Finite element analysis (FEA) depends on meshes that approximate the artifact to be analyzed. Starting with an initial mesh, an FEA development pipeline produces more and more refined meshes in an iterative process until the solution of the partial differential equation (PDE) on the mesh is accurate enough. This paper presents the design and massively parallel implementation of a 2D mesh generator that efficiently and fully automatically produces the initial mesh. The presentation focuses on the domain of computational fluid dynamics via an analysis of the airflow around a 2D slice of an aircraft wing.

The core of the paper describes the various stages of the algorithm, which computes the anisotropic boundary layer via Delaunay triangulation and the isotropic mesh region via Delaunay refinement, both by parallel algorithms that apply recursive domain splitting. All processes engage in both activities where the workers independently balance their load using global information periodically updated in the root process. The accuracy of the solution is validated against public references. Performance results, based on message passing interface (MPI) and POSIX threads, demonstrate more than 75 percent efficiency on a cluster with 512 processors.

While the details of the algorithm are mainly targeted to experts in FEA, the description of the parallel implementation will also interest parallel program developers in other fields; however, a more detailed evaluation of the effectiveness of work balancing would have been helpful. The presented work has great potential; in particular, the authors envision its generalization to 3D domains.