Kármán Conference on Sustainable Computational Science & Engineering 2025
, which took place at the scenic Steinfeld Abbey in North Rhine-Westphalia. It was organized primarly by Julia Kowalski (RWTH Aachen 威尼斯赌博游戏_威尼斯赌博app-【官网】), and the HPSC Lab was a member of the organizer team and program committee. Our key goal for the conference was to bring together computational scientists from different domains, IT and HPC center representatives, as welll as software developers from industry, to discuss how to merge the three concepts of sustainable software, sustainable computing, and computing for sustainability. We thus had only a limited number of talks and ample times for discussion, putting a strong focus on interactions between the participants. The conference was a great opportunity to meet a lot of experienced and engaged researchers, with plenty of enlightening discussions during session breaks and in the evening.
Together with Arpit Babbar and Hendrik Ranocha, we have submitted our paper "Automatic differentiation for Lax-Wendroff-type discretizations".
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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.