Layer-by-layer ordering in parallel finite element composition on shared-memory multiprocessors

In this paper, we present new partitioning algorithms for unstructured meshes that prevent conflicts during parallel assembling of FEM matrices and vectors in shared memory. These algorithms use a ratio which we introduce to determine if any two mesh cells are adjacent. This adjacency ratio defines mesh layers, which are combined into domains and assigned to different parallel processes/threads. The proposed partitioning algorithms are compared with the existing algorithms on quasi-structured and unstructured meshes by the number of potential conflicts and by the load imbalance.