Multi-Criteria Mesh Partitioning for an Explicit Temporal Adaptive Task-Distributed Finite-Volume Solver

The aerospace industry is one of the largest users of numerical simulation, which is an essential tool in the field of aerodynamic engineering, where many fluid dynamics simulations are involved. In order to obtain the most accurate solutions, some of these simulations use unstructured finite volume solvers that cope with irregular meshes by using explicit time-adaptive integration methods. Modern parallel implementations of these solvers rely on task-based runtime systems to perform fine-grained load balancing and to avoid unnecessary synchronizations. Although such implementations greatly improve performance compared to a classical fork-join MPI+OpenMP variants, it remains a challenge to keep all cores busy throughout the simulation loop. In this article, we first investigate the origins of this lack of parallelism. We emphasize that the irregular structure of the task graph plays a major role in the inefficiency of the computation distribution. Our main contribution is to improve the shape of the task graph by using a new mesh partitioning strategy. The originality of our approach is to take the temporal level of mesh cells into account during the mesh partitioning phase. We evaluate our approach by integrating our solution in an ArianeGroup production code used by Airbus. We show that our partitioning method leads to a more balanced task graph. The resulting task scheduling is up to two times faster for meshes ranging from 200,000 to 12,000,000 components.