光栅衍射问题数值计算的最小二乘方法

吉林大学学报(理学版)

光栅衍射问题数值计算的最小二乘方法

栾天^1,2, 王玉洁², 郑恩希^2,3

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;3. 大连海事大学理学院, 辽宁大连 116026

收稿日期:2013-03-26 出版日期:2013-11-26 发布日期:2013-11-21
通讯作者: 栾天 E-mail:luantian@163.com

LeastSquares Method of Numerical Computation for Grating Diffraction

LUAN Tian^1,2, WANG Yujie², ZHENG Enxi^2,3

1. School of Mathematics and Statistics, Beihua University, Jilin 132033, Jilin Province, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China;3. College of Science, Dalian Maritime University, Dalian 116026, Liaoning Province, China

Received:2013-03-26 Online:2013-11-26 Published:2013-11-21
Contact: LUAN Tian E-mail:luantian@163.com

摘要/Abstract

摘要：

针对光栅衍射问题提出一种最小二乘算法. 在计算区域简单剖分的基础上, 选取平面波函数近似解的局部性态, 并利用Rayleigh展开的有限项截断近似解在无穷远处的性态. 结果表明, 该方法适用于一般形状的衍射光栅和大波数情形, 应用过程简单, 所需剖分单元少, 收敛速度快. 数值实验验证了算法的有效性.

关键词: 光栅衍射, Rayleigh展开, 平面波函数

Abstract:

A leastsquares method was proposed for grating diffraction. Based on the partition of the computational domain, the local property of the solution is approximated by plane wave functions, and the property of the solution toward infinite is represented by a truncation of the Rayleigh expansion.
The method with a fast convergence rate is easy to apply and needs few elements. It is appropriate to normal diffraction gratings and the cases with large wave number. Numerical examples show the effectiveness of the approach.

Key words: grating diffraction, Rayleigh expansion, plane wave function

中图分类号:

O241.82

栾天, 王玉洁, 郑恩希. 光栅衍射问题数值计算的最小二乘方法[J]. 吉林大学学报(理学版), 2013, 51(06): 1037-1040.

LUAN Tian, WANG Yujie, ZHENG Enxi. LeastSquares Method of Numerical Computation for Grating Diffraction[J]. Journal of Jilin University Science Edition, 2013, 51(06): 1037-1040.

[1]	栾天, 刘明辉. 近场散射问题数值计算的超弱变分方法[J]. 吉林大学学报(理学版), 2014, 52(01): 39-44.
[2]	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(05): 811-814.