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A significant amount of the computational time in large Monte Carlo simulations of lattice field theory is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized… (More)

The main focus of this paper is the numerical solution of the Boltzmann transport equation for neutral particles through mixed material media in a spherically symmetric geometry. Standard solution strategies, like the Discrete Ordinates Method (DOM), may lead to nonphysical approximate solutions. In particular, a point source at the center of the sphere… (More)

SUMMARY The Dirac equation of quantum electrodynamics (QED) describes the interaction between electrons and photons. Large-scale numerical simulations of the theory require repeated solution of the two-dimensional Dirac equation, a system of two first-order partial differential equations coupled to a background U(1) gauge field. Traditional discretizations… (More)

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