A hybrid Hermite-discontinuous Galerkin method for hyperbolic systems with application to Maxwell's equations

被引：14
|
作者：
Chen, Xi [1 ]
Appeloe, Daniel [2 ]
Hagstrom, Thomas [3 ]
机构：
[1] Univ Arizona, Coll Opt Sci, ACMS, Tucson, AZ 85721 USA
[2] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87131 USA
[3] So Methodist Univ, Dept Math, Dallas, TX 75275 USA
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 257卷
关键词：
Hyperbolic initial-boundary value problems; Spectral elements; Hybrid grids; BOUNDARY VALUE-PROBLEMS; DIFFERENCE TIME-DOMAIN; GRIDS;
D O I：
10.1016/j.jcp.2013.09.046
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
A high order discretization strategy for solving hyperbolic initial-boundary value problems on hybrid structured-unstructured grids is proposed. The method leverages the capabilities of two distinct families of polynomial elements: discontinuous Galerkin discretizations which can be applied on elements of arbitrary shape, and Hermite discretizations which allow highly efficient implementations on staircased Cartesian grids. We demonstrate through numerical experiments in 1 + 1 and 2 + 1 dimensions that the hybridized method is stable and efficient. (C) 2013 Published by Elsevier Inc.
引用
收藏
页码：501 / 520
页数：20
相关论文
共 50 条
  • [1] The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations
    Koshkarov, O.
    Manzini, G.
    Delzanno, G. L.
    Pagliantini, C.
    Roytershteyn, V.
    COMPUTER PHYSICS COMMUNICATIONS, 2021, 264
  • [2] The use of hybrid meshes to improve the efficiency of a discontinuous Galerkin method for the solution of Maxwell's equations
    Sevilla, Ruben
    Hassan, Oubay
    Morgan, Kenneth
    COMPUTERS & STRUCTURES, 2014, 137 : 2 - 13
  • [3] Stabilized discontinuous Galerkin method for hyperbolic equations
    Calle, JLD
    Devloo, PRB
    Gomes, SM
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2005, 194 (17) : 1861 - 1874
  • [4] Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation
    Beznosov, Oleksii
    Appelo, Daniel
    COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2021, 3 (03) : 391 - 418
  • [5] Discontinuous Galerkin method based on quadrilateral mesh for Maxwell's equations
    Min, MS
    2005 IEEE/ACES INTERNATIONAL CONFERENCE ON WIRELESS COMMUNICATIONS AND APPLIED COMPUTATIONAL ELECTROMAGNETICS, 2005, : 719 - 723
  • [6] Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation
    Oleksii Beznosov
    Daniel Appelö
    Communications on Applied Mathematics and Computation, 2021, 3 : 391 - 418
  • [7] Discontinuous Galerkin method for the time-domain Maxwell's equations
    Kabakian, AV
    Shankar, VY
    Hall, VF
    COMPUTATIONAL FLUID DYNAMICS 2002, 2003, : 153 - 158
  • [8] Space-Time Discontinuous Galerkin Method for Maxwell's Equations
    Xie, Ziqing
    Wang, Bo
    Zhang, Zhimin
    COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2013, 14 (04) : 916 - 939
  • [9] On the order of convergence of the discontinuous Galerkin method for hyperbolic equations
    Richter, Gerard R.
    MATHEMATICS OF COMPUTATION, 2008, 77 (264) : 1871 - 1885
  • [10] TEMPORAL CONVERGENCE OF A LOCALLY IMPLICIT DISCONTINUOUS GALERKIN METHOD FOR MAXWELL'S EQUATIONS
    Moya, Ludovic
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2012, 46 (05): : 1225 - 1246
12345