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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.

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Projects 2009 2021

numerical method
modeling
wave phenomena
wavelength
upscaling

EPSRC LMS Durham Symposia

Graham, I. & Scheichl, R.

1/03/1030/11/10

Project: Research council

website
mathematics
event
accommodation
reputation

Research Output 1994 2019

Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption

Bonazzoli, M., Dolean, V., Graham, I., Spence, E. & Tournier, P-H., 8 Mar 2019, (Accepted/In press) In : Mathematics of Computation (MCOM).

Research output: Contribution to journalArticle

Open Access
File
Domain Decomposition
Preconditioning
Maxwell's equations
Preconditioner
Absorption
2 Citations (Scopus)

Analysis of circulant embedding methods for sampling stationary random fields

Graham, I. G., Kuo, F. Y., Nuyens, D., Scheichl, R. & Sloan, I. H., 2018, In : SIAM Journal on Numerical Analysis (SINUM). 56, 3, p. 1871-1895 25 p.

Research output: Contribution to journalArticle

Open Access
File
Random Field
Regular hexahedron
Positive Definiteness
Circulant Matrix
Correlation Length
1 Citation (Scopus)

A two-level domain-decomposition preconditioner for the time-harmonic maxwell’s equations

Bonazzoli, M., Dolean, V., Graham, I. G., Spence, E. A. & Tournier, P. H., 1 Jan 2018, Domain Decomposition Methods in Science and Engineering XXIV. DD 2017. Bjorstad, P. (ed.). Cham, Switzerland: Springer Verlag, p. 149-157 9 p. (Lecture Notes in Computational Science and Engineering; vol. 125).

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients

Graham, I., Kuo, F. Y., Nuyens, D., Scheichl, R. & Sloan, I. H., 1 Oct 2018, In : Numerische Mathematik. 140, 2, p. 479-511 33 p.

Research output: Contribution to journalArticle

Open Access
Quasi-Monte Carlo
Elliptic PDE
Monte Carlo methods
Random Field
Sampling
2 Citations (Scopus)

Modern Monte Carlo variants for uncertainty quantification in neutron transport

Graham, I. G., Parkinson, M. J. & Scheichl, R., 23 May 2018, Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing, p. 455-481 27 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Thesis

A new adaptive multiscale finite element method with applications to high contrast interface problems

Author: Millward, R., 1 May 2011

Supervisor: Graham, I. (Supervisor)

Student thesis: Doctoral ThesisPhD

File

Asymptotic and numerical methods for high-frequency scattering problems

Author: Kim, T., 31 Mar 2012

Supervisor: Graham, I. (Supervisor) & Smyshlyaev, V. (Supervisor)

Student thesis: Doctoral ThesisPhD

File

Domain Decomposition Methods for Nuclear Reactor Modelling with Diffusion Acceleration

Author: Blake, J., 29 Jul 2016

Supervisor: Graham, I. (Supervisor), Spence, A. (Supervisor) & Smith, P. (External person) (Supervisor)

Student thesis: Doctoral ThesisPhD

File

Iterative Methods for