31 research outputs found
Full QCD with the L\"uscher local bosonic action
We investigate L\"uscher's method of including dynamical Wilson fermions in a
lattice simulation of QCD with two quark flavours. We measure the accuracy of
the approximation by comparing it with Hybrid Monte Carlo results for gauge
plaquette and Wilson loops. We also introduce an additional global Metropolis
step in the update. We show that the complexity of L\"uscher's algorithm
compares favourably with that of the Hybrid Monte Carlo.Comment: 21 pages Late
Algorithms in Lattice QCD
The enormous computing resources that large-scale simulations in Lattice QCD
require will continue to test the limits of even the largest supercomputers into
the foreseeable future. The efficiency of such simulations will therefore concern
practitioners of lattice QCD for some time to come.
I begin with an introduction to those aspects of lattice QCD essential to the
remainder of the thesis, and follow with a description of the Wilson fermion
matrix M, an object which is central to my theme.
The principal bottleneck in Lattice QCD simulations is the solution of linear
systems involving M, and this topic is treated in depth. I compare some of the
more popular iterative methods, including Minimal Residual, Corij ugate Gradient
on the Normal Equation, BI-Conjugate Gradient, QMR., BiCGSTAB and
BiCGSTAB2, and then turn to a study of block algorithms, a special class of iterative
solvers for systems with multiple right-hand sides. Included in this study
are two block algorithms which had not previously been applied to lattice QCD.
The next chapters are concerned with a generalised Hybrid Monte Carlo algorithm
(OHM C) for QCD simulations involving dynamical quarks. I focus squarely
on the efficient and robust implementation of GHMC, and describe some tricks
to improve its performance. A limited set of results from HMC simulations at
various parameter values is presented.
A treatment of the non-hermitian Lanczos method and its application to the
eigenvalue problem for M rounds off the theme of large-scale matrix computations
Improved integral equation methods for transient wave scattering.
Imperial Users onl
Real-Space Mesh Techniques in Density Functional Theory
This review discusses progress in efficient solvers which have as their
foundation a representation in real space, either through finite-difference or
finite-element formulations. The relationship of real-space approaches to
linear-scaling electrostatics and electronic structure methods is first
discussed. Then the basic aspects of real-space representations are presented.
Multigrid techniques for solving the discretized problems are covered; these
numerical schemes allow for highly efficient solution of the grid-based
equations. Applications to problems in electrostatics are discussed, in
particular numerical solutions of Poisson and Poisson-Boltzmann equations.
Next, methods for solving self-consistent eigenvalue problems in real space are
presented; these techniques have been extensively applied to solutions of the
Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue
problems arising in semiconductor and polymer physics. Finally, real-space
methods have found recent application in computations of optical response and
excited states in time-dependent density functional theory, and these
computational developments are summarized. Multiscale solvers are competitive
with the most efficient available plane-wave techniques in terms of the number
of self-consistency steps required to reach the ground state, and they require
less work in each self-consistency update on a uniform grid. Besides excellent
efficiencies, the decided advantages of the real-space multiscale approach are
1) the near-locality of each function update, 2) the ability to handle global
eigenfunction constraints and potential updates on coarse levels, and 3) the
ability to incorporate adaptive local mesh refinements without loss of optimal
multigrid efficiencies.Comment: 70 pages, 11 figures. To be published in Reviews of Modern Physic