Isogeometric analysis for time-dependent Maxwell's equations in complex media

被引：0
|
作者：
Fan, Enyu [1 ]
Li, Jichun [2 ]
Liu, Yang [1 ]
Zhang, Yangpeng [2 ]
机构：
[1] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
[2] Univ Nevada Las Vegas, Dept Math Sci, Las Vegas, NV 89154 USA
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2025年 / 465卷
基金：
中国国家自然科学基金;
关键词：
Isogeometric analysis; B-spline; Finite element method; Maxwell's equations; Fractional derivative; Perfectly matched layers; DISCONTINUOUS GALERKIN METHODS; SCHEMES; ABSORPTION; GEOPDES; SPLINE; FORMS; GRIDS;
D O I：
10.1016/j.cam.2025.116566
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper considers solving time-dependent Maxwell's equations in a Cole-Cole dispersive medium and a Perfectly Matched Layer (PML) model by B-spline finite element method. First, we develop a reformulated Cole-Cole model by eliminating the magnetic field, then we propose two schemes to approximate the fractional time derivative in the model. The discrete stabilities of both schemes are established. Numerical results for the Cole-Cole model in complex domains are presented to demonstrate the flexibility and efficiency of the finite element method with B-spline basis functions. Finally, we also extend the B-spline method to solve a complicated PML model.
引用
收藏
页数：17
相关论文
共 50 条
  • [1] Superconvergence analysis for time-dependent Maxwell's equations in metamaterials
    Huang, Yunqing
    Li, Jichun
    Lin, Qun
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2012, 28 (06) : 1794 - 1816
  • [2] Isogeometric analysis of the time-dependent incompressible MHD equations
    Ahn, J. S.
    Bluck, M. J.
    INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS, 2020, 34 (03) : 226 - 248
  • [3] Numerical solution of the time-dependent Maxwell's equations for random dielectric media
    Harshawardhan, W
    Su, Q
    Grobe, R
    PHYSICAL REVIEW E, 2000, 62 (06): : 8705 - 8712
  • [4] Finite element study of time-dependent Maxwell's equations in dispersive media
    Li, Jichun
    Chen, Yitung
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 24 (05) : 1203 - 1221
  • [5] A priori and posteriori error analysis for time-dependent Maxwell's equations
    Li, Jichun
    Lin, Yanping
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2015, 292 : 54 - 68
  • [6] Numerical analysis of a PML model for time-dependent Maxwell's equations
    Huang, Yunqing
    Li, Jichun
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (13) : 3932 - 3942
  • [7] Regularity in time of the time-dependent Maxwell equations
    Assous, F
    Ciarlet, P
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 327 (08): : 719 - 724
  • [8] Time-dependent Maxwell's equations with charges in singular geometries
    Assous, F.
    Ciarlet, P., Jr.
    Garcia, E.
    Segre, J.
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 196 (1-3) : 665 - 681
  • [9] Weak Galerkin methods for time-dependent Maxwell's equations
    Shields, Sidney
    Li, Jichun
    Machorro, Eric A.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (09) : 2106 - 2124
  • [10] Numerical solution techniques to the time-dependent Maxwell equations for highly scattering media
    Mandel, S
    Menon, S
    Harshawardhan, W
    Su, Q
    Grobe, R
    PHOTON MIGRATION, OPTICAL COHERENCE TOMOGRAPHY, AND MICROSCOPY, 2001, 4431 : 165 - 168
12345