威尼斯赌博游戏_威尼斯赌博app-【官网】

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威尼斯赌博游戏_威尼斯赌博app-【官网】

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High-Performance Scientific Computing

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New lab member: Vivienne Ehlert

Vivienne Ehlert has joined the High-Performance Scientific Computing Lab on 15th May 2025 as a PhD student.

She will work on HPC related topics within the Trixi Framework and help build up the lecture series on advanced mathematics. During her Bachelor and Master studies in Computer Science (with a minor in Mathematics) and Visual Computing at the Otto-von-Guericke 威尼斯赌博游戏_威尼斯赌博app-【官网】 of Magdeburg she focused on topics in scientific computing, of particular interest to her are structure-preserving discretisations of continuous mechanical systems, and high-performance computing. Both of her theses address problems in fluid mechanics; her master’s thesis focuses more specifically in atmospheric dynamics, which, at large scales, can be approximated by a two-dimensional fluid, for which spectral(-like) methods were developed and implemented.

Welcome to the HPSC Lab, Vivienne ?! We are looking forward to working with you!

Together with Arpit Babbar and Hendrik Ranocha, we have submitted our paper "Automatic differentiation for Lax-Wendroff-type discretizations".

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arXiv:2506.11719 reproduce me!

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Abstract

Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbolic conservation laws. In this work, we introduce automatic differentiation (AD) in the element-local time average flux computation step (the predictor step) of Lax-Wendroff methods. The application of AD is similar for methods of any order and does not need positivity corrections during the predictor step. This contrasts with the approximate Lax-Wendroff procedure, which requires different finite difference formulas for different orders of the method and positivity corrections in the predictor step for fluxes that can only be computed on admissible states. The method is Jacobian-free and problem-independent, allowing direct application to any physical flux function. Numerical experiments demonstrate the order and positivity preservation of the method. Additionally, performance comparisons indicate that the wall-clock time of automatic differentiation is always on par with the approximate Lax-Wendroff method.

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