Parallel computing solutions to the Balitsky-Kovchegov equation

Hillebrand-Viljoen, Charlotte Stephanie

Parallel computing solutions to the Balitsky-Kovchegov equation

Master Thesis

2016

Publisher

University of Cape Town

Department

Department of Physics

Faculty

Faculty of Science

Abstract

The JIMWLK (Jalilian-Marian, Iancu, McLerran,Weigert, Leonodiv and Kovner; pronounced "gym walk") equation describes the energy evolution of observables in the colour glass condensate (CGC) state of matter, which is particularly relevant to collider physics. Currently there are many implementations of JIMWLK evolution in the spirit of the factorised Balitsky-Kovchegov (BK) equation for the total cross section, including a number of efforts to consistently implement evolution at next-to-leading-order[1-5]. Aside from NLO there is a growing interest in studying new, more exclusive, observables, such as single transverse spin asymmetries and transverse momentum distributions[6-8]. These require the inclusion of new degrees of freedom, which can be done systematically by extending the Gaussian truncation of the JIMWLK equation[9][10]. This necessarily increases the computational demands, both in terms of floating point operations and of storage requirements. After a discussion of the theoretical context, we address the first computational step and introduce new, parallelised methods in code that evolves the BK equation. Parallelisation of BK evolution using NVIDIA CUDA with implementation on a commercially available graphical processing unit (GPU) results in performance improvements of roughly an order of magnitude over comparable serial programmes. This also allows us to implement test cases which are often neglected. The code presented here covers only the total cross section case, but it is written with extension to more interesting cases in mind and we discuss some such potential applications.

Keywords

Physics

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