A Generic Data Structure with Parallel Applications

High performance, massively-parallel multi-physics simulations are built on efficient mesh data structures. Most data structures are designed from the bottom up, focusing on the implementation of linear algebra routines. In this thesis, we explore a top-down approach to design, evaluating the various needs of many aspects of simulation, not just the implementation of a matrix-vector product. With this as motivation, we have developed a generic data structure that both provides efficient linear algebra subroutines by optimizing the computation at a fine-grained level and allows for rapid, reusable implementations of complex geometric algorithms. We demonstrate both through various experiments including directly measuring the efficiency of matrix-vector multiplication; implementation and analysis of a multi-frontal indefinite direct solver; approximation of the medial axis; and the development of a hybrid, two-phase mesh partitioner. The efficiency of matrix-vector multiplication is compared against a theoretical value derived from a simple model of computing hardware. The direct solver uses our data structure to remove a search step normally required for pivoting in indefinite solvers. We demonstrate that pairwise pivoting may have advantages over partial pivoting for ill-conditioned sparse matrices arising from meshes. We also present a novel, parallel algorithm that consistently approximates the medial axis of a domain of arbitrary dimension. By leveraging our data structure, a single implementation can be used for any type of mesh (\emph{e.g.}, 2-D, 3-D, space-time, or mixed element). Finally, we develop a hybrid approach to mesh partitioning in parallel. Using the medial axis of the mesh, large features are separated and partitioned independently using a geometric partitioner. In this way, complex domains are broken down into pieces that are better suited for geometric partitioning.unpublishednot peer reviewe