HPSC Lab at JuliaCon 2024
From July 9th through 13th, JuliaCon 2024 took place at the PSV soccer stadium in Eindhoven, Netherlands. It presented a great opportunity to meet a lot of fellow Julia users and developers and enabled many interesting face-to-face discussions with core Julia developers. It was also nice to meet a number of members of the Trixi Framework development team, such as Hendrik Ranocha (University of Mainz), Erik Faulhaber and Benedict Geihe (both University of Cologne), and Daniel Doehring (RWTH Aachen University). Niklas (HLRS Stuttgart/HPSC Lab) and Michael (HPSC Lab) were also present and gave talks on particle-based multiphysics simulations with
TrixiParticles.jl?and on
secure numerical computations with fully homomorphic encryption. Overall, it was a great event and we are looking forward to next year! ?
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.