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math.NA2026

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…

math.NA2026

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…

math.NA2026

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…

math.NA2026

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…

math.NA2025

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…