A balanced accumulation scheme for parallel PDE solvers

We present a load balancing technique for a boundary data accumulation algorithm for non-overlapping domain decompositions. The technique is used to speed up a parallel conjugate gradient algorithm with an algebraic multigrid preconditioner to solve a potential problem on an unstructured tetrahedral finite element mesh. The optimized accumulation algorithm significantly improves the performance of the parallel solver and we show a nearly 50 percent runtime improvement over the standard approach in a benchmark run with 48 MPI processes. The load balancing problem itself is a global optimization problem that is solved approximately by local optimization algorithms in parallel that require no communication during the optimization process.