Efficient Global Element Indexing for Parallel Adaptive Flow Solvers

Many grid-based solvers for partial differential equations (PDE) assemble matrices explicitly for discretizing the underlying PDE operators and/or for the underlying (non-) linear systems of equations. Often, the data structures or solver packages require a consecutive global numbering of the degrees of freedom across the boundaries of different parallel subdomains. Straightfor- ward approaches to realize this global indexing in parallel frequently result in serial parts of the assembling algorithms which causes a considerable bottleneck, in particular in large-scale applications.We present an efficient way to set up such a global indexing numbering scheme for large configurations via a position-based numeration on all parallel processes locally. The global number of shared nodes is determined via a tree-based communication pattern. We verified our implementation via state-of-the-art benchmark scenarios for incompressible flow simulations. A small performance study shows the parallel capability of our approach. The corresponding results can be generalized to other grid-based solvers that demand for global indexing in the context of large-scale parallelization.