This thesis is concerned with the efficient simulation of lattice QCD with dynamical fermions. We discuss two aspects of this theme, the tuning of existing algorithms and the investigation of novel algorithms. We begin with an introduction to lattice QCD and Monte Carlo Methods for its simulation. Particular emphasis is placed on the difficulties of the lattice formulation of fermion fields. We then continue with a description of the Hybrid Monte Carlo (HMC) algorithm, focusing on the conditions the algorithm must obey for correctness and on some of the numerical methods required for its implementation. We then discuss issues of reversibility and instability for the Molecular Dynamics part of HMC algorithm. After considering the source of instabilities in the context of free field theory we adopt a working hypothesis by which we can relate this instability to the case of lattice QCD. Our tuning studies of HMC attempt to investigate the behaviour of reversibility violations and simulation cost in the molecular dynamics with varying solver target residue <i>r.</i> We also investigate the onset of instabilities in the molecular dynamics while varying the solver residue <i>r</i> and the stepsize dt. Our second subject is the investigation of novel simulation algorithms. We consider the Parallel Tempering (PT) algorithm and its application to lattice QCD. We give an introduction to the algorithm and discuss the use of action matching technologies to tune the simulation parameters for maximal swap acceptance rates. We then discuss issues of cost for PT simulations by considering the CPU time needed by the algorithm for the estimation of the expectation value of an observable of interest and comparing this with the cost of reference HMC simulations. Finally we present some numerical results which indicate that we have a reasonable understanding of the algorithm but that we have not managed to maximise the acceptance rate through action matching. Due to large errors on our measured autocorrelation time we reserve judgements on the question of cost efficiency of the algorithm.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:653013 |
| Date | January 1999 |
| Creators | Joo, Balint |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/12319 |
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