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Stabilized interior penalty methods for the time-harmonic Maxwell equations

I. Perugia, D. Schötzau, P. Monk
2002 Computer Methods in Applied Mechanics and Engineering  
We propose stabilized interior penalty discontinuous Galerkin methods for the indefinite time-harmonic Maxwell system.  ...  We prove optimal error estimates for the methods in the special case of smooth coefficients and perfectly conducting boundary using a duality approach.  ...  A mixed formulation for the time-harmonic Maxwell equations In this section, we introduce the time-harmonic Maxwell equations and present a mixed formulation for the continuous problem which will be the  ... 
doi:10.1016/s0045-7825(02)00399-7 fatcat:gajgohsj5rhpzlea32dxlv2cx4

Page 6216 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
Zheng Hui Xie (Beijing) 96j:65123 65N30 65N15 Ihlenburg, F. (1-MD-T; College Park, MD); BabuSka, I. (1-MD-T; College Park, MD) Finite element solution of the Helmholtz equation with high wave number.  ...  Manfred Dobrowolski (D-WRZB-A; Wiirzburg) 96j:65124 65N30 78A45 Kirsch, Andreas (D-ERL-A; Erlangen); Monk, Peter (1-DE; Newark, DE) A finite element /spectral method for approximating the time-harmonic  ... 

Interior penalty method for the indefinite time-harmonic Maxwell equations

Paul Houston, Ilaria Perugia, Anna Schneebeli, Dominik Schötzau
2005 Numerische Mathematik  
This paper is a continuation of a series of papers that has been concerned with the development of DG finite element methods for the numerical approximation of the time-harmonic Maxwell equations.  ...  This is in contrast to the recent INTERIOR PENALTY METHOD FOR MAXWELL EQUATIONS  ...  In this paper, we present and analyze the interior penalty discontinuous Galerkin (DG) finite element method for the numerical discretization of the indefinite time-harmonic Maxwell equations in a lossless  ... 
doi:10.1007/s00211-005-0604-7 fatcat:za3sp4egpnafvdgigrqhliuwae

A hybridizable discontinuous Galerkin method combined to a Schwarz algorithm for the solution of 3d time-harmonic Maxwell's equation

Liang Li, Stéphane Lanteri, Ronan Perrussel
2014 Journal of Computational Physics  
is presented for the solution of the sys- tem of 3d time-harmonic Maxwell equations.  ...  Inria HDG method and Schwarz DD algorithm for the 3d time-harmonic Maxwell equations 23 contains 802,532 vertices and 4,495,769 elements.  ... 
doi:10.1016/j.jcp.2013.09.003 fatcat:d5ougurcnzhtrhpiei3f2ddrim

Finite Element Methods for Maxwell's Equations [article]

Peter Monk, Yangwen Zhang
2019 arXiv   pre-print
We survey finite element methods for approximating the time harmonic Maxwell equations. We concentrate on comparing error estimates for problems with spatially varying coefficients.  ...  For the conforming edge finite element methods, such estimates allow, at least, piecewise smooth coefficients.  ...  Acknowledgements The research of P.B. Monk and Y. Zhang is partially supported by the US National Science Foundation (NSF) under grant number DMS-1619904. Research of P.B.  ... 
arXiv:1910.10069v1 fatcat:v5ympnmqvzcdrmewddldrydkbu

Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case

Paul Houston, Ilaria Perugia, Anna Schneebeli, Dominik Schötzau
2005 Mathematical Modelling and Numerical Analysis  
We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form.  ...  The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci.  ...  The numerical experiments presented in this article were performed using the University of Leicester Mathematical Modeling Center's supercomputer which was purchased through the EPSRC Strategic Equipment  ... 
doi:10.1051/m2an:2005032 fatcat:vcmd2onzqjhrze45exerbxz6mq

A discontinuous least squares finite element method for time-harmonic Maxwell equations [article]

Ruo Li, Qicheng Liu, Fanyi Yang
2020 arXiv   pre-print
We propose and analyze a discontinuous least squares finite element method for solving the indefinite time-harmonic Maxwell equations.  ...  The scheme is based on the L^2 norm least squares functional with the weak imposition of the continuity across the interior faces.  ...  Acknowledgements This research was supported by the Science Challenge Project (No. TZ2016002) and the National Science Foundation in China (No. 11971041).  ... 
arXiv:2007.06791v1 fatcat:db3skc2qvzborkqzdmg5jeu2ai

Solution of the time-harmonic Maxwell equations using discontinuous Galerkin methods [article]

Victorita Dolean, Hugo Fol (INRIA Sophia Antipolis), Stephane Lanteri, Ronan Perrussel (INRIA Sophia Antipolis)
2007 arXiv   pre-print
We present numerical results concerning the solution of the time-harmonic Maxwell's equations discretized by discontinuous Galerkin methods.  ...  In particular, a numerical study of the convergence, which compares different strategies proposed in the literature for the elliptic Maxwell equations, is performed in the two-dimensional case.  ...  Previous works have shown convergence results for discontinuous Galerkin methods applied to the time-harmonic Maxwell equations, studied in the form of second-order vector wave equations.  ... 
arXiv:math/0610508v2 fatcat:ey7pkvoezzfs5fmbzcuqmq2mbu

