Date of Award

12-2019

Degree Name

Doctor of Philosophy

Department

Computer Science

First Advisor

Dr. Elise de Doncker

Second Advisor

Dr. John A. Kapenga

Third Advisor

Dr. Joseph W. McKean

Keywords

High performance computing, multivariate numerical integration, GPU, CUDA

Abstract

The evaluation of numerical integrals finds applications in fields such as High Energy Physics, Bayesian Statistics, Stochastic Geometry, Molecular Modeling and Medical Physics. The erratic behavior of some integrands due to singularities, peaks, or ridges in the integration region suggests the need for reliable algorithms and software that not only provide an estimation of the integral with a level of accuracy acceptable to the user, but also perform this task in a timely manner. We developed ParAdapt, a numerical integration software based on a classic global adaptive strategy, which employs Graphical Processing Units (GPUs) in providing integral evaluations. Specifically, ParAdapt applies adaptive region partitioning strategies developed for efficient integration and mapping to GPUs. The resulting methods render the framework of the classic global adaptive scheme suitable for general functions in moderate dimensions, say 10 to 25. The algorithms presented have been determined to be scalable as evidenced by speedup values in the double and triple digits up to very large numbers of subdivisions. An analysis of the various partitioning and parallelization strategies is given.

Access Setting

Dissertation-Open Access

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