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R. C. Brower

Publications and source records attributed to R. C. Brower.

At least 37 records · Page 2Linked to original sources
arXiv2009

Solving Lattice QCD systems of equations using mixed precision solvers on GPUs

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40 Gflops, 135 Gflops and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

hep-lat↗
arXiv2007

Adaptive Multigrid Algorithm for the QCD Dirac-Wilson Operator

We present a new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields. The key behind the success of the algorithm is an adaptive projection onto the coarse grids that preserves the near null space. The resulting algorithm has weak dependence on the gauge coupling and exhibits mild critical slowing down in the chiral limit. Results are presented for the Wilson Dirac operator of the 2d U(1) Schwinger model.

hep-lat↗
arXiv2007

Adaptive Multigrid Algorithm for Lattice QCD

We present a new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields. The key behind the success of the algorithm is an adaptive projection onto the coarse grids that preserves the near null space. The resulting algorithm has weak dependence on the gauge coupling and exhibits very little critical slowing down in the chiral limit. Results are presented for the Wilson Dirac operator of the 2d U(1) Schwinger model.

hep-lat↗
arXiv2005

Moebius Fermions

We introduce a new domain wall operator that represents a full (real) Moebius transformation of a given non-chiral Dirac kernel. Shamir's and Borici's domain wall fermions are special cases of this new class. By tuning the parameters of the Moebius operator and by introducing a new Red/Black preconditioning, we are able to reduce the computational effort substantially.

hep-lat↗
arXiv2004

Insight into nucleon structure from lattice calculations of moments of parton and generalized parton distributions

This talk presents recent calculations in full QCD of the lowest three moments of generalized parton distributions and the insight they provide into the behavior of nucleon electromagnetic form factors, the origin of the nucleon spin, and the transverse structure of the nucleon. In addition, new exploratory calculations in the chiral regime of full QCD are discussed.

hep-lat↗
arXiv2003

Moments of nucleon spin-dependent generalized parton distributions

We present a lattice measurement of the first two moments of the spin-dependent GPD H-tilde(x,xi,t). From these we obtain the axial coupling constant and the second moment of the spin-dependent forward parton distribution. The measurements are done in full QCD using Wilson fermions. In addition, we also present results from a first exploratory study of full QCD using Asqtad sea and domain-wall valence fermions.

hep-lat↗
arXiv2002

Hard Scattering in the M-Theory Dual for the QCD String

Conventional superstring amplitudes in flat space exhibits exponential fall off at wide angle in contrast to the power law behavior found in QCD. It has recently been argued by Polchinski and Strassler that this conflict can be resolved via String/Gauge duality. They carried out their analysis in terms of strings in a deformed $AdS^5$ background. On the other hand, an equally valid approach to the String/Gauge duality for 4-d QCD is based on M-theory in a specific Black Hole deformation of $AdS^7 \times S^4$. We show that a very natural extension to this phenomenologically interesting M-theory background also gives the correct hard scattering power laws. In the Regge limit we extend the analysis to show the co-existence of both the hard BFKL-like Pomeron and the soft Pomeron Regge pole.

hep-th↗
arXiv1998

Magnetic Monopole Content of Hot Instantons

We study the Abelian projection of an instanton in $R^3 \times S^1$ as a function of temperature (T) and non-trivial holonomic twist ($ω$) of the Polyakov loop at infinity. These parameters interpolate between the circular monopole loop solution at T=0 and the static 't Hooft-Polyakov monopole/anti-monopole pair at high temperature.

hep-lat↗
arXiv1998

Heavy quark potential in the instanton liquid model

We study the heavy quark potential in the instanton liquid model by carefully measuring Wilson loops out to a distance of order 3$fm$. A random instanton ensemble with a fixed radius $ρ$ = 1/3$fm$ generates a potential $V(R)$ growing very slowly at large $R$. In contrast, a more realistic size distribution growing as $ρ^6$ at small $ρ$ and decaying as $ρ^{-5}$ at large $ρ$, leads to a potential which grows linearly with $R$. The string tension, however, is only about 1/10 of the phenomenological value.

