List of Abstracts
Ashby, Tom (University of Edinburgh)
Modules and Solvers
Friday, 04 July, 09:30
Abstract:
Krylov subspace solvers come in a myriad of slightly different flavours.
Rather than treat each algorithm as a black box, we have attempted to write a
toolbox of self-contained pieces from which the algorithms can be created.
This will hopefully make it easier to prototype new methods and/or to easily
add useful algorithmic pieces to certain methods. This talk will cover the
design, implementation and efficiency concerns of the framework.
Boriçi, Artan (University of Edinburgh)
Computational methods for the fermion determinant and the link between overlap and domain wall fermions
Tuesday, 01 July, 14:00
Abstract:
This lecture comprises in two parts.
- The first part reviews numerical methods which are used in
lattice QCD to compute the determinant of the lattice Dirac
operator. These include methods which are based on:
- Gaussian integral representaion
- Krylov subspace evaluation of matrix functions
- Sparse approximate inverses
- The second part of the lecture deals with the formal relationship andalgebraic structure of domain wall and overlap fermions using:
- Truncated overlap fermions as the hybrid of both formulations
- Transfer matrix formalism in 4+1 dimensions
- Dimensional reduction
Boriçi, Artan (University of Edinburgh)
Determinant and Order Statistics
Thursday, 03 July, 09:30
Abstract:
This is a follow up of the introductory talk on the determinant
computations. It describes an approximate stochastic representation
of the quark determinant in terms of a certain order statistics
distribution. Approximation errors are discussed and illustrated
in the Monte Carlo simulation of the lattice Schwinger model.
de Forcrand, Philippe (ETH Zurich and CERN)
Monte Carlo Overrelaxation for SU(N) Gauge Theories
Thursday, 03 July, 12:00
Abstract:
We take a fresh look at Monte Carlo overrelaxation for the
case of SU(N) Yang-Mills theories. We compare the approach of
performing N(N-1)/2 microcanonical SU(2) steps with that of performing
a single SU(N) step. We show that the latter strategy provides
superior decorrelation for a similar amount of work.
Edwards, Robert (Thomas Jefferson National Accelerator Facility)
Computational Methods for Chiral Fermions
Monday, 30 June, 15:45
Abstract:
I describe properties of chiral fermion operators and methods to implement it
numerically. I use the results from the
spectral flow of the operator to illuminate the difficulties in practical
implementations of chiral fermions. I will describe related
variants of chiral fermions that attempt to avoid these difficulties.
Numerical methods for both quenched and dynamical methods will also be
given.
Fleming, George (Thomas Jefferson National Accelerator Laboratory)
What Can Lattice QCD Learn from NMR Spectroscopists
Thursday, 03 July, 14:00
Abstract:
Euclidean-time hadron correlation functions computed in Lattice QCD
(LQCD) are modeled by a sum of decaying exponentials,
reminiscent of the exponentially damped sinusoid models
of free induction decay (FID) in Nuclear Magnetic Resonance (NMR)
spectroscopy. We present our initial progress in studying how data
modelling techniques commonly used in NMR perform when applied
to LQCD data.
Follana, Eduardo (University of Glasgow)
Improved Staggered Fermions
Friday, 04 July, 11:00
Abstract:
We examine several variants of improved staggered fermions. We
discuss how to construct meson operators. In order to show the improvement
on the taste-symmetry breaking interactions, we compute the pion spectrum.
Frommer, Andreas (Wuppertal University)
QCD for Numerical Analysts
Monday, 30 June, 14:00
Abstract:
The purpose of this talk is to present those topics
and objects in lattice QCD which are important to understand the
numerical analysis challenges in computations in QCD simulations.
We will discuss the Wilson-Fermion matrix in some detail, then
turn to progress in recent years due to improved techniques from
numerical linear algebra and finally review the current challenges
for the simulation of Neuberger fermions.
Golub, Gene (Stanford University)
Variance Reduction by Control Variates in Monte Carlo Simulations of Large Scale Matrix Functions
Tuesday, 01 July, 15:45
Abstract:
In numerical simulation of lattice QCD and physical applications,
computational kernels involve the calculation of matrix functions f(A)
of a very large matrix A, where f is a smooth function. This includes
the determinant and trace of f(A). Based on the theory of moments, we
have been able to derive efficient algorithms which lead to highly
accurate results. In this talk, we will first briefly review the theory
of moments and the corresponding quadrature rules and show how they can
be effectively used in these calculations. Then we will focus on a
variance reduction technique in the Monte Carlo simulation which
uses the first few moments of the matrix A as control variates.
Hart, Alistair (University of Edinburgh)
Computational Techniques for Lattice Perturbation Theory
Friday, 04 July, 11:45
Abstract:
I discuss the need for automated techniques for lattice perturbation
theory, and a particular method for carrying this out. I present an
implementation of this. Perturbative calculations of the anisotropy
and of the heavy quark propagator renormalisation in NRQCD will be
used to illustrate the technique.
Higham, Nicholas (University of Manchester)
Matrix functions: theory and algorithms
Wednesday, 02 July, 09:30
Abstract:
We describe some recent work on matrix functions,
covering both theory and algorithms.
We discuss general matrix functions,
the special case of $p$th roots,
and computation of $f(A)b$ without explicitly forming $f(A)$.
