Some useful strategies for unstructured edge‐based solvers on shared memory machines

Three strategies for shared memory parallel edge‐based solvers are proposed which guarantee that nodes belonging to one thread are not accessed by other threads for vertex‐centered discretizations (replace nodes by cells in case of cell‐centered discretizations). The algorithms reorder the edges in groups in order for the parallelization to take place at the edge level, possibly through multiple passes, which constitutes the bulk of the work in an edge‐based solver. These strategies are presented in an increasing order of programming effort and their performances are also compared. Various renumbering algorithms are considered. Results and timings are given for a classical Computational Fluid Dynamics compressible edge‐based solver and a Numerical Weather Prediction compressible dynamic solver for dry air, as well as computational details to illustrate the efficiency of the proposed approach. The influence of the point renumbering on the final edge grouping and efficiency is also studied through numerical results.