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

页码：628 / 639

页数：12

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