A semi-analytical approach for radiation and scattering problems with circular boundaries
A semi-analytical approach for radiation and scattering problems with circular boundaries
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DOI：
10.1016/j.cma.2007.02.004
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发表时间：
2007-05
影响因子：
7.2
通讯作者：
Jeng-Tzong Chen;C. T. Chen;Pocheng Chen;I. Chen
中科院分区：
文献类型：
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作者：
Jeng-Tzong Chen;C. T. Chen;Pocheng Chen;I. Chen
为了避免计算Cauchy主值和Hadamard主值，本文将零场积分方程与退化核和傅立叶级数相结合，研究了具有圆形边界的辐射和散射问题。在实现中，由于引入了基本解的简并核，使得零域点可以定位在实边界上。考虑了一种充分利用退化核特性的极坐标自适应观测器系统。对于超奇异方程，仔细考虑了径向梯度和切向梯度的矢量分解。由于误差来自于傅里叶级数的截断，这种方法可以看作是一种半解析方法。无论是Burton和Miller方法中的超奇异性还是CHIEF概念都不需要处理不规则频率的问题。该方法实现了四种增益：适定模型、无奇点、无边界层效应和指数收敛。在边界元法中，级数展开式具有指数级收敛速度快于代数级收敛速度的特点。通过三个算例验证了该公式的有效性，并证明了该公式比边界元法更准确。
In this paper, the radiation and scattering problems with circular boundaries are studied by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. In implementation, the null-field point can be located on the real boundary owing to the introduction of degenerate kernels for fundamental solution. An adaptive observer system of polar coordinate is considered to fully employ the property of degenerate kernels. For the hypersingular equation, vector decomposition for the radial and tangential gradient is carefully considered. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. Neither hypersingularity in Burton and Miller approach nor the CHIEF concepts were required to deal with the problem of irregular frequencies. Four gains, well-posed model, singularity free, boundary-layer effect free and exponential convergence are achieved by using the present approach. A fast convergence rate in exponential order than algebraic one in BEM stems from the series expansions. Three examples were demonstrated to see the validity of the present formulation and show the better accuracy than BEM.