Snapshot: Trixi.jl HPC performance tested for up to 61,440 MPI ranks
HPC numerical codes have been largely developed using Fortran or C due to their speed. More accessible languages, like Matlab or Python have found little use for such codes due to their poorer performance. Julia offers both, speed and accessibility for serial calculations and on small clusters. But how a Julia/MPI code scales on large HPC facilities has not been tested yet. ? problem in three dimensions. We compare the results with the Fortran code FLUXO and see that Trixi.jl scales well for all used MPI ranks and outperforms FLUXO. ?
Using the Julia code Trixi.jl we test if Julia scales well on large HPC clusters. Trixi.jl uses the MPI library for parallelization and is well suited for this test. Using resources from the Jülich Supercomputing Centre we run simulations on up to 61,440 MPI ranks on 480 compute nodes for a Taylor-Green vortex
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.