High-Performance Scientific Computing

  1. University
  2. Faculties
  3. Faculty of Mathematics, Natural Sciences, and Materials Engineering
  4. Institute of Mathematics
  5. Chairs
  6. High-Performance Scientific Computing
  7. News

High-Performance Scientific Computing Lab starts June 2024

Astrophysical blob simulation with Trixi.jl
CC BY-NC-ND
Jet noise prediction from a direct-hybrid CFD-CAA simulation
CC BY-NC-ND

The High-Performance Scientific Computing Lab focuses on the development of high-performance computing software and algorithms for scientific applications at the intersection of mathematics, computer science, and domain sciences such as physics or engineering.

As an interdisciplinary research group, our focus is on the development of scalable algorithms for large-scale simulations, with a special emphasis on adaptive multi-physics simulations, research software engineering, and scientific machine learning. Among other activities, our lab is currently involved in the following research projects:

  • DFG Research Unit FOR5409 SNuBIC:
    Structure-Preserving Numerical Methods for Bulk- and Interface Coupling of Heterogeneous Models
  • DFG Project ACTRIX:
    Accessible extreme-scale computing with Trixi.jl and the Julia programming language
  • BMBF Project ADAPTEX:
    Adaptive Earth system modelling with strongly reduced computation time for exascale-supercomputers

The HPSC Lab promotes good research software engineering practices and open-source software, and members of the lab are key contributors to the Trixi Framework, especially in the following software projects:

  • Trixi.jl: Adaptive high-order numerical simulations of conservation laws in Julia
  • libtrixi: Interface library for using Trixi.jl from C/C++/Fortran
  • TrixiParticles.jl: Particle-based multiphysics simulations in Julia

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.

Search