A Parallel Shape Optimizing Load Balancer

Load balancing is an important issue in parallel numerical simulations. However, state-of-the-art libraries addressing this problem show several deficiencies: they are hard to parallelize, focus on small edge-cuts rather than few boundary vertices, and often produce disconnected partitions. We present a distributed implementation of a load balancing heuristic for parallel adaptive FEM simulations. It is based on a disturbed diffusion scheme embedded in a learning framework. This approach incorporates a high degree of parallelism that can be exploited and it computes well-shaped partitions as shown in previous publications. Our focus lies on improving the condition of the involved matrix and solving the resulting linear systems with local accuracy. This helps to omit unnecessary computations as well as allows to replace the domain decomposition by an alternative data distribution scheme reducing the communication overhead, as shown by experiments with our new MPI based implementation.