GPU-libs

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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.

Meshless Methods for Photonic Crystal Modelling

Kamal Djidjeli, Marc Molinari, Simon Cox (Investigators), Neil O'Brien, Elizabeth Hart

We apply meshless methods to the problems of simulating photonic crystals. The meshless methods utilise compactly-supported radial basis functions (CSRBFs) and offer a promising alternative to the conventional plane-wave expansion method for calculating the band structure of photonic crystals.

Soft x-ray science on a tabletop

Peter Horak, Jeremy Frey, Bill Brocklesby (Investigators), Patrick Anderson

Complex numerical simulations are being performed to aid experimentalists at Southampton realize the next generation of high brightness tabletop sources of coherent soft x-rays. 