Upcoming: CAAPS event on Julia for scientific computing

On Wednesday, 18th December 2024, 4pm, we host the CAAPS Connect event "Julia for Scientific Computing and Data Science" at the University of Augsburg. The idea is to bring together scientists who already use Julia (or are interested in doing so) for their research. The event is co-organized with Tatjana Stykel of the Chair for Computational Mathematics and takes place at the building I2, room 1309, at the University of Augsburg.

No registration is required. For more details, please visit the event website. We are looking forward to seeing you there!

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

 

arXiv:2506.11719 reproduce me!

 

 

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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