An absolutely stable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations with large wave number [article]

Xiaobing Feng, Haijun Wu
2012 arXiv   pre-print
This paper develops and analyzes an interior penalty discontinuous Galerkin (IPDG) method using piecewise linear polynomials for the indefinite time harmonic Maxwell equations with the impedance boundary  ...  weak stability readily infers wave-number explicit a priori estimates for the solution of the Maxwell problem, which plays an important role in the error analysis for the IPDG method.  ...  The authors would like to thank Dr. Huangxin Chen of Xiamen University of China for his helpful suggestions on the construction and analysis of the Hpcurl, Ωq-elliptic projection in section 5.1.  ... 
arXiv:1210.5837v2 fatcat:5hh3hdkbdrb2hgl42enxmx25uu

Solution of the time-harmonic Maxwell equations using discontinuous Galerkin methods

V. Dolean, H. Fol, S. Lanteri, R. Perrussel
2008 Journal of Computational and Applied Mathematics  
We present numerical results concerning the solution of the time-harmonic Maxwell equations discretized by discontinuous Galerkin methods.  ...  In particular, a numerical study of the convergence, which compares different strategies proposed in the literature for the elliptic Maxwell equations, is performed in the two-dimensional case.  ...  Previous works have shown convergence results for discontinuous Galerkin methods applied to the time-harmonic Maxwell equations, studied in the form of second-order vector wave equations.  ... 
doi:10.1016/j.cam.2007.05.026 fatcat:53khjt3vorcytihixi3ixx3kyq

An implicit hybridized discontinuous Galerkin method for the 3D time-domain Maxwell equations

Alexandra Christophe, Stéphane Descombes, Stéphane Lanteri
2018 Applied Mathematics and Computation  
We present a time-implicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations.  ...  The proposed method has been implemented for dealing with general 3D problems discretized using unstructured tetrahedral meshes.  ...  already knonw for the time-harmonic Maxwell equations [27] - [28] - [29] .  ... 
doi:10.1016/j.amc.2017.04.023 fatcat:e5gb4jbonnhtlaxrpg74hdvvva

Interior penalty discontinuous Galerkin method for Maxwell's equations: optimal L2-norm error estimates

M. J. Grote, A. Schneebeli, D. Schotzau
2007 IMA Journal of Numerical Analysis  
We consider the symmetric, interior penalty discontinuous Galerkin (DG) method for the time-dependent Maxwell's equations in second-order form. In Grote et al. (2007, J. Comput. Appl.  ...  The theoretical convergence rates are validated by a series of numerical experiments in two-space dimensions, which also illustrate the usefulness of the interior penalty DG method for timedependent computational  ...  Different finite-element discretizations of Maxwell's equations are available, such as the edge-element methods of INTERIOR PENALTY DG METHOD FOR MAXWELL'S EQUATIONS 441 Nédélec (1980 Nédélec ( , 1986  ... 
doi:10.1093/imanum/drm038 fatcat:zg2sraku3be3ja7fn44fow23xq

A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations

Håkon Sem Fure, Sébastien Pernet, Margot Sirdey, Sébastien Tordeux
2020 SN Partial Differential Equations and Applications  
computed thanks to an auxiliary Nédélec finite element method.  ...  Trefftz methods are known to be very efficient to reduce the numerical pollution when associated to plane wave basis.  ...  Introduction Numerical methods like the Finite Element Method (FEM), see [3, 26, 32] , and the Finite Difference Method (FDM), see [41] for example, are widely used to solve time-harmonic electromagnetic  ... 
doi:10.1007/s42985-020-00024-0 fatcat:j5s4e3r2jbgynneycihju3dz3a

A Parallel Full Geometric Multigrid Solver for Time Harmonic Maxwell Problems

M. Chanaud, L. Giraud, D. Goudin, J. J. Pesqué, J. Roman
2014 SIAM Journal on Scientific Computing  
In this paper we address the solution of 3D harmonic Maxwell's equations using a parallel geometric full multigrid scheme where only a coarse mesh, tied to geometry, has to be supplied by an external mesh  ...  The design of scalable parallel simulation codes for complex phenomena is challenging.  ...  Some background on time harmonic Maxwell's equations With the time harmonic assumption, all the fields have a periodic behavior in time.  ... 
doi:10.1137/130909512 fatcat:mzo4w4p34jg3fhqj6qvmlvxc3y

An absolutely stable hp-HDG method for the time-harmonic Maxwell equations with high wave number [article]

Peipei Lu, Huangxin Chen, Weifeng Qiu
2016 arXiv   pre-print
The method is shown to be an absolutely stable HDG method for the indefinite time-harmonic Maxwell equations with high wave number.  ...  We present and analyze a hybridizable discontinuous Galerkin (HDG) method for the time-harmonic Maxwell equations.  ...  Acknowledgment The authors are very grateful to the anonymous referees and the editor for their many valuable comments and suggestions that led to an improved presentation of this paper.  ... 
arXiv:1503.07696v3 fatcat:q4ddib6pgvd5ljtnam442sqjeq
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