Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Optimal Runge-Kutta methods for first order pseudospectral operators
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Short note: a new minimum storage Runge-Kutta scheme for computational acoustics
Journal of Computational Physics
Journal of Computational Physics
Performance analysis and optimization of finite-difference schemes for wave propagation problems
Journal of Computational Physics
Journal of Computational Physics
GNU Octave Manual Version 3
High-accuracy large-step explicit Runge-Kutta (HALE-RK) schemes for computational aeroacoustics
Journal of Computational Physics
A general strategy for the optimization of Runge-Kutta schemes for wave propagation phenomena
Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
CFL Conditions for Runge-Kutta discontinuous Galerkin methods on triangular grids
Journal of Computational Physics
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We study the performance of methods of lines combining discontinuous Galerkin spatial discretizations and explicit Runge-Kutta time integrators, with the aim of deriving optimal Runge-Kutta schemes for wave propagation applications. We review relevant Runge-Kutta methods from literature, and consider schemes of order q from 3 to 4, and number of stages up to q+4, for optimization. From a user point of view, the problem of the computational efficiency involves the choice of the best combination of mesh and numerical method; two scenarios are defined. In the first one, the element size is totally free, and a 8-stage, fourth-order Runge-Kutta scheme is found to minimize a cost measure depending on both accuracy and stability. In the second one, the elements are assumed to be constrained to such a small size by geometrical features of the computational domain, that accuracy is disregarded. We then derive one 7-stage, third-order scheme and one 8-stage, fourth-order scheme that maximize the stability limit. The performance of the three new schemes is thoroughly analyzed, and the benefits are illustrated with two examples. For each of these Runge-Kutta methods, we provide the coefficients for a 2N-storage implementation, along with the information needed by the user to employ them optimally.