A method for computing guided waves in integrated optics. Part II: Numerical approximation and error analysis

被引：8
|
作者：
Pedreira, DG [1 ]
Joly, P
机构：
[1] Univ Santiago Compostela, Dept Math Appl, Santiago De Compostela 15706, Spain
[2] Inria Rocquencourt, F-78153 Le Chesnay, France
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2002年 / 39卷 / 05期
关键词：
eigenvalue problems; error estimates; integrated optics; transparent boundary conditions;
D O I：
10.1137/S0036142900377711
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are interested in the numerical approximation of the method for computing guided modes in integrated optics introduced in our earlier paper [Gomez Pedreira and Joly, SIAM J. Numer. Anal., 39 (2001), pp. 596-623]. We saw that the main step of the computation of the guided modes consists of computing the eigenvalues of a compact operator K depending on the frequency and the wavenumber beta. This second paper is devoted to the discretization of this problem and to the corresponding convergence analysis. In particular, we derive error estimates in the eigenvalue approximation, which will be of exponential accuracy.
引用
收藏
页码：1684 / 1711
页数：28
相关论文
共 35 条
  • [1] A method for computing guided waves in integrated optics. part I: Mathematical analysis
    Gomez, D
    Joly, P
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2001, 39 (02) : 596 - 623
  • [2] Error analysis of the numerical method for correcting the propagation of EM waves in the troposphere
    Liu, Yuanzhi
    Tang, Tao
    Liu, Guo
    Olaimat, M.
    1600, Sociedade Brasileira de Microondas e Optoeletronica (SBMO) (19) : 407 - 414
  • [3] A practical error estimator in elastoplastic problems with large strains. Part II:: analysis of numerical results
    Pinto, C
    Avilés, R
    Albizuri, J
    Hernández, A
    ENGINEERING COMPUTATIONS, 2002, 19 (5-6) : 617 - 639
  • [4] A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part II: justification as a shallow water approximation
    Duchene, Vincent
    Iguchi, Tatsuo
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2024,
  • [5] Analysis of quantitative relationship between laser-generated guided waves and the adhesive interface by the numerical method
    Zhang, Kuanshuang
    Zhou, Zhenggan
    Ma, Liyin
    JOURNAL OF SANDWICH STRUCTURES & MATERIALS, 2019, 21 (02) : 483 - 502
  • [6] A unified spectral method for FPDEs with two-sided derivatives; Part II: Stability, and error analysis
    Samiee, Mehdi
    Zayernouri, Mohsen
    Meerschaert, Mark M.
    JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 385 : 244 - 261
  • [7] Numerical analysis of a non-singular boundary integral method: Part II: The general case
    Dreyfuss, P
    Rappaz, J
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2002, 25 (07) : 557 - 570
  • [8] An integrated approach for the analysis and modeling of road tunnel ventilation. Part II: Numerical model and its calibration
    Cingi P.
    Angeli D.
    Cavazzuti M.
    Levoni P.
    Stalio E.
    Cipollone M.
    Transportation Engineering, 2021, 4
  • [9] Finite Element Analysis of Attraction-Repulsion Chemotaxis System. Part II: Time Convergence, Error Analysis and Numerical Results
    Hashim, Mohammed Homod
    Harfash, Akil J.
    COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2022, 4 (03) : 1057 - 1104
  • [10] Finite Element Analysis of Attraction-Repulsion Chemotaxis System. Part II: Time Convergence, Error Analysis and Numerical Results
    Mohammed Homod Hashim
    Akil J. Harfash
    Communications on Applied Mathematics and Computation, 2022, 4 : 1057 - 1104
1234