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

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 languageUndefined
Place of PublicationEnschede
PublisherDepartment of Applied Mathematics, University of Twente
Number of pages31
StatePublished - 21 Jan 2007

Publication series

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

Fingerprint

Fourier analysis
Runge Kutta methods
Maxwell equations
Wave propagation
Polynomials

Keywords

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

Cite this

Sarmany, D., Bochev, M. A., & van der Vegt, J. J. W. (2007). Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisation of the Maxwell eqations. Enschede: Department of Applied Mathematics, University of Twente.

Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W. / Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisation of the Maxwell eqations.

Enschede : Department of Applied Mathematics, University of Twente, 2007. 31 p.

Research output: ProfessionalReport

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Sarmany, D, Bochev, MA & van der Vegt, JJW 2007, Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisation of the Maxwell eqations. Department of Applied Mathematics, University of Twente, Enschede.

Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisation of the Maxwell eqations. / Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W.

Enschede : Department of Applied Mathematics, University of Twente, 2007. 31 p.

Research output: ProfessionalReport

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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.

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Sarmany D, Bochev MA, van der Vegt JJW. Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisation of the Maxwell eqations. Enschede: Department of Applied Mathematics, University of Twente, 2007. 31 p.