My Research
This is concerned with the design, analysis, implementation and
application of numerical algorithms for the reliable and efficient
computational solution of partial differential equations (PDEs).
The main components in this work include...
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Unstructured finite element methods and algorithms in 2 and 3 space
dimensions.
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Analysis and implementation of adaptive methods in space and time.
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Error estimation and control.
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Development of efficient sparse linear algebra and preconditioning
techniques.
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Design and analysis of parallel linear algebra and finite element
algorithms.
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Applications in computational fluid dynamics (CFD) -- including both
compressible and incompressible flows, Newtonian and non-Newtonian flows
and the solution of free boundary problems.
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Applications in spectral theory.
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Industrial applications (please visit the
CPDE Unit Home Page).
Some of my current and past research collaborators are
Phil Gaskell,
John Summers and
Harvey Thompson (of the School of Mechanical Engineering, Leeds),
Thomas Apel (Institut fur Mathematik und Bauinformatik,
Universitat der Bundeswehr Munchen),
Randy Bank (Mathematics, UCSD),
Martin Berzins (Computing, Utah),
Malcolm Brown (Computer Science, Cardiff),
David Gubbins and
Greg Houseman
(Earth Science, Leeds),
Matthew Hubbard (Computing, Leeds),
Tom McLeish (Physics, Durham),
Oliver Harlen and
Mark Kelmanson (Applied Maths, Leeds),
Arnd Meyer (Mathematics, Chemnitz) and
Andy Mullis (Materials, Leeds).
Publications
Please click here for a list of my
publications.
Current research funding
- Novel Asynchronous Algorithms and Software for Large Sparse Systems,
EPSRC (2010, £191307) (Leeds principal investigator).
- Rapid Alloy Solidification: A Quantitative Phase-Field Modelling Technique,
EPSRC (2010, £411913) (co-investigator).
- Engine Efficiency, EU Commission/Shell (2008, 300000 euro) (Leeds PI).
Previous research funding
- HPC Software for Modelling Chemical Diffusion through Skin Membranes,
EPSRC (2007, £121928) (principal investigator).
- Phase-Field Software for the Quantitative Prediction of Coupled
Thermal-Chemical Alloy Solidification, EPSRC (2007, £152,947)
(principal investigator)
- Parallelised Algorithms for Computing Viscoelastic Deformation in 3D
Non-linear Media, EPSRC (2006, £139173) (co-investigator).
- Optimising Cement Delivery in Total Joint Arthroplasty and other
Musculoskeletal Applications, Arthritis Research Campaign (2005,
£148669) (co-investigator).
- The Microscale Polymer Processing Consortium for Macromolecular
Engineering: Toolbox Development and Application, EPSRC (2005, £2599490)
(co-investigator).
- Scale Invariant Moving Mesh Finite Elements for Multidimensional
Nonlinear Partial Differential Equations (2005, £5284)
(co-investigator).
- Intelligent Infrastructure to Support the Atmospheric Composition
Community,
NERC E-science studentship (2005, £60000) (co-investigator).
- Self-Adapting Software for Grid-Based Numerical Simulation, EPSRC (2005,
£187450) (principal investigator).
- Towards Global Optimization in CFD Design Through the use of
Discrete Adjoint Methods, EPSRC studentship (2005, £59464)
(principal investigator).
- Why Does the Earth's Magnetic Field Reverse and What Causes Superchrons?
NERC E-science studentship (2005, £60000) (co-investigator).
- Phase-Field Model for Simulating the Coupled Thermal-Chemical
Solidification of Alloys, EPSRC (2004, £129647) (co-investigator).
- Mesh Evolution in Two and Three Space Dimensions Based on Geometric
Conservation Laws, EPSRC (2002, £3840) (principal investigator).
- A Grid-Based Approach to the Validation and Testing of Lubrication
Models, EPSRC (2002, £27546) (co-investigator).
- Adaptive Techniques for Computational Solution of 3-D Surface-Tension
Dominated Free-Surface Flow Problems, EPSRC (2001, £148439) (principal
investigator).
- Digital Jet Priniting on Textiles, EPSRC (2001, £720435)
(co-investigator).
- A British Council Anglo-German Collaborative Research (ARC) Grant
to work with the Numerical Mathematics Group and the Technical
University of Chemnitz, Germany (1998 £5850) (principal
invesitigator).
- A Leverhulme Trust Research Grant to visit the Scientific
Computation group at UCSD, USA (1998, £ 8650) (principal
investigator).
- Anisotropic Mesh Adaption and error Estimation for FE Solutions of 3-D
Convection-Dominated PDEs, EPSRC (1998, £ 87655) (principal
invesigator).
Present Ph.D. students
Note that all e-mail addresses are @leeds.ac.uk
- Keeran Brabazon (email: scs5kjb)
- Sarfraz (email: scsa)
- Feng Yang (email: fy06fwy)
Past Ph.D. students
Other Ph.D. students supervised (outside my main research areas)
- William Hsu (2007)
The Process of Information Systems Strategic Planning in Higher Education
Institutions in Taiwan
- Abdullah Akbar (2003)
Patient Information System for National Healthcare- An Intranet and Internet-based
Model for the State of Kuwait
- Sharifullah Khan (2003)
Optimisation of Continual Queries
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