7 citations · 17 across the 10 of their papers we have counts for
11 papers
GPU-Accelerated Nested Schur-Complement Solvers for Atmospheric Flow Simulations Using Horizontally-Explicit, Vertically-Implicit Schemes and Discontinuous Galerkin Methods
Marco Artiano, Andrés Rueda-Ramírez, Oswald Knoth +2
Horizontally explicit, vertically implicit (HEVI) time integration removes the acoustic time-step restriction imposed by fine vertical grids in nonhydrostatic atmospheric models, b…
Multi-Solver Coupling for Parallel Adaptive Multi-Physics Simulations with Trixijl and dealII
Vivienne Ehlert, Gregor Gassner, Martin Kronbichler +2
Many standalone frameworks for numerical solvers have been developed to tackle the simulation of specific single- or multi-physics problems. For solving coupled problems, common ap…
Massively parallel numerical simulations with Julia
Simon Candelaresi, Benedict Geihe, Marco Artiano +6
The Julia programming language aims to provide a modern approach to develop high-performance computing (HPC) applications. It tries to achieve this by combining a high-level, dynam…
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…
Jin-Xin relaxation as a shock-capturing method for high-order DG/FR schemes
Marco Artiano, Arpit Babbar, Michael Schlottke-Lakemper +2
Jin-Xin relaxation is a method for approximating non-linear hyperbolic conservation laws by a linear system of hyperbolic equations with an dependent stiff source ter…
Robust and efficient pre-processing techniques for particle-based methods including dynamic boundary generation
Niklas S. Neher, Erik Faulhaber, Sven Berger +3
Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a pre…
Mimetic Metrics for the DGSEM
Daniel Bach, Andrés Rueda-Ramírez, David A. Kopriva +1
Free-stream preservation is an essential property for numerical solvers on curvilinear grids. Key to this property is that the metric terms of the curvilinear mapping satisfy discr…
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…
Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods
Jan Glaubitz, Hendrik Ranocha, Andrew R. Winters +3
High-order numerical methods for conservation laws are highly sought after due to their potential efficiency. However, it is challenging to ensure their robustness, particularly fo…
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…