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20242026
most citedMany-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations

7 citations · 17 across the 10 of their papers we have counts for

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math.NA2026

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…

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…