Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version

SIAM Journal on Numerical Analysis ◽

10.1137/090761057 ◽

2011 ◽

Vol 49 (1) ◽

pp. 264-284 ◽

Author(s):

R. Hiptmair ◽

A. Moiola ◽

I. Perugia

Keyword(s):

Helmholtz Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Equation Analysis

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Optimization of plane wave directions in plane wave discontinuous Galerkin methods for the Helmholtz equation

Portugaliae Mathematica ◽

10.4171/pm/1993 ◽

2017 ◽

Vol 74 (1) ◽

pp. 69-89 ◽

Author(s):

Akshay Agrawal ◽

Ronald Hoppe

Keyword(s):

Helmholtz Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods

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Plane wave discontinuous Galerkin methods for the Helmholtz equation and Maxwell equations in anisotropic media

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.06.008 ◽

2021 ◽

Vol 97 ◽

pp. 355-374

Author(s):

Long Yuan ◽

Qiya Hu

Keyword(s):

Helmholtz Equation ◽

Discontinuous Galerkin ◽

Maxwell Equations ◽

Discontinuous Galerkin Methods ◽

Anisotropic Media ◽

Galerkin Methods

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Staggered discontinuous Galerkin methods for the Helmholtz equation with large wave number

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2020.09.019 ◽

2020 ◽

Vol 80 (12) ◽

pp. 2676-2690

Author(s):

Lina Zhao ◽

Eun-Jae Park ◽

Eric T. Chung

Keyword(s):

Helmholtz Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Wave Number ◽

Galerkin Methods ◽

Large Wave Number

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Pre-asymptotic error analysis of hp-interior penalty discontinuous Galerkin methods for the Helmholtz equation with large wave number

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2015.06.007 ◽

2015 ◽

Vol 70 (5) ◽

pp. 917-933 ◽

Author(s):

Lingxue Zhu ◽

Yu Du

Keyword(s):

Error Analysis ◽

Helmholtz Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Wave Number ◽

Galerkin Methods ◽

Asymptotic Error ◽

Large Wave Number ◽

Asymptotic Error Analysis

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Numerical Investigation of the Conditioning for Plane Wave Discontinuous Galerkin Methods

Lecture Notes in Computational Science and Engineering - Numerical Mathematics and Advanced Applications ENUMATH 2017 ◽

10.1007/978-3-319-96415-7_44 ◽

2019 ◽

pp. 493-500 ◽

Author(s):

Scott Congreve ◽

Joscha Gedicke ◽

Ilaria Perugia

Keyword(s):

Numerical Investigation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods

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Preasymptotic Error Analysis of High Order Interior Penalty Discontinuous Galerkin Methods for the Helmholtz Equation with High Wave Number

Journal of Scientific Computing ◽

10.1007/s10915-015-0074-8 ◽

2015 ◽

Vol 67 (1) ◽

pp. 130-152 ◽

Author(s):

Yu Du ◽

Lingxue Zhu

Keyword(s):

Error Analysis ◽

Helmholtz Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Wave Number ◽

Galerkin Methods ◽

High Wave Number ◽

Interior Penalty ◽

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Absolutely stable local discontinuous Galerkin methods for the Helmholtz equation with large wave number

Mathematics of Computation ◽

10.1090/s0025-5718-2012-02652-4 ◽

2012 ◽

Vol 82 (283) ◽

pp. 1269-1296 ◽

Author(s):

Xiaobing Feng ◽

Yulong Xing

Keyword(s):

Helmholtz Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Wave Number ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Large Wave Number

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High Order Local Discontinuous Galerkin Methods for the Allen-Cahn Equation: Analysis and Simulation

Journal of Computational Mathematics ◽

10.4208/jcm.1510-m2014-0002 ◽

2016 ◽

Vol 34 (2) ◽

pp. 135-158 ◽

Author(s):

Ruihan Guo

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Cahn Equation ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Equation Analysis

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$hp$-Discontinuous Galerkin methods for the Helmholtz equation with large wave number

Mathematics of Computation ◽

10.1090/s0025-5718-2011-02475-0 ◽

2011 ◽

Vol 80 (276) ◽

pp. 1997-1997 ◽

Author(s):

Xiaobing Feng ◽

Haijun Wu

Keyword(s):

Helmholtz Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Wave Number ◽

Galerkin Methods ◽

Large Wave Number

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Dispersion analysis of plane wave discontinuous Galerkin methods

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.4626 ◽

2014 ◽

Vol 98 (5) ◽

pp. 313-323 ◽

Author(s):

Claude J. Gittelson ◽

Ralf Hiptmair

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Dispersion Analysis ◽

Galerkin Methods

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