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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)

One of the key tasks in many areas of subsurface flow, most notably in radioactive waste disposal and oil recovery, is an efficient treatment of data uncertainties and the quan-tification of how these uncertainties propagate through the system. Mathematically speaking this leads to high-dimensional quadrature problems with integrands that involve the… (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)

In this talk we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo (MCMC) methods for large–scale applications with high dimensional parameter spaces, e.g. uncertainty quantification in porous media flow. We propose a new multilevel Metropolis-Hastings algorithm, and give an abstract, problem dependent… (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)

Introduction We describe a stable, efficient, parallel algorithm for the solution of diagonally dominant tridiagonal linear systems that scales well on distributed memory parallel computers. This algorithm is in the class of partitioning algorithms. Its multi-level recursive design makes it well suited for distributed memory parallel computers with very… (More)

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