Parallel methods for large-scale applications in computational electromagnetics and materials science

Abstract

In most parallel algorithms for scientific applications, domain decomposition constitutes an important first step that greatly influences subsequent inter-processor communication patterns. This in turn affects the overall performance of the application itself. Space filling curves (SFCs) are a popular tool to partition multidimensional data across processors because of their ability to preserve data locality while incurring little computational overhead. Despite their wide usage, the efficiency of SFCs for parallel data partitioning has always been empirically justified due to the challenge that a rigorous analysis poses. The first part of this thesis presents such a formal analysis of SFCs. The second part highlights their use in the construction of compressed octrees - a hierarchical tree data structure that forms the basis of an efficient parallel algorithm for the fast multipole algorithm (FMM). FMM offers the only linear time numerical solution of the n-body problem encountered in various areas of scientific research. The motivation for our renewed interest in the FMM is due to a recently invented numerical formulation based on accelerated Cartesian expansions (ACE), that generalizes this method to include a far larger class of potentials than originally designed for. We present runtime and scaling results of a parallel ACE-based FMM implementation on two different parallel architectures. Finally, an efficient parallel algorithm to analyze time series three dimensional atom probe (3DAP) microscopy data is presented. Analysis of such data is used to characterize properties of material samples. Due to recent advances in microscopy, typical sizes of 3DAP data sets are as large as ∼ 108−9 atoms. Faced with such enormous volumes of data, the challenge has shifted to the design of algorithms that can analyze such large data sets and yield clustering information of the various atomic species present therein. A novel algorithm for this purpose will be described and its performance results on the BlueGene/L discussed.