Year

2014

Degree Name

Doctor of Philosophy

Department

School of Engineering Physics

Abstract

Gauge field theories have been very successful in their description of quantum many-body field interactions. For interactions with strong coupling constrants a computational approach is needed since analytic techniques fail to provide convergent solutions, such as occurs in the study of the strong nuclear force between quarks and gluons of atomic nuclei and other hadrons. The key computational bottleneck in such calculations is the solution of an extremely large linear algebra problem of finding solutions to non symmetric Wilson-Dirac matrices with maybe a billion unknowns. with a floating point performance requirement that challenges even the fastes petaflop supercomputers, finding algorithms that scale well over massively parallel distributed architectures is an ever present necessity. Results of an investigation into the use of small cost effective reconfigurable devices is presented here, along with the solver methods currently being used, and those currently being researched as possible improvements. A reconfigurable design is considered and a research software library is presented as a means to efficiently investigate potential new algorithms. Resluta collected from this research software library are presented leading up to an improved preconditioning technique that addresses the time consuming critical slowing down problem inherent in calculations for low mass spin-half particles near the lattice physical point. This proposed preconditioner is a hybrid combination of existing algorithms factored together in a highly configurable manner that can be dynamically adapted to any specific matrix during the solve to increase performance. Applications to solid state physics problems such as the conductivity and optical properties of graphene are discussed with regards to how these solvers are also of interest due to the existence of massless spin-half quasi particles interacting strongly with the hexagonal carbon lattice.

FoR codes (2008)

0103 NUMERICAL AND COMPUTATIONAL MATHEMATICS, 0206 QUANTUM PHYSICS, 0805 DISTRIBUTED COMPUTING

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Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.