Dynamic load balancing for parallel adaptive finite element techniques

The application of the non-overlapping domain decomposition method to finite element problems involves the partitioning of the complex geometry into an appropriate number of disjoint subdomains. The solution of the problem is obtained from the solution of a number of local problems and the solution of the global problem describing the interface continuity. For a given finite element discretisation the partitioning is based on an element distribution. Automatic domain partitioning tools are available to ensure a balanced distribution according to the expected computational effort spent in the assembly and solution steps of the finite element procedure. This load balance is disturbed during an adaptive finite element computation with a-posteriori error estimation and local mesh refinement procedures (h-adaptivity) or due to non-uniform computational load per element. The load imbalance occurs during runtime and requires a load redistribution to ensure an efficient parallel solution procedure. Therefore, a dynamic load balancing method was implemented based on the multistage diffusion method. Finite elements and finite nodes are migrating between neighbouring processors. The parallelization of the finite element method is described with emphasis on the adaptive load balancing and an example.