798 research outputs found
An adaptive preconditioner for steady incompressible flows
This paper describes an adaptive preconditioner for numerical continuation of
incompressible Navier--Stokes flows. The preconditioner maps the identity (no
preconditioner) to the Stokes preconditioner (preconditioning by Laplacian)
through a continuous parameter and is built on a first order Euler
time-discretization scheme. The preconditioner is tested onto two fluid
configurations: three-dimensional doubly diffusive convection and a reduced
model of shear flows. In the former case, Stokes preconditioning works but a
mixed preconditioner is preferred. In the latter case, the system of equation
is split and solved simultaneously using two different preconditioners, one of
which is parameter dependent. Due to the nature of these applications, this
preconditioner is expected to help a wide range of studies
Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers
In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system, and the design of data structures to take advantage of serial, coarse grain parallel and massively parallel computer architectures, are considered in detail. We put forward arguments as to why integration of the system within a sparse simplex solver is important and outline how the system is designed to achieve this integration
Parallel Solution Methods for Aerostructural Analysis and Design Optimization
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83550/1/AIAA-2010-9308-579.pd
Efficient sensitivity analysis of chaotic systems and applications to control and data assimilation
Sensitivity analysis is indispensable for aeronautical engineering applications that require optimisation, such as flow control and aircraft design. The adjoint method is the standard approach for sensitivity analysis, but it cannot be used for chaotic systems. This is due to the high sensitivity of the system trajectory to input perturbations; a characteristic of many turbulent systems. Although the instantaneous outputs are sensitive to input perturbations, the sensitivities of time-averaged outputs are well-defined for uniformly hyperbolic systems, but existing methods to compute them cannot be used. Recently, a set of alternative approaches based on the shadowing property of dynamical systems was proposed to compute sensitivities. These approaches are computationally expensive, however. In this thesis, the Multiple Shooting Shadowing (MSS) [1] approach is used, and the main aim is to develop computational tools to allow for the implementation of MSS to large systems.
The major contributor to the cost of MSS is the solution of a linear matrix system. The matrix has a large condition number, and this leads to very slow convergence rates for existing iterative solvers. A preconditioner was derived to suppress the condition number, thereby accelerating the convergence rate. It was demonstrated that for the chaotic 1D Kuramoto Sivashinsky equation (KSE), the rate of convergence was almost independent of the #DOF and the trajectory length. Most importantly, the developed solution method relies only on matrix-vector products.
The adjoint version of the preconditioned MSS algorithm was then coupled with a gradient descent method to compute a feedback control matrix for the KSE. The adopted formulation allowed all matrix elements to be computed simultaneously. Within a single iteration, a stabilising matrix was computed. Comparisons with standard linear quadratic theory (LQR) showed remarkable similarities (but also some differences) in the computed feedback control kernels.
A preconditioned data assimilation algorithm was then derived for state estimation purposes. The preconditioner was again shown to accelerate the rate of convergence significantly. Accurate state estimations were computed for the Lorenz system.Open Acces
Accelerating Certifiable Estimation with Preconditioned Eigensolvers
Convex (specifically semidefinite) relaxation provides a powerful approach to
constructing robust machine perception systems, enabling the recovery of
certifiably globally optimal solutions of challenging estimation problems in
many practical settings. However, solving the large-scale semidefinite
relaxations underpinning this approach remains a formidable computational
challenge. A dominant cost in many state-of-the-art (Burer-Monteiro
factorization-based) certifiable estimation methods is solution verification
(testing the global optimality of a given candidate solution), which entails
computing a minimum eigenpair of a certain symmetric certificate matrix. In
this paper, we show how to significantly accelerate this verification step, and
thereby the overall speed of certifiable estimation methods. First, we show
that the certificate matrices arising in the Burer-Monteiro approach
generically possess spectra that make the verification problem expensive to
solve using standard iterative eigenvalue methods. We then show how to address
this challenge using preconditioned eigensolvers; specifically, we design a
specialized solution verification algorithm based upon the locally optimal
block preconditioned conjugate gradient (LOBPCG) method together with a simple
yet highly effective algebraic preconditioner. Experimental evaluation on a
variety of simulated and real-world examples shows that our proposed
verification scheme is very effective in practice, accelerating solution
verification by up to 280x, and the overall Burer-Monteiro method by up to 16x,
versus the standard Lanczos method when applied to relaxations derived from
large-scale SLAM benchmarks.Comment: 8 pages, 6 figure
Optimization of Nanoparticle-Based SERS Substrates through Large-Scale Realistic Simulations
Surface-enhanced Raman scattering (SERS) has
become a widely used spectroscopic technique for chemical
identification, providing unbeaten sensitivity down to the singlemolecule
level. The amplification of the optical near field
produced by collective electron excitations plasmons in
nanostructured metal surfaces gives rise to a dramatic increase
by many orders of magnitude in the Raman scattering intensities
from neighboring molecules. This effect strongly depends on
the detailed geometry and composition of the plasmonsupporting
metallic structures. However, the search for
optimized SERS substrates has largely relied on empirical
data, due in part to the complexity of the structures, whose
simulation becomes prohibitively demanding. In this work, we
use state-of-the-art electromagnetic computation techniques to
produce predictive simulations for a wide range of nanoparticle-based SERS substrates, including realistic configurations
consisting of random arrangements of hundreds of nanoparticles with various morphologies. This allows us to derive rules of
thumb for the influence of particle anisotropy and substrate coverage on the obtained SERS enhancement and optimum spectral
ranges of operation. Our results provide a solid background to understand and design optimized SERS substrates.Peer ReviewedPostprint (published version
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