New lab member: Ioana Lupu
Ioana Lupu
has joined our group on 1st June 2024 as the new team assistant. After obtaining a BA in Romanian and English literature, she soon recognized that her skills as a highly organized and detail-oriented individual would be much better suited in the field of administration. Her past work experience helped her develop a solid foundation in administration, equipping her with a comprehensive understanding of office management. Among other things, she is responsible for the smooth operation of our office financial matters, personnel management, and general administration in our group. Welcome to HPSC Lab, Ioana ?! 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.