We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex limiting technique introduced by Guermond et al. (SIAM J. Sci. Comput. 40, A3211-A3239, 2018). As such it is invariant-domain preserving, i.e., the solver maintains important physical invariants and is guaranteed to be stable without the use of ad-hoc tuning parameters. This stability comes at the expense of a significantly more involved algorithmic structure that renders conventional high-performance discretizations challenging. We develop an algorithmic design that allows SIMD vectorization of the compute kernel, identify the main ingredients for a good node-level performance, and report excellent weak and strong scaling of a hybrid thread/MPI parallelization.

翻译：我们讨论高效实施高性能二级合用合用型有限元素计划,以解决无结构的乳房上气体动态的可压缩电磁方程式。解决方案的基础是Guermond等人(SIAM J. Sci. Comput. 40, A3211-A3239, 2018)引进的锥形限制技术。因此,它具有无差异性,即,溶剂保持了重要的物理差异性,并且保证不使用临时调节参数而保持稳定。这种稳定性的牺牲了使传统高性能离散性具有挑战性的更大规模参与的算法结构。我们开发了一种算法设计,允许SIMD将计算内核作矢量化,确定良好节点性工作的主要成份,并报告混合线/MPI平行化的极弱和强大的规模。