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
相关论文
共 50 条
  • [1] AN ADAPTIVE FINITE ELEMENT METHOD FOR THE DIFFRACTION GRATING PROBLEM WITH TRANSPARENT BOUNDARY CONDITION
    Wang, Zhoufeng
    Bao, Gang
    Li, Jiaqing
    Li, Peijun
    Wu, Haijun
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (03) : 1585 - 1607
  • [2] Finite element method of solving diffraction problem of dielectric optical grating
    Qin, Wei-Ping
    Fang, Da-Gang
    Dianbo Kexue Xuebao/Chinese Journal of Radio Science, 2001, 16 (04):
  • [3] Transparent Boundary Conditions for Finite Element Method-Based Parabolic Equation
    Ahn, Sungjin
    Kim, Jongyoung
    Kwon, Kyungil
    Cho, Yongheui
    Chung, Young-seek
    JOURNAL OF ELECTROMAGNETIC ENGINEERING AND SCIENCE, 2024,
  • [4] An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition
    Zhoufeng Wang
    Advances in Computational Mathematics, 2022, 48
  • [5] An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition
    Wang, Zhoufeng
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2022, 48 (04)
  • [6] The finite element method as applied to the diffraction by an anisotropic grating
    Demesy, Guillaume
    Zolla, Frederic
    Nicolet, Andre
    Commandre, Mireille
    Fossati, Caroline
    OPTICS EXPRESS, 2007, 15 (26) : 18089 - 18102
  • [7] A finite element method for a noncoercive elliptic problem with neumann boundary conditions
    Kavaliou, Klim
    Tobiska, Lutz
    Computational Methods in Applied Mathematics, 2012, 12 (02) : 168 - 183
  • [8] Transparent boundary conditions for the harmonic diffraction problem in an elastic waveguide
    Baronian, V.
    Bonnet-Ben Dhia, A. S.
    Luneville, E.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (06) : 1945 - 1952
  • [9] Finite element method for the diffraction problem in a waveguide
    A. L. Delitsyn
    Computational Mathematics and Mathematical Physics, 2010, 50 : 1825 - 1829
  • [10] Finite element method for the diffraction problem in a waveguide
    Delitsyn, A. L.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2010, 50 (11) : 1825 - 1829
12345