Optimal Runge-Kutta schemes for discontinuous Galerkin space discretizations applied to wave propagation problems

DOI10.1016/j.jcp.2011.11.024zbMath1242.65190OpenAlexW2127234110MaRDI QIDQ423030

Wim Desmet, Thomas Toulorge

Publication date: 18 May 2012

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2011.11.024

zbMATH Keywords

stabilitywave equationwave propagationnumerical examplesdiscontinuous Galerkin methodRunge-Kutta methodsemidiscretizationcomputational efficiency

Mathematics Subject Classification ID

Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Complexity and performance of numerical algorithms (65Y20)

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Uses Software

• Octave

Cites Work

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• CFL conditions for Runge-Kutta discontinuous Galerkin methods on triangular grids
• Optimized Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics
• A new minimum storage Runge-Kutta scheme for computational acoustics
• Solution of the Euler equations for two dimensional transonic flow by a multigrid method
• Performance analysis and optimization of finite-difference schemes for wave propagation problems
• Stability analysis for linear discretisations of the advection equation with Runge-Kutta time integration
• High-accuracy large-step explicit Runge-Kutta (HALE-RK) schemes for computational aeroacoustics
• A general strategy for the optimization of Runge-Kutta schemes for wave propagation phenomena
• Low-dissipation and low-dispersion fourth-order Runge-Kutta algorithm
• Low-storage Runge-Kutta schemes
• \(2N\)-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics
• Optimal Runge-Kutta methods for first order pseudospectral operators
• Minimum storage Runge-Kutta schemes for computational acoustics.
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
• Optimization of time integration schemes coupled to spatial discretization for use in CAA applications
• Strong Stability-Preserving High-Order Time Discretization Methods
• Natural mode analysis of hollow and annular elliptical cylindrical cavities
• Global optimization of explicit strong-stability-preserving Runge-Kutta methods