Research Interests

My research is in Numerical Analysis and Scientific Computing, and concentrates mainly on the numerical solution of (systems of) partial differential equations with highly varying (discontinuous) coefficients including

Research Group

Current Group Members:

Past Group Members:

Here is an out-of-date list of past and current research projects:

(For a more up-to-date list see my CV.)

EPSRC Project on Multilevel Monte Carlo for Radioactive Waste Management

Further Details

Domain Decomposition for Multiscale PDEs

The work on overlapping additive Schwarz is joint work with Ivan Graham (Bath), Eero Vainikko (University of Tartu, Estonia) and Jan Van lent. Recently I have extended the work, together with Clemens Pechstein (Linz), also to FETI methods, and started to work with Frederic Nataf (Paris) on two-level DD methods with Robin-type interface conditions. The novel coarsenings and the theoretical results are also of interest in the context of multiscale numerical approximation and have lead to recent collaborations with Tom Hou (Caltech) and Ludmil Zikatanov (Penn State). [Further Details]

Preconditioning for Multiphase Flow in Porous Media

This is a project in collaboration with the Institut Francais du Petrole (IFP), Paris, France, notably Roland Masson, Philippe Quandalle, Stephane Requena (all three Division Informatique Scientifique et Mathematiques Appliquees), and Johannes Wendebourg (Division Geologie-Geochimie). [Further Details]

Algebraic Preconditioners for High-Contrast Media

This is joint work with Ivan Graham (Bath), Burak Aksoylu (Louisiana State) and Hector Klie (Austin) on rigorously justified algebraic preconditioners for high-contrast media using singular perturbation arguments, and initiated from a visit in Mary Wheeler's group at Austin. For first results see Further work and some mathematical details will be available soon in

Numerical Computation of Spectra for PDEs on Infinite Domains - Application in Bandgap Calculations for Photonic Crystal Fibres

This is work that initiated through discussion with David Bird (Physics, Bath). Together with my PhD student Richard Norton (ORS Award) we carried out a rigorous numerical analysis of planewave expansion (or spectral Galerkin) methods for elliptic eigenproblems in 1D and 2D as they are used in the physics community in bandgap computations for photonic crystal fibres. Three papers on this work are in preparation. For first results see [Extended Abstract for Waves '07].
I have recently started another collaboration on the subject with Marco Marletta (Cardiff) to exploit novel theoretical ideas to numerical compute localised modes of Schroedinger-type operators avoiding spectral pollution. A new PhD student, Chris Hart, has started to work on this project in October 2008, under our joint supervision (funded from/based in Bath).

Numerical Methods for Weather and Climate Models

This is joint work with Mike Cullen (The Met Office), Jon Thuburn (Exeter), and my PhD student Sean Buckeridge (GWR Grant). It concentrates on the development and analysis of fast parallel multigrid preconditioners for elliptic PDEs in spherical geometries arising in weather, climate, and data assimilation models.

Quasi-Monte Carlo and Multilevel Monte Carlo Techniques for Stochastic PDEs

These are two very recently started projects with Ivan Graham (Bath), Ian Sloan, Dirk Nuyens, Frances Kuo (all UNSW, Sydney) and Mike Giles (Oxford).

Preconditioning Techniques for Discontinuous Galerkin Methods

This is a recent project in collaboration with Peter Bastian, Markus Blatt, Christian Engwer (all Stuttgart) and with David Kay (Oxford).

Emergence in Random Microstructures

This is project in collaboration with Darryl Almond (Mech Eng, Bath) and Nick McCullen (Maths, Bath) from BICS Theme C, which I have worked on in three MSc summer projects Clare Judd (2005), Sean Buckeridge (2006), Tristan Brindle (2007).

Iterative Solution of Saddle Point Problems with Applications to Uncertainty Quantification in Groundwater Flow

This is a project I started during my PhD at the University of Bath under the joint supervision of Ivan Graham (University of Bath) and Andrew Cliffe (University of Nottingham). Part of the work has also been done in collaboration with Linda Stals (Old Dominion University, Norfolk, VA). [Further Details]

Permeation of Gases in Polymers: Parameter Identification and Nonlinear Regression Analysis

This is a project in collaboration with the Institut Francais du Petrole (IFP), Paris, France, in particular Zakia Benjelloun-Dabaghi (Applied Mathematics Department), Marie-Helene Klopffer and Bruno Flaconneche (both Applied Chemistry and Physical Chemistry Department). [Further Details]

Parallel Solution of the Multigroup Neutron Diffusion Equations

This is work I did for my master's thesis during a one-year undergraduate placement at Siemens, Munich, under the joint supervision of Ulrich Langer (University of Linz, Austria) and Meinhard Paffrath (Siemens ZT, Munich, Germany), and in collaboration with Herbert Finnemann (Siemens KWU, Erlangen, Germany). [Further Details]

[Home] [Department of Mathematical Sciences] [University of Bath]

Last updated 15/09/2016