hep-lat↗
arXiv1997

D-Theory: Field Theory via Dimensional Reduction of Discrete Variables

A new non-perturbative approach to quantum field theory --- D-theory --- is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model emerges from the (2+1)-d quantum Heisenberg model formulated in terms of quantum spins. Dimensional reduction is demonstrated explicitly by simulating correlation lengths up to 350,000 lattice spacings using a loop cluster algorithm. In the framework of D-theory, gauge theories are formulated in terms of quantum links --- the gauge analogs of quantum spins. Quantum links are parallel transporter matrices whose elements are non-commuting operators. They can be expressed as bilinears of anticommuting fermion constituents. In quantum link models dimensional reduction to four dimensions occurs, due to the presence of a 5-d Coulomb phase, whose existence is confirmed by detailed simulations using standard lattice gauge theory. Using Shamir's variant of Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of a 5-d slab. This naturally protects their chiral symmetries without fine-tuning. The first efficient cluster algorithm for a gauge theory with a continuous gauge group is formulated for the U(1) quantum link model. Improved estimators for Wilson loops are constructed, and dimensional reduction to ordinary lattice QED is verified numerically.

hep-lat↗
arXiv1996

Instanton Distribution in Quenched and Full QCD

In order to optimize cooling as a technique to study the instanton content of the QCD vacuum, we have studied the effects of alternative algorithms, improved actions and boundary conditions on the evolution of single instantons and instanton anti-instanton pairs. Using these results, we have extracted and compared the instanton content of quenched and full QCD.

hep-lat↗
arXiv1996

Calculation of Moments of Nucleon Structure Functions

Preliminary results are presented in our program to calculate low moments of structure functions for the proton and neutron on a $24^3\times32$ lattice at $β=6.2$. A comparison is made for a variety of smeared nucleon sources and preliminary results for the calculation of the nucleon tensor charge are presented.

hep-lat↗
arXiv1996

Instantons in the Maximally Abelian Gauge

We investigate the Maximally Abelian (MA) Projection for a single $SU(2)$ instanton in continuum gauge theory. We find that there is a class of solutions to the differential MA gauge condition with circular monopole loops of radius $R$ centered on the instanton of width $ρ$. However, the MA gauge fixing functional $G$ decreases monotonically as $R/ρ\rightarrow 0$. Its global minimum is the instanton in the singular gauge. We point out that interactions with nearby anti-instantons are likely to excite these monopole loops.

hep-lat↗
arXiv1996

Chronological Inversion Method for the Dirac Matrix in Hybrid Monte Carlo

In Hybrid Monte Carlo simulations for full QCD, the gauge fields evolve smoothly as a function of Molecular Dynamics time. Here we investigate improved methods of estimating the trial or starting solutions for the Dirac matrix inversion as superpositions of a chronological sequence of solutions in the recent past. By taking as the trial solution the vector which minimizes the residual in the linear space spanned by the past solutions, the number of conjugate gradient iterations per unit MD time is decreased by at least a factor of 2. Extensions of this basic approach to precondition the conjugate gradient iterations are also discussed.

hep-lat↗
arXiv1995

Critical Behavior of Simplicial Chiral Models

The large-N saddle-point equations for the principal chiral models defined on a d-1 dimensional simplex are derived from the external field problem for unitary integrals. The saddle point equation are studied analytically and numerically in many relevant instances, including d=4 and $d\rightarrow\infty$, with special attention to the critical domain, which is found to correspond to $β_c=1/d$ for all d. Related models (chiral chains) are discussed and large-N solutions are analyzed.

hep-th↗
arXiv1995

The Chiral Extension of Lattice QCD

The chiral extension of Quantum Chromodynamics (XQCD) adds to the standard lattice action explicit pseudoscalar meson fields for the chiral condensates. With this action, it is feasible to do simulations at the chiral limit with zero mass Goldstone modes. We review the arguments for why this is expected to be in the same universality class as the traditional action. We present preliminary results on convergence of XQCD for naive fermions and on the methodology for introducing counter terms to restore chiral symmetry for Wilson fermions.

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