GRiTS: Global re-indexing for triangular (tetrahedral) simplices

Grant Boquet

Finite Elements is one of the most popular approaches for finding numerical solutions of PDEs. For problems arising in complex engineering and scientific applications, the number of variables can easily reach millions or even billions. To reduce the associated computational time, one of the most popular approaches is parallel computation, in which the computational load is spread over hundreds of processors. Even with decreasing latency of networks, one major challenge is the data transmission. To distribute the amount of computational work evenly over processors (load balancing), ParMETIS, a hypergraph partitioning package, is used in conjunction with several mapping algorithms. This paper introduces various algorithms for mapping a hypergraph to a Finite Element mesh, which are able to reduce computational time by preventing stalling and reducing network communication. Analysis of each algorithm and experimental results follow. (advisors Borggaard and Iliescu)