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Center for Nonlinear Studies |
Quantum Chromodynamics (QCD) is the predominant theory that describes the strong interactions in the standard model of particle physics. This strong force is what confines quarks together inside of composite particles like protons and neutrons. Unlike particles prevalent in quantum electrodynamics (QED), the forces between quarks get stronger as the distance between the particles increases. This makes the standard asymptotic techniques employed in QED inadequate as a means of characterizing the strong force. As a result, large scale numerical simulations are necessary to model these interactions for physically realistic parameters. The large computational obstacle in such simulations is the numerical solution of a large system of partial different equations which we discretize on a four dimensional space-time lattice. For physically interesting parameters the resulting linear system is highly disordered and near singular, making traditional iterative solution methods insufficient. We explore the use of adaptive smoothed aggregation multigrid as a preconditioner for the solution process. A brief introduction to the fundamentals of QCD as well as smoothed aggregation multigrid will be given. Results will be provided that demonstrate that this method shows potential for overcoming the numerical difficulties that these systems present.
Host: Markus Berndt and Dave Moulton