Load balancing plays an important role in parallel numerical
  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.  Furthermore, libraries like Metis and Jostle
  focus on a small edge-cut and cannot obey constraints like
  connectivity and straight partition boundaries, 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 parallelism 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.