Efficient low-storage Runge-Kutta schemes with optimized stability regions

Authors:
Jens Niegemann;Richard Diehl;Kurt Busch
Affiliations:
Institut für Theoretische Festkörperphysik and DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straíe 1, 76131 Karlsruhe, Ger ...;Institut für Theoretische Festkörperphysik and DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straíe 1, 76131 Karlsruhe, Ger ...;Institut für Theoretische Festkörperphysik and DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straíe 1, 76131 Karlsruhe, Ger ...
Venue:
Journal of Computational Physics
Year:
2012

Citing 8
Cited 0

A principle for construction of one-step integration methods with maximum imaginary stability limits

Mathematics and Computers in Simulation
2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics

Journal of Computational Physics
Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations

Applied Numerical Mathematics
Nodal high-order methods on unstructured grids

Journal of Computational Physics
Essentially optimal explicit Runge–Kutta methods with application to hyperbolic–parabolic equations

Numerische Mathematik
Highly Efficient Strong Stability-Preserving Runge-Kutta Methods with Low-Storage Implementations

SIAM Journal on Scientific Computing
High-accuracy large-step explicit Runge-Kutta (HALE-RK) schemes for computational aeroacoustics

Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

Quantified Score

Hi-index	31.45

Visualization

Abstract

A variety of numerical calculations, especially when considering wave propagation, are based on the method-of-lines, where time-dependent partial differential equations (PDEs) are first discretized in space. For the remaining time-integration, low-storage Runge-Kutta schemes are particularly popular due to their efficiency and their reduced memory requirements. In this work, we present a numerical approach to generate new low-storage Runge-Kutta (LSRK) schemes with optimized stability regions for advection-dominated problems. Adapted to the spectral shape of a given physical problem, those methods are found to yield significant performance improvements over previously known LSRK schemes. As a concrete example, we present time-domain calculations of Maxwell's equations in fully three-dimensional systems, discretized by a discontinuous Galerkin approach.