Balancing parallel adaptive FEM computations by solving systems of linear equations

Abstract. Load balancing plays an important role in parallel numer-ical simulations. State-of-the-art libraries addressing this problem base on vertex exchange heuristics that are embedded in a multilevel scheme. However, these are hard to parallelize due to their sequential nature. Fur-thermore, libraries like Metis and Jostle focus on a small edge-cut and cannot obey constraints like connectivity and straight partition bound-aries, which are important for some numerical solvers. In this paper we present an alternative approach to balance the load in parallel adaptive finite element simulations. We compute a distribution that is based on solutions of linear equations. Integrated into a learning framework, we obtain a heuristic that contains a high degree of paral-lelism and computes well shaped connected partitions. Furthermore, our experiments indicate that we can find solutions that are comparable to those of the two state-of-the-art libraries Metis and Jostle also regarding the classic metrics like edge-cut and boundary length