The University of Southampton
University of Southampton Institutional Repository

Algorithms for scientific computing

Algorithms for scientific computing
Algorithms for scientific computing
There has long been interest in algorithms for simulating physical systems. We are concernedwith two areaswithin this field: fastmultipolemethods andmeshlessmethods. Since Greengard and Rokhlin’s seminal paper in 1987, considerable interest has arisen in fast multipole methods for finding the energy of particle systems in two and three dimensions, and more recently in many other applications where fast matrix-vector multiplication is called for. We develop a new fast multipole method that allows the calculation of the energy of a system of N particles in O(N) time, where the particles’ interactions are governed by the 2D Yukawa potential which takes the form of a modified Bessel function Kv. We then turn our attention to meshless methods. We formulate and test a new radial basis function finite differencemethod for solving an eigenvalue problemon a periodic domain. We then applymeshlessmethods to modelling photonic crystals. After an initial background study of the field, we detail the Maxwell equations, which govern the interaction of the light with the photonic crystal, and show how photonic band gaps may be given rise to. We present a novel meshless weak-strong form method with reduced computational cost compared to the existing meshless weak form method. Furthermore, we develop a new radial basis function finite differencemethod for photonic band gap calculations. Throughout the work we demonstrate the application of cutting-edge technologies such as cloud computing to the development and verification of algorithms for physical simulations.
O'Brien, Neil
7856f2e1-73fc-4cb9-a1f4-9b6c8b9373e7
O'Brien, Neil
7856f2e1-73fc-4cb9-a1f4-9b6c8b9373e7
Cox, Simon
0e62aaed-24ad-4a74-b996-f606e40e5c55

O'Brien, Neil (2012) Algorithms for scientific computing University of Southampton, Faculty of Engineering and the Environment, Doctoral Thesis , 197pp.

Record type: Thesis (Doctoral)

Abstract

There has long been interest in algorithms for simulating physical systems. We are concernedwith two areaswithin this field: fastmultipolemethods andmeshlessmethods. Since Greengard and Rokhlin’s seminal paper in 1987, considerable interest has arisen in fast multipole methods for finding the energy of particle systems in two and three dimensions, and more recently in many other applications where fast matrix-vector multiplication is called for. We develop a new fast multipole method that allows the calculation of the energy of a system of N particles in O(N) time, where the particles’ interactions are governed by the 2D Yukawa potential which takes the form of a modified Bessel function Kv. We then turn our attention to meshless methods. We formulate and test a new radial basis function finite differencemethod for solving an eigenvalue problemon a periodic domain. We then applymeshlessmethods to modelling photonic crystals. After an initial background study of the field, we detail the Maxwell equations, which govern the interaction of the light with the photonic crystal, and show how photonic band gaps may be given rise to. We present a novel meshless weak-strong form method with reduced computational cost compared to the existing meshless weak form method. Furthermore, we develop a new radial basis function finite differencemethod for photonic band gap calculations. Throughout the work we demonstrate the application of cutting-edge technologies such as cloud computing to the development and verification of algorithms for physical simulations.

PDF Thesis_Neil_S_OBrien_Oct2012.pdf - Other
Download (4MB)

More information

Published date: 1 October 2012
Organisations: University of Southampton, Faculty of Engineering and the Environment

Identifiers

Local EPrints ID: 355716
URI: http://eprints.soton.ac.uk/id/eprint/355716
PURE UUID: 760bc035-0538-4193-9fe6-f72703be3d68

Catalogue record

Date deposited: 21 Oct 2013 09:31
Last modified: 18 Jul 2017 03:44

Export record

Contributors

Author: Neil O'Brien
Thesis advisor: Simon Cox

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×