A unified framework of multi-objective cost functions for partitioning unstructured finite element meshes

Good performance of parallel finite element computations on unstructured meshes requires high-quality mesh partitioning. Such a decomposition task is normally done by a graph-based partitioning approach. However, the main shortcoming of graph partitioning algorithms is that minimizing the so-called edge cut is not entirely the same as minimizing the communication overhead. This paper thus proposes a unified framework of multi-objective cost functions, which take into account several factors that are not captured by the graph-based partitioning approach. Freely adjustable weighting parameters in the framework also promote a flexible treatment of different optimization objectives. A greedy-style post-improvement procedure is designed to use these cost functions to improve the quality of subdomain meshes arising from the graph-based partitioning approach. Both serial and parallel implementation of the post-improvement procedure have been done. Numerical experiments show that communication overhead can indeed be reduced by this improvement procedure, thereby increasing the performance of parallel finite element computations.