An improved recursive graph bipartitioning algorithm for well balanced domain decomposition

In the context of hybrid sparse linear solvers based on domain decomposition and Schur complement approaches, getting a domain decomposition tool leading to a good balancing of both the internal node set size and the interface node set size for all the domains is a critical point for load balancing and efficiency issues in a parallel computation context. For this purpose, we revisit the original algorithm introduced by Lipton, Rose and Tarjan [1] in 1979 which performed the recursion for nested dissection in a particular manner. From this specific recursive strategy, we propose in this paper several variations of the existing algorithms in the multilevel Scotch partitioner that take into account these multiple criteria and we illustrate the improved results on a collection of graphs corresponding to finite element meshes used in numerical scientific applications.