89,254 research outputs found
An Optimized and Scalable Eigensolver for Sequences of Eigenvalue Problems
In many scientific applications the solution of non-linear differential
equations are obtained through the set-up and solution of a number of
successive eigenproblems. These eigenproblems can be regarded as a sequence
whenever the solution of one problem fosters the initialization of the next. In
addition, in some eigenproblem sequences there is a connection between the
solutions of adjacent eigenproblems. Whenever it is possible to unravel the
existence of such a connection, the eigenproblem sequence is said to be
correlated. When facing with a sequence of correlated eigenproblems the current
strategy amounts to solving each eigenproblem in isolation. We propose a
alternative approach which exploits such correlation through the use of an
eigensolver based on subspace iteration and accelerated with Chebyshev
polynomials (ChFSI). The resulting eigensolver is optimized by minimizing the
number of matrix-vector multiplications and parallelized using the Elemental
library framework. Numerical results show that ChFSI achieves excellent
scalability and is competitive with current dense linear algebra parallel
eigensolvers.Comment: 23 Pages, 6 figures. First revision of an invited submission to
special issue of Concurrency and Computation: Practice and Experienc
A Parallel Iterative Method for Computing Molecular Absorption Spectra
We describe a fast parallel iterative method for computing molecular
absorption spectra within TDDFT linear response and using the LCAO method. We
use a local basis of "dominant products" to parametrize the space of orbital
products that occur in the LCAO approach. In this basis, the dynamical
polarizability is computed iteratively within an appropriate Krylov subspace.
The iterative procedure uses a a matrix-free GMRES method to determine the
(interacting) density response. The resulting code is about one order of
magnitude faster than our previous full-matrix method. This acceleration makes
the speed of our TDDFT code comparable with codes based on Casida's equation.
The implementation of our method uses hybrid MPI and OpenMP parallelization in
which load balancing and memory access are optimized. To validate our approach
and to establish benchmarks, we compute spectra of large molecules on various
types of parallel machines.
The methods developed here are fairly general and we believe they will find
useful applications in molecular physics/chemistry, even for problems that are
beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.Comment: 20 pages, 17 figures, 3 table
Replica Monte Carlo Simulation (Revisited)
In 1986, Swendsen and Wang proposed a replica Monte Carlo algorithm for spin
glasses [Phys. Rev. Lett. 57 (1986) 2607]. Two important ingredients are
present, (1) the use of a collection of systems (replicas) at different of
temperatures, but with the same random couplings, (2) defining and flipping
clusters. Exchange of information between the systems is facilitated by fixing
the tau spin (tau=sigma^1\sigma^2) and flipping the two neighboring systems
simultaneously. In this talk, we discuss this algorithm and its relationship to
replica exchange (also known as parallel tempering) and Houdayer's cluster
algorithm for spin glasses. We review some of the early results obtained using
this algorithm. We also present new results for the correlation times of
replica Monte Carlo dynamics in two and three dimensions and compare them with
replica exchange.Comment: For "Statistical Physics of Disordered Systems and Its Applications",
12-15 July 2004, Shonan Village Center, Hayama, Japan, 7 page
Efficient Rank Reduction of Correlation Matrices
Geometric optimisation algorithms are developed that efficiently find the
nearest low-rank correlation matrix. We show, in numerical tests, that our
methods compare favourably to the existing methods in the literature. The
connection with the Lagrange multiplier method is established, along with an
identification of whether a local minimum is a global minimum. An additional
benefit of the geometric approach is that any weighted norm can be applied. The
problem of finding the nearest low-rank correlation matrix occurs as part of
the calibration of multi-factor interest rate market models to correlation.Comment: First version: 20 pages, 4 figures Second version [changed content]:
21 pages, 6 figure
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