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. Straightforward 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.