Efficient Parallel 3D Computation of the Compressible Euler Equations with an Invariant-domain Preserving Second-order Finite-element Scheme Academic Article uri icon


  • 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 etal.(SIAM J. Sci. Comput. 40, A3211A3239, 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.

published proceedings


author list (cited authors)

  • Maier, M., & Kronbichler, M.

citation count

  • 8

complete list of authors

  • Maier, Matthias||Kronbichler, Martin

publication date

  • January 2021