论文标题
具有不变域的二阶有限元方案的可压缩欧拉方程的有效平行3D计算
Efficient parallel 3D computation of the compressible Euler equations with an invariant-domain preserving second-order finite-element scheme
论文作者
论文摘要
我们讨论了高性能的二阶搭配型有限元元素方案的有效实现，该方案用于求解非结构化网格上气体动力学的可压缩欧拉方程。该求解器基于Guermond等人引入的凸限制技术。 （Siam J.Sci。Comput。40，A3211-A3239，2018）。因此，它是不变的域保存，即求解器保持重要的物理不变性，并保证不使用临时调整参数而保持稳定。这种稳定性是以付出更多涉及算法结构的代价，这使传统的高性能离散化具有挑战性。我们开发了一种算法设计，该设计允许对计算内核进行SIMD矢量化，确定良好节点级别性能的主要成分，并报告混合线/MPI并行化的出色弱且强的缩放。
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.
