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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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Grant awarded: Scientific exchange with NPS on GPU-accelerated weather simulations

Valentin Churavy has successfully applied for a travel grant at the Bavaria California Technology Center (BaCaTec,? https://bacatec.de).?Over the next two years, we will collaborate with Frank Giraldo and Lucas Wilcox?at the Navel Postgraduate School in Monterey, California. A multi-week visit of Valentin to California is planned for 2025, which will be reciprocated by scientist from NPS in 2026. Congratulations Valentin!

Abstract

Predictive modeling of extreme weather events is a key tool for addressing the impacts of climate change at both regional and global scales. Regions like California and Bavaria face immense challenges from the increasing frequency of such events. By employing predictive simulation methods, regional and municipal authorities can better plan and appropriately scale climate-resilient infrastructure. However, large-scale, high-fidelity numerical simulations are extremely computationally demanding and require advanced computational and mathematical methods for efficient prediction of regional climate impacts. To meet this need, our project will work towards extending the Julia-based simulation framework Trixi.jl to simulate local extreme weather events with solution-adaptive algorithms for GPU-based supercomputers. In addition, integrating machine learning and automatic differentiation will facilitate sensitivity analyses and enable more sophisticated surrogate modeling.?

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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