Decomposition of unstructured meshes for efficient parallel computation

• Main Author: Davey, Robert A.
• Published: University of Edinburgh 1997
• Subjects: 502.85
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.649137

This thesis addresses issues relating to the use of parallel high performance computer architectures for unstructured mesh calculations. The finite element and finite volume methods are typical examples of such calculations which arise in a wide range of scientific and engineering applications. The work in this thesis is focused on the development at Edinburgh Parallel Computing Centre of a software library to support static mesh decomposition, known as PUL-md. The library provides a variety of mesh decomposition and graph partitioning algorithms, including both global methods and local refinement techniques. The library implements simple random, cyclic and lexico-graphic partitioning, Farhat's greedy algorithm, recursive layered, coordinate, inertial and spectral bisections, together with subsequent refinement by either the Kernighan and Lin algorithm or by one of two variants of the Mob algorithm. The decomposition library is closely associated with another library, PUL-sm, which provides run-time support for unstructured mesh calculations. The decomposition of unstructured meshes is related to the partitioning of undirected graphs. We present an exhaustive survey of algorithms for these related tasks. Implementation of the decomposition algorithms provided by PUL-md is discussed, and the tunable parameters that optimise the algorithm's behaviour are detailed. On the basis of various metrics of decomposition quality, we evaluate the relative merits of the algorithms and explore the tunable parameter space. To validate these metrics, and further demonstrate the utility of the library, we examine how the runtime of a demonstration application (a finite element code) depends on decomposition quality. Additional related work is presented, including research into the development of a novel 'seed-based' optimisation approach to graph partitioning. In this context gradient descent, simulated annealing and parallel genetic algorithms are explored.