| 求解开腔体时谐散射问题的数值算法 |
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| 引用本文： | 栾天,谭希丽,李庆春.求解开腔体时谐散射问题的数值算法[J].吉林大学学报(理学版),2015,53(1):37-40. |
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| 作者姓名： | 栾天 谭希丽 李庆春 |
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| 作者单位： | 1. 北华大学 数学与统计学院, 吉林 吉林 132033; 2. 吉林大学 数学研究所, 长春 130012 |
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| 基金项目： | 国家自然科学基金，吉林省教育厅科学技术研究项目 |
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| 摘 要： | 针对一类开腔体时谐散射问题提出一种有效的数值算法. 该算法先对计算区域进行简单剖分, 再利用Fourier Bessel函数和平面波函数去近似解的局部性态, 并利用散射场的多极展开式逼近解在无穷远处的性态; 然后借助最小二乘算法迫使数值解在子区域内边界处近似满足连续性条件. 数值模拟验证了算法的有效性.
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| 关 键 词： | Helmholtz方程 Fourier Bessel函数 平面波 多极展开式 |
| 收稿时间： | 2014-02-24 |
Numerical Method for Time Harmonic Scattering by Open Cavity |
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| LUAN Tian,TAN Xili,LI Qingchun.Numerical Method for Time Harmonic Scattering by Open Cavity[J].Journal of Jilin University: Sci Ed,2015,53(1):37-40. |
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| Authors: | LUAN Tian TAN Xili LI Qingchun |
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| Institution: | 1. College of Mathematics and Statistics, Beihua University, Jilin 132033, Jilin Province, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | A numerical method was proposed for time harmonic scattering of an open cavity. The computational domain was partitioned firstly. Then on subdomains Fourier Bessel functions and plane wave functions were used to approximate the local properties of the solution, and scattered field toward infinite was approximated by a multipole expansion. Then the continuity across the inner interfaces between elements was enforced by the least squares scheme. Finally, the effectiveness of the approach was demonstrated by numerical example. |
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| Keywords: | Helmholtz equation Fourier-Bessel functions plane waves multipole expansion |
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