Computational Modelling Group

Multipole methods

Fast multipole methods were introduced in Greengard and Rokhlin's seminal paper in the Journal of Computational Physics in 1987, in which they reduced an O(N-squared) evaluation of the potential and force fields in N-body systems with Coulombic or gravitational potentials to an O(N) computation. They have since become a popular tool in many fields of computational science and modelling, having applications to N-body problems with various potential functions as well as electromagnetic scattering and incompressible fluid dynamics.

For queries about this topic, contact Neil O'Brien.

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Projects

A Fast Multipole Method for the Bessel potential

Marc Molinari, Simon Cox (Investigators), Neil O'Brien

The fast multipole method (FMM) proposed by Greengard and Rokhlin provides a method by which the O(N-squared) many-body problem can be reduced to O(N) complexity. In this project, a multipole method is developed to calculate the energy of a system of vortices in a high temperature superconductor, where the many-body interactions give rise to rich and complex physics. The method developed here is suitable for systems where the interactions are governed by a Bessel potential rather than the usual logarithmic potentials occurring in gravitational and electrostatic problems. We derive and apply vectorised forms of the Gegenbauer addition formulae in order to achieve the O(N) scaling associated with fast multipole methods.

Centre for Doctoral Training in Next Generation Computational Modelling

Hans Fangohr, Ian Hawke, Peter Horak (Investigators), Susanne Ufermann Fangohr, Ryan Pepper, Hossam Ragheb, Emanuele Zappia, Ashley Setter, David Lusher, Alvaro Perez-Diaz, Kieran Selvon, Thorsten Wittemeier, Mihails Milehins, Stephen Gow, Ioannis Begleris, Jonathon Waters, James Harrison, Joshua Greenhalgh, Rory Brown, Robert Entwistle, Paul Chambers, Jan Kamenik, Craig Rafter

The £10million Centre for Doctoral Training was launched in November 2013 and is jointly funded by EPSRC, the University of Southampton, and its partners.

The NGCM brings together world-class simulation modelling research activities from across the University of Southampton and hosts a 4-year doctoral training programme that is the first of its kind in the UK.

People

Simon Cox
Professor, Engineering Sciences (FEE)
Hans Fangohr
Professor, Engineering Sciences (FEE)
Carsten Gundlach
Professor, Mathematics (FSHS)
Graeme Day
Reader, Chemistry (FNES)
Nicolas Green
Reader, Electronics and Computer Science (FPAS)
Peter Horak
Reader, Optoelectronics Research Centre
Neil Broderick
Lecturer, Optoelectronics Research Centre
Gwenael Gabard
Lecturer, Institute of Sound & Vibration Research (FEE)
Ian Hawke
Lecturer, Mathematics (FSHS)
Rie Sugimoto
Senior Research Fellow, Institute of Sound & Vibration Research (FEE)
Ioannis Begleris
Postgraduate Research Student, Engineering Sciences (FEE)
Rory Brown
Postgraduate Research Student, Civil Engineering & the Environment (FEE)
Paul Chambers
Postgraduate Research Student, Engineering Sciences (FEE)
Robert Entwistle
Postgraduate Research Student, Engineering Sciences (FEE)
Stephen Gow
Postgraduate Research Student, Engineering Sciences (FEE)
Joshua Greenhalgh
Postgraduate Research Student, Engineering Sciences (FEE)
James Harrison
Postgraduate Research Student, Engineering Sciences (FEE)
Jan Kamenik
Postgraduate Research Student, Engineering Sciences (FEE)
David Lusher
Postgraduate Research Student, Engineering Sciences (FEE)
Juraj Mihalik
Postgraduate Research Student, Engineering Sciences (FEE)
Neil O'Brien
Postgraduate Research Student, Engineering Sciences (FEE)
Alvaro Perez-Diaz
Postgraduate Research Student, Engineering Sciences (FEE)
Lyuboslav Petrov
Postgraduate Research Student, Electronics and Computer Science (FPAS)
Craig Rafter
Postgraduate Research Student, Engineering Sciences (FEE)
Hossam Ragheb
Postgraduate Research Student, Engineering Sciences (FEE)
Álvaro Ruiz-Serrano
Postgraduate Research Student, Chemistry (FNES)
Kieran Selvon
Postgraduate Research Student, Engineering Sciences (FEE)
Ashley Setter
Postgraduate Research Student, Engineering Sciences (FEE)
Jonathon Waters
Postgraduate Research Student, Engineering Sciences (FEE)
Thorsten Wittemeier
Postgraduate Research Student, Engineering Sciences (FEE)
Emanuele Zappia
Postgraduate Research Student, Engineering Sciences (FEE)
Petrina Butler
Administrative Staff, Research and Innovation Services
Susanne Ufermann Fangohr
Administrative Staff, Civil Engineering & the Environment (FEE)
Mihails Milehins
Alumnus, University of Southampton
Marc Molinari
Alumnus, Engineering Sciences (FEE)
Ian Bush
External Member, NAG Ltd, Oxford