2021/01/04 by Andrew J. Christlieb, Andrew Christlieb, Christlieb, Andrew J. +4
Computer Science · Engineering · Mathematics · #35L03 #65M12 #65M60 #65Y20 #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Computational science #Computer science #Discontinuous Galerkin method #Distributed memory #FOS: Mathematics #Finite element method #Galerkin method #Geometry #Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Operating system #Parallel computing #Physics #Quadrature (astronomy) #Scalability #Scaling #Shared memory #Supercomputer #Xeon #Xeon Phi #cs.NA #math.NA #msc:35L03 #msc:65M12 #msc:65M60 #msc:65Y20
paper · pdf · doi:10.48550/arxiv.2101.01231
26 pages, 2 figures, 6 tables
openalex publication_date 2021/01/04 · openalex created_date 2021/01/18 · arxiv created 2021/02/20 · arxiv updated 2021/02/23 · openalex updated_date 2026/07/28
In this work we investigate the parallel scalability of the numerical method developed in Guthrey and Rossmanith [The regionally implicit discontinuous Galerkin method: Improving the stability of DG-FEM, SIAM J. Numer. Anal. (2019)]. We develop an implementation of the regionally-implicit discontinuous Galerkin (RIDG) method in DoGPack, which is an open source C++ software package for discontinuous Galerkin methods. Specifically, we develop and test a hybrid OpenMP and MPI parallelized implementation of DoGPack with the goal of exploring the efficiency and scalability of RIDG in comparison to the popular strong stability-preserving Runge-Kutta discontinuous Galerkin (SSP-RKDG) method. We demonstrate that RIDG methods are able to hide communication latency associated with distributed memory parallelism, due to the fact that almost all of the work involved in the method is highly localized to each element, producing a localized prediction for each region. We demonstrate the enhanced efficiency and scalability of the of the RIDG method and compare it to SSP-RKDG methods and show extensibility to very high order schemes. The two-dimensional scaling study is performed on machines at the Institute for Cyber-Enabled Research at Michigan State University, using up to 1440 total cores on Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz CPUs. The three dimensional scaling study is performed on Livermore Computing clusters at at Lawrence Livermore National Laboratory, using up to 28672 total cores on Intel Xeon CLX-8276L CPUs with Omni-Path interconnects.