| 求解近场散射问题的最小二乘方法 |
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| 引用本文： | 栾天,王玉洁,郑恩希.求解近场散射问题的最小二乘方法[J].吉林大学学报(理学版),2013,51(5):811-814. |
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| 作者姓名： | 栾天 王玉洁 郑恩希 |
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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(批准号:51178001);吉林省教育厅科学技术研究项目(批准号:2012152;2013439) |
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| 摘 要： | 应用最小二乘方法数值求解全内反射显微镜模型对应的时谐散射问题. 先利用平面波函数和倏逝波函数构造试探函数空间, 再利用解及其法向导数在单元内边界处的跃度和外边界条件定义目标泛函. 结果表明, 该方法简单易行, 所需剖分单元少, 算法精度高. 数值实验验证了算法的有效性.
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| 关 键 词： | Helmholtz方程 最小二乘方法 平面波函数 |
| 收稿时间： | 2012-12-31 |
Least Squares Method for Near Field Scattering Problem |
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| LUAN Tian;WANG Yu-jie;ZHENG En-xi.Least Squares Method for Near Field Scattering Problem[J].Journal of Jilin University: Sci Ed,2013,51(5):811-814. |
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| Authors: | LUAN Tian;WANG Yu-jie;ZHENG En-xi |
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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 least squares method was used to solve the time harmonic scattering problem corresponding to total internal reflection microscopy. The trial space was constructed via plane wave functions and evanescent wave functions and the functional was defined by means of the interface jumps of the solutionand its normal derivative and the discrepancy with respect to the boundary condition. Our method easily used needs fewer elements with high accuracy. Numerical
examples presented illustrate the effectiveness of the approach. |
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| Keywords: | Helmholtz equation least squares method plane wave function |
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