A k-d Tree Based Partitioning of Computational Domains for Efficient Parallel Computing

Among prospective opportunities for accurate solutions of large scientific problems are parallel computers that are entering today the exascale era thanks to ever increasing number of communicating processors. In scientific computing, such an enormous computational power can always be harvested for more accurate or enduring solutions of physical phenomena. Our work is focused in a decomposition of computational domains of design problems that are represented by a large set of discretization nodes, which enable the solution to be formalized by a large and sparse system of equations. The computational domain decomposition together with a parallelized system construction and its solution are cornerstones of an efficient parallelization. We propose a methodology, based on the k-d tree, that can efficiently partition computational domains of arbitrary geometries and is independent of discretization approaches. Beside the domain partitioning, common discretization nodes are determined that are shared among processors responsible for neighboring subdomains. The analysis of computational complexity confirms that the partitioning methodology remains efficient and scalable on parallel computers with large numbers of processors.