7 citations · 7 across the 2 of their papers we have counts for
5 papers · 1 filter
Volume Term Adaptivity for Discontinuous Galerkin Schemes
Daniel Doehring, Jesse Chan, Hendrik Ranocha +3
We introduce the concept of volume term adaptivity for high-order discontinuous Galerkin (DG) schemes solving time-dependent partial differential equations. Termed v-adaptivity, we…
Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Stable High-Order Optimized Multirate Time Integration
Daniel Doehring, Hendrik Ranocha, Manuel Torrilhon
We present novel entropy-conservative and entropy-stable multirate Runge-Kutta methods based on Paired Explicit Runge-Kutta (P-ERK) schemes with relaxation for conservation laws an…
Fourth-Order Paired-Explicit Runge-Kutta Methods
Daniel Doehring, Lars Christmann, Michael Schlottke-Lakemper +2
In this paper, we extend the Paired-Explicit Runge-Kutta schemes by Vermeire et. al. to fourth-order of consistency. Based on the order conditions for partitioned Runge-Kutta metho…
Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations
Daniel Doehring, Gregor J. Gassner, Manuel Torrilhon
A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic par…
Multirate Time-Integration based on Dynamic ODE Partitioning through Adaptively Refined Meshes for Compressible Fluid Dynamics
Daniel Doehring, Michael Schlottke-Lakemper, Gregor J. Gassner +1
In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et. al. (2019, 2022) to dynamically partitioned systems arising from adaptive mesh refinement. T…