two-dimensional Helmholtz equation in smooth domains. The equation contains a hyper-singular operator. The authors develop an error analysis in a H\"{o}lder space setting with point-wise estimates and prove an exponential convergence rate for analytic boundaries and boundary data. Finally the numerical example is given to show the validity of the method. |
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Keywords: | Helmholtz equation Impedance boundary condition Integral equation Hyper-singular operator |
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