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.

翻译：在这项工作中,我们调查了Guthrey 和 Rossmanith 所开发的数字方法的平行伸缩性。我们开发了DG-FEM、SIAM J. Numer. Anal. (2019年) 。我们开发了DoGPack 中区域不透不透的Galerkin (RIDG) 方法的实施,这是用于不连续的 Galerkin 方法的开放源C++ 软件包。具体地说,我们开发和测试了DoGPack 的混合 OpenMP 和 MPI 平行实施,目的是探索RID 的效率和伸缩性,以与流行的稳健的ROD-Kuta不连续的Galerkin (SSP-RKDG) 方法进行比较。我们证明,RIDG方法能够隐藏与分布式记忆力平行的C++L(LGO),因为该方法所涉及的几乎全部工作都是针对每个要素的,产生局部预测。我们展示了RIGD方法的效率和伸缩性和伸缩性和伸缩性,在C-C-C-C-LD研究所的CS-LDGM-S-C 上,在C-C-C-C-C-LOLOLOLS-S-S-S-S-S-S-S-S-SAL-S-S-S-S-S-S-S-S-S-S-S-SAL-S-S-SAL-S-S-SAL-S-SAL-SAL-SAL-SAL-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-C-C-SAL-SAL-SAL-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-