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)