New lab member: Valentin Churavy
On August 1st, 2024, Valentin Churavy has joined our team in the HPSC Lab as a postdoctoral researcher and research software engineer. He will primarily work on the DFG project ACTRIX, which aims to support accessible extreme-scale computing with Trixi.jl and the Julia programming language. The project is a collaboration between the HPSC Lab and the team of
Hendrik Ranocha at the 威尼斯赌博游戏_威尼斯赌博app-【官网】 of Mainz, where Valentin is also affiliated. Valentin has a background in cognitive and computer science. During his PhD at MIT's Julia Lab, he worked on the Julia programming language and its application to high-performance computing. Next to being a core contributor to the Julia language itself, he is the lead developer or core contributor to a number of key Julia packages. These include the JuliaGPU and JuliaParallel ecosystems, specifically KernelAbstractions.jl for hardware-agnostic parallel programming, Enzyme.jl for compiler-enhanced automatic differentiation, or Cthulhu.jl for debugging type inference issues. Furthermore, he is also the initiator and host of the monthly Julia HPC call and an ardent community advocate for using Julia for high-performance computing. Welcome to the HPSC Lab, Valentin??! We are looking forward to working with you!
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.