Title: Optimal Runge-Kutta Schemes for Discontinuous Galerkin Space Discretizations Applied to Wave Propagation Problems
Authors: Toulorge, Thomas ×
Desmet, Wim #
Issue Date: 20-Feb-2012
Publisher: Academic Press
Series Title: Journal of Computational Physics vol:231 issue:4 pages:2067-2091
Abstract: 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.
ISSN: 0021-9991
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Production Engineering, Machine Design and Automation (PMA) Section
× corresponding author
# (joint) last author

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