| 二维分段均匀波导的基于DtN映射的四阶差分算法 |
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| 引用本文： | 张洪宾,宋子龙,李建英,黄晋阳.二维分段均匀波导的基于DtN映射的四阶差分算法[J].北京化工大学学报(自然科学版),2015,42(5):120. |
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| 作者姓名： | 张洪宾 宋子龙 李建英 黄晋阳 |
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| 作者单位： | 北京化工大学理学院,北京,100029;香港城市大学数学系,香港,999077 |
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| 摘 要： | 给出了利用二阶导数的四阶差分近似计算DtN映射的一种新方法。与Chebyshev配置算法比较,该方法直接给出简化计算所需的特征值和特征向量,且充分利用原方程信息,从而简化了计算过程,降低了计算误差。算例(Cost 268 modeling task)表明,此算法是一种高效算法。
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| 关 键 词： | 光波导 DtN映射 数值计算 近似二阶导数 |
| 收稿时间： | 2015-03-18 |
A 4th-order difference algorithm for 2-D piecewise uniform waveguides based on Dirichlet-to-Neumann maps |
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| ZHANG HongBin,SONG ZiLong,LI JianYing,HUANG JinYang.A 4th-order difference algorithm for 2-D piecewise uniform waveguides based on Dirichlet-to-Neumann maps[J].Journal of Beijing University of Chemical Technology,2015,42(5):120. |
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| Authors: | ZHANG HongBin SONG ZiLong LI JianYing HUANG JinYang |
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| Institution: | 1.School of Science, Beijing University of Chemical Technology, Beijing 100029; 2.Department of Mathmatics, City University of Hong Kong, Hong Kong 999077, China |
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| Abstract: | A new algorithm to compute DtN maps that uses a 4th-order difference scheme to approximate the 2nd derivative is developed in this paper. Compared with the Chebyshev collocation algorithm, this algorithm directly gives the eigenvalues and eigenvectors needed to simplify the computation and takes full advantage of the information in the original equation such that the computation process can be simplified and the computation error can be reduced. A numerical experiment (Cost 268 modeling task) shows that the algorithm is efficient. |
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