Massively parallel 3D computation of the compressible Euler equations with an invariant-domain preserving second-order finite-element scheme

We discuss the efficient implementation of a high-performance second-order colocation-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 demonstrate that it is nevertheless possible to achieve an appreciably high throughput of the computing kernels of such a scheme. We discuss the algorithmic design that allows a SIMD vectorization of the compute kernel, analyze the node-level performance and report excellent weak and strong scaling of a hybrid thread/MPI parallelization.     «

We discuss the efficient implementation of a high-performance second-order colocation-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 paramete...     »