Joó, Bálint (University of Edinburgh)
Reversibility and Instability in HMC Simulations
Thursday, 03 July, 15:30
Abstract:
We review the problem of instabilities in the molecular dynamics
integrators used in Hybrid Monte Carlo and other molecular dynamics
based algorithms. In Hybrid Monte Carlo simulations, reversible and
area preserving molecular dynamics integration schemes are needed
to ensure that detailed balance is satisfied. The simplest and most
frequently used scheme is the leap-frog scheme. We demonstrate the
onset of instabilities in this scheme using the harmonic oscillator.
We demonstrate instabilities in lattice simulations using Wilson-Clover
dynamical fermions. Finally we discuss the potential effects of instabilities
for inexact simulation algorithms and for exact simulations with
very light quarks, the latter being what is chiefly desired from
simulations using dynamical Ginsparg-Wilson Fermions.
Note: This talk is meant to be pedagogical, and chiefly for the numerical analysts in the audience -- as the lattice guys have heard it already, probably more than once :)
Kennedy, Anthony D. (University of Edinburgh)
Zolotarev on the Fly
Tuesday, 01 July, 09:30
Abstract:
We review the theory of optimal polynomial and rational Chebyshev
approximations, and the theory of elliptic functions leading to Zolotarevs
formula for the sign function over the range $R =
\{z:\varepsilon\leq|z|\leq1\}$. We show how Gauss arithmetic-geometric mean
allows us to compute the Zolotarev coefficients on the fly as a function of
$\varepsilon$. This allows us to calculate $\sgn(H)$ quickly and accurately
for a Hermitian matrix $H$ whose spectrum lies in $R$.
Liu, Keh-Fei (University of Kentucky)
An Algorithm for Finite Density
Thursday, 03 July, 11:00
Abstract:
I will review the difficulty of lattice QCD simulation for finite baryon
density at zero temperature and propose an algorithm in the canonical ensemble
approach which projects out the baryon number in each gauge configuration. I
will also discuss its potential application to odd number of flavors.
Neuberger, Herbert (Rutgers University)
An Introduction to Lattice Chiral Fermions
Monday, 30 June, 11:15
Abstract:
This introduction will focus on two topics: The first deals with
the basic mathematical aspects of lattice chirality; the second,
with practical implementation. For both topics a brief overview
will be given, followed up by the presentation of a new and yet
unexplored idea.
Peardon, Michael (Trinity College, Dublin)
Monte Carlo Algorithms for QCD
Monday, 30 June, 09:30
Abstract:
An introduction to the simulation technology used in current Monte Carlo
simulations of QCD with dynamical fermions is presented. The Markov processes
used to generate an ensemble of gauge field configurations are described and
some of the key problems and bottlenecks are outlined. Current research
directions are then discussed.
Saad, Yousef (Minnesota University)
Introduction to Krylov Subspace Methods
Tuesday, 01 July, 11:15
Abstract:
Krylov subspace techniques have been used in many different areas of
scientific computing as a means for projecting the original problem
into one of smaller dimension. This basic principle is best
illustrated when solving matrix problems such as eigenvalue problems
or linear systems where they give rise to the Lanczos and the
conjugate gradient algorithms. There are however many other uses of
what may be termed Krylov projection. This lecture will introduce
Krylov subspace methods and give an overview of these applications
van den Eshof, Jasper (Utrecht University)
Iterative linear system solvers with inexact matrix-vector products
Wednesday , 02 July, 11:00
Abstract:
Simulations in quantum chromodynamics involving overlap fermions require the
frequent solution of a linear system where the operator partly consists of a
matrix sign function. To solve this system, a two-level iteration method is
often employed where the outer iteration is a standard iterative solver for
linear system that invokes, in every iteration step, a vector iteration method
to approximate the action of the matrix sign function to a vector (the inner
iteration).
In this talk we discuss the impact of approximately computed matrix-vector
products on a wide class of Krylov subspace methods for linear systems. We
will argue that, in general, it is the choice of the basis for the Krylov
subspace that determines the sensitivity to inexactness in the matrix-vector
products. Subsequently, we give an overview of various choices for the basis
that occur in practical methods and we review and discuss known strategies
(relaxation strategies) for controlling the accuracy of the matrix-vector
products. Unfortunately, a suitable choice for the basis (and therefore
method) can depend on the particular problem to be solved. We give a flowchart
with suggestions for the selection of an inexact iterative method for general
problems. In the second part of the talk, we discuss some practical issues
concerning the efficieny of the two-level iteration scheme.
Wenger, Urs (Oxford University)
Optimised Continued Fractions for Inverting the Ginsparg-Wilson Operator
Wednesday, 02 July, 12:00
Abstract:
We use a continued fraction expansion of the sign-function in order to
obtain a five dimensional formulation of the overlap lattice Dirac
operator. Within this formulation the inverse of the overlap operator
can be calculated by a single Krylov space method where nested
conjugate gradient procedures are avoided. We show that the five
dimensional linear system can be made well conditioned using
equivalence transformations on the continued fractions. This is of
significant importance when dynamical overlap fermions are simulated.
Young, Ross (University of Adelaide)
Chiral Effective Field Theory for Lattice QCD
Thursday, 03 July, 16:15
Abstract:
The extrapolation of lattice QCD simulations, performed at relatively
large quark mass, to the chiral regime is a nontrivial problem. Here we
demonstrate the difficulty associated with the direct application of the
standard formulation of chiral perturbation theory. To overcome this
difficulty, we present the implementation of a finite-range regulator
(FRR) in chiral field theory. Results show that modern lattice QCD can
constrain the extrapolation to minimal systematic errors. Simulations in
the chiral regime are still necessary to reduce statistical errors and
directly observe chiral nonanalytic behaviour.
Copyright © 2007
