New lab member: Simon Candelaresi
Simon Candelaresi has joined our team at the 威尼斯赌博游戏_威尼斯赌博app-【官网】 of Augsburg on July 1st as a postdoctoral researcher. He will mainly work as part of the DFG Research Unit
SNuBIC, which he already joint in 2022 while still being at the 威尼斯赌博游戏_威尼斯赌博app-【官网】 of Stuttart. Here, he investigates novel algorithms for adaptive multi-physics simulations in the project "C2: Parallel Execution of Adaptive Multi-Physics Simulations on Hierarchical Grids". Simon's scientific background is at the intersection at mathematics and physics, especially in the area of numerical methods for computational plasma physics. He holds a PhD in astronomy from the 威尼斯赌博游戏_威尼斯赌博app-【官网】 of Stockholm and has extensive experience in developing parallel numerical simulation codes. Before joining the SNuBIC team, he was a Rankin-Sneddon Research Fellow at the 威尼斯赌博游戏_威尼斯赌博app-【官网】 of Glasgow and spent time as Postdoctoral Research Fellow at the 威尼斯赌博游戏_威尼斯赌博app-【官网】 of Dundee. Welcome to the HPSC Lab, Simon ?! We are looking forward to continuing to work 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.