Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisation of the Maxwell eqations

D. Sarmany; Mikhail A. Bochev; Jacobus J.W. van der Vegt

Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisation of the Maxwell eqations

D. Sarmany, Mikhail A. Bochev, Jacobus J.W. van der Vegt

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Abstract

Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared to fixed-order schemes. This comes without a significant increase in the computation work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the complete scheme. The analysis also provides practical information on the convergence of the dissipation and dispersion error, which is important when studying wave propagation phenomena.

Original language	Undefined
Place of Publication	Enschede
Publisher	University of Twente, Department of Applied Mathematics
Number of pages	31
Publication status	Published - 21 Jan 2007

Publication series

Name
Publisher	Department of Applied Mathematics, University of Twente
No.	2/1821
ISSN (Print)	1874-4850
ISSN (Electronic)	1874-4850

Keywords

MSC-65L06
MSC-65M60
EWI-9168
METIS-242036
MSC-78M10
IR-66899

Access to Document

http://www.math.utwente.nl/publications

Cite this

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abstract = "Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared to fixed-order schemes. This comes without a significant increase in the computation work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the complete scheme. The analysis also provides practical information on the convergence of the dissipation and dispersion error, which is important when studying wave propagation phenomena.",

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AU - Bochev, Mikhail A.

AU - van der Vegt, Jacobus J.W.

N1 - Please note possible different spellings of the second author's name: "Botchev" or "Bochev".

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N2 - Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared to fixed-order schemes. This comes without a significant increase in the computation work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the complete scheme. The analysis also provides practical information on the convergence of the dissipation and dispersion error, which is important when studying wave propagation phenomena.

AB - Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared to fixed-order schemes. This comes without a significant increase in the computation work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the complete scheme. The analysis also provides practical information on the convergence of the dissipation and dispersion error, which is important when studying wave propagation phenomena.

KW - MSC-65L06

KW - MSC-65M60

KW - EWI-9168

KW - METIS-242036

KW - MSC-78M10

KW - IR-66899

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