Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations

被引:109
作者
Nguyen, N. C. [1 ]
Peraire, J. [1 ]
Cockburn, B. [2 ]
机构
[1] MIT, Dept Aeronaut & Astronaut, Cambridge, MA 02139 USA
[2] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA
基金
美国国家科学基金会;
关键词
Finite element method; Discontinuous Galerkin methods; Hybrid/mixed methods; Postprocessing; Maxwell's equations; Computational electromagnetics; INCOMPRESSIBLE FINITE-ELEMENTS; 2ND-ORDER ELLIPTIC PROBLEMS; STOKES-FLOW; HDG METHODS; SPACE DIMENSIONS; ORDER; SYSTEM; MESHES; ERROR; BASES;
D O I
10.1016/j.jcp.2011.05.018
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
We present two hybridizable discontinuous Galerkin (HDG) methods for the numerical solution of the time-harmonic Maxwell's equations. The first HDG method explicitly enforces the divergence-free condition and thus necessitates the introduction of a Lagrange multiplier. It produces a linear system for the degrees of freedom of the approximate traces of both the tangential component of the vector field and the Lagrange multiplier. The second HDG method does not explicitly enforce the divergence-free condition and thus results in a linear system for the degrees of freedom of the approximate trace of the tangential component of the vector field only. For both HDG methods, the approximate vector field converges with the optimal order of k + 1 in the L-2-norm, when polynomials of degree k are used to represent all the approximate variables. We propose elementwise postprocessing to obtain a new H-curl-conforming approximate vector field which converges with order k + 1 in the H-curl-norm. We present extensive numerical examples to demonstrate and compare the performance of the HDG methods. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:7151 / 7175
页数:25
相关论文
共 50 条
[1]   A class of locally well-posed hybridizable discontinuous Galerkin methods for the solution of time-harmonic Maxwell's equations [J].
Li, Liang ;
Lanteri, Stephane ;
Perrussel, Ronan .
COMPUTER PHYSICS COMMUNICATIONS, 2015, 192 :23-31
[2]   Solution of the time-harmonic, Maxwell equations using discontinuous Galerkin methods [J].
Dolean, V. ;
Fol, H. ;
Lanteri, S. ;
Perrussel, R. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 218 (02) :435-445
[3]   Numerical investigation of a high order hybridizable discontinuous Galerkin method for 2d time-harmonic Maxwell's equations [J].
Li, Liang ;
Lanteri, Stephane ;
Perrussel, Ronan .
COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 2013, 32 (03) :1112-1138
[4]   ERROR ANALYSIS OF TREFFTZ-DISCONTINUOUS GALERKIN METHODS FOR THE TIME-HARMONIC MAXWELL EQUATIONS [J].
Hiptmair, Ralf ;
Moiola, Andrea ;
Perugia, Ilaria .
MATHEMATICS OF COMPUTATION, 2013, 82 (281) :247-268
[5]   Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics [J].
Nguyen, N. C. ;
Peraire, J. .
JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (18) :5955-5988
[6]   A hybridizable discontinuous Galerkin method combined to a Schwarz algorithm for the solution of 3d time-harmonic Maxwell's equation [J].
Li, Liang ;
Lanteri, Stephane ;
Perrussel, Ronan .
JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 256 :563-581
[7]   The Hybridizable Discontinuous Galerkin Methods [J].
Cockburn, Bernardo .
PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, VOL IV: INVITED LECTURES, 2010, :2749-2775
[8]   Optimal Penalty Parameters for Symmetric Discontinuous Galerkin Discretisations of the Time-Harmonic Maxwell Equations [J].
Sarmany, D. ;
Izsak, F. ;
van der Vegt, J. J. W. .
JOURNAL OF SCIENTIFIC COMPUTING, 2010, 44 (03) :219-254
[9]   Optimized Schwarz algorithms for solving time-harmonic Maxwell's equations discretized by a discontinuous Galerkin method [J].
Dolean, Victorita ;
Lanteri, Stephane ;
Perrussel, Ronan .
IEEE TRANSACTIONS ON MAGNETICS, 2008, 44 (06) :954-957
[10]   A UNIFIED ERROR ANALYSIS OF HYBRIDIZABLE DISCONTINUOUS GALERKIN METHODS FOR THE STATIC MAXWELL EQUATIONS [J].
Du, Shukai ;
Sayas, Francisco-Javier .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2020, 58 (02) :1367-1391