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

Lina Zhao; Eun Jae Park; Eric T. Chung

doi:10.1016/j.camwa.2020.09.019

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

Lina Zhao, Eun Jae Park, Eric T. Chung

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper we investigate staggered discontinuous Galerkin method for the Helmholtz equation with large wave number on general polygonal meshes. The method is highly flexible by allowing rough grids such as the trapezoidal grids and highly distorted grids, and at the same time, is numerical flux free. Furthermore, it allows hanging nodes, which can be simply treated as additional vertices. By exploiting a modified duality argument, the stability and convergence can be proved under the condition that [Formula presented], where m is the polynomial order, κ is the wave number, h is the mesh size and C₀ is a positive constant independent of κ,h. Error estimates for both the scalar and vector variables in L² norm are established. Several numerical experiments are tested to verify our theoretical results and to present the capability of our method for capturing singular solutions.

Original language	English
Pages (from-to)	2676-2690
Number of pages	15
Journal	Computers and Mathematics with Applications
Volume	80
Issue number	12
DOIs	https://doi.org/10.1016/j.camwa.2020.09.019
Publication status	Published - 2020 Dec 15

Bibliographical note

Funding Information:
The research of Eric T. Chung is partially supported by the Hong Kong RGC General Research Fund (Project numbers 14304217 and 14302018 ) and CUHK Faculty of Science Direct Grant 2019–20. The research of Eun-Jae Park was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT ( NRF-2015R1A5A1009350 and NRF-2019R1H1A2080222 ).

Publisher Copyright:
© 2020 Elsevier Ltd

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2020.09.019

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title = "Staggered discontinuous Galerkin methods for the Helmholtz equation with large wave number",

abstract = "In this paper we investigate staggered discontinuous Galerkin method for the Helmholtz equation with large wave number on general polygonal meshes. The method is highly flexible by allowing rough grids such as the trapezoidal grids and highly distorted grids, and at the same time, is numerical flux free. Furthermore, it allows hanging nodes, which can be simply treated as additional vertices. By exploiting a modified duality argument, the stability and convergence can be proved under the condition that [Formula presented], where m is the polynomial order, κ is the wave number, h is the mesh size and C0 is a positive constant independent of κ,h. Error estimates for both the scalar and vector variables in L2 norm are established. Several numerical experiments are tested to verify our theoretical results and to present the capability of our method for capturing singular solutions.",

author = "Lina Zhao and Park, {Eun Jae} and Chung, {Eric T.}",

note = "Funding Information: The research of Eric T. Chung is partially supported by the Hong Kong RGC General Research Fund (Project numbers 14304217 and 14302018 ) and CUHK Faculty of Science Direct Grant 2019–20. The research of Eun-Jae Park was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT ( NRF-2015R1A5A1009350 and NRF-2019R1H1A2080222 ). Publisher Copyright: {\textcopyright} 2020 Elsevier Ltd",

year = "2020",

month = dec,

day = "15",

doi = "10.1016/j.camwa.2020.09.019",

language = "English",

volume = "80",

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AU - Zhao, Lina

AU - Park, Eun Jae

AU - Chung, Eric T.

N1 - Funding Information: The research of Eric T. Chung is partially supported by the Hong Kong RGC General Research Fund (Project numbers 14304217 and 14302018 ) and CUHK Faculty of Science Direct Grant 2019–20. The research of Eun-Jae Park was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT ( NRF-2015R1A5A1009350 and NRF-2019R1H1A2080222 ). Publisher Copyright: © 2020 Elsevier Ltd

PY - 2020/12/15

Y1 - 2020/12/15

N2 - In this paper we investigate staggered discontinuous Galerkin method for the Helmholtz equation with large wave number on general polygonal meshes. The method is highly flexible by allowing rough grids such as the trapezoidal grids and highly distorted grids, and at the same time, is numerical flux free. Furthermore, it allows hanging nodes, which can be simply treated as additional vertices. By exploiting a modified duality argument, the stability and convergence can be proved under the condition that [Formula presented], where m is the polynomial order, κ is the wave number, h is the mesh size and C0 is a positive constant independent of κ,h. Error estimates for both the scalar and vector variables in L2 norm are established. Several numerical experiments are tested to verify our theoretical results and to present the capability of our method for capturing singular solutions.

AB - In this paper we investigate staggered discontinuous Galerkin method for the Helmholtz equation with large wave number on general polygonal meshes. The method is highly flexible by allowing rough grids such as the trapezoidal grids and highly distorted grids, and at the same time, is numerical flux free. Furthermore, it allows hanging nodes, which can be simply treated as additional vertices. By exploiting a modified duality argument, the stability and convergence can be proved under the condition that [Formula presented], where m is the polynomial order, κ is the wave number, h is the mesh size and C0 is a positive constant independent of κ,h. Error estimates for both the scalar and vector variables in L2 norm are established. Several numerical experiments are tested to verify our theoretical results and to present the capability of our method for capturing singular solutions.

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

Abstract

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