Projects per year
Personal profile
Research interests
I held positions at the University of New South Wales and the University of Melbourne before coming to Bath in 1985. I have held the position of Professor of Numerical Analysis at Bath since May 2000.
I have had substantial research collaborations in USA, Germany, Australia and Switzerland and visiting positions at University of Iowa, University of Kiel, University of New South Wales, Max-Planck Institute Leipzig, California Institute of Technology, Radon Institute Austria, University of Zuerich and the Chinese University of Hong Kong.
Most of my research concerns various aspects of the numerical analysis of partial differential equations. Applications in which I am currently working include: fluid flow in uncertain media, seismic imaging of the earth's subsurface and the analysis of the safety of reactors.
My research is currently supported by Schlumberger Gould Research and by Amec Foster Wheeler plc.
Recent invited plenary talks include the 9th ENUMath Conference (Leicester 2011), the 11th International Conference on Mathematical and Numerical Aspects of Waves (Tunisia 2013) and the 24th International Conference on Domain Decomposition Methods in Science and Engineering (Svalbard, Norway 2017).
I am currently an Associate Editor of the journals: SIAM Review, Mathematics of Computation, IMA Journal of Numerical Analysis, Advances in Computational Mathematics and Journal of Integral Equations and Applications.
I am a Member of the Society of Industrial and Applied Mathematics and the London Mathematical Society and currently serve on the EPSRC Peer Review College.
Expertise related to UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This person’s work contributes towards the following SDG(s):
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Fast solvers for frequency-domain wave-scattering problems and applications
Graham, I., Gazzola, S. & Spence, E.
Engineering and Physical Sciences Research Council
1/01/19 → 31/12/22
Project: Research council
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Bifurcation Theory, Numerical Linear Algebra and Applications
Freitag, M. & Graham, I.
1/05/13 → 30/09/13
Project: UK charity
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Numerical Analysis of Stochastic Partial Differential Equations
1/05/12 → 12/09/12
Project: UK charity
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Adaptive Multiscale Methods for Approximation and Preconditioning
Engineering and Physical Sciences Research Council
1/05/10 → 31/07/11
Project: Research council
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EPSRC LMS Durham Symposia
Engineering and Physical Sciences Research Council
1/03/10 → 30/11/10
Project: Research council
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Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification
Graham, I., Pembery, O. & Spence, E., 3 Sep 2021, In: Advances in Computational Mathematics. 47, 68.Research output: Contribution to journal › Article › peer-review
Open Access -
Domain decomposition preconditioners for high-order discretisations of the heterogeneous Helmholtz equation
Gong, S., Graham, I. & Spence, E., 31 Jul 2021, In: IMA Journal of Numerical Analysis. 41, 3, p. 2139–2185Research output: Contribution to journal › Article › peer-review
Open Access -
Error Analysis and Uncertainty Quantification for the Heterogeneous Transport Equation in Slab Geometry
Graham, I. G., Parkinson, M. J. & Scheichl, R., 31 Oct 2021, In: IMA Journal of Numerical Analysis. 41, 4, p. 2331–2361Research output: Contribution to journal › Article › peer-review
Open AccessFile16 Downloads (Pure) -
Multigrid preconditioners for the hybridized Discontinuous Galerkin discretisation of the shallow water equations
Betteridge, J., Gibson, T., Graham, I. & Müller, E., 1 Feb 2021, In: Journal of Computational Physics. 426, 42 p., 109948.Research output: Contribution to journal › Article › peer-review
Open AccessFile1 Downloads (Pure) -
Stability and error analysis for the Helmholtz equation with variable coefficients
Graham, I. & Sauter, S., 2020, In: Mathematics of Computation. 89, 321, p. 105-138 24 p.Research output: Contribution to journal › Article › peer-review