A tensor product finite element method for the diffraction grating problem with transparent boundary conditions

被引：2
|
作者：
Xia, Zhi [1 ]
Du, Kui [1 ,2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[2] Xiamen Univ, Fujian Prov Key Lab Math Modelling & High Perform, Xiamen 361005, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 73卷 / 04期
基金：
中国国家自然科学基金; 国家教育部博士点专项基金资助;
关键词：
Helmholtz equation; Transparent boundary condition; Tensor product finite element method; FFT; PERIODIC SCATTERING PROBLEMS; FAST DIRECT SOLVER; 2ND-HARMONIC GENERATION; ELECTROMAGNETIC SCATTERING; CYLINDERS; SYSTEMS; ARRAYS; LAYERS; WAVES;
D O I：
10.1016/j.camwa.2017.01.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the diffraction grating problem in optics, which has been modeled by a boundary value problem governed by a Helmholtz equation with transparent boundary conditions. A tensor-product finite element method is proposed to numerically solve the problem. An FFT-based matrix decomposition algorithm is developed to solve the linear system arising in the vertically layered medium case, which can be used as a preconditioning technique for the general case. Numerical examples are presented to illustrate the accuracy and efficiency of the method. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：628 / 639
页数：12
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