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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Snapshot: SNuBIC Fellows Meeting Augsburg

On the 30th of January the High-Performance Scientific Computing Lab hosted the SNuBIC Fellow meeting. PhD Students and Post-Docs of the SNuBIC project gathered in Augsburg and presented their latest progress on their projects on numerical methods and discussed challenges and open questions. For the first time, this event was held as a hybrid event, allowing those who could not be present in person to attend and present their work. To conclude the meeting, the fellows went on a tour of the historic town and enjoyed a dinner with traditional local food.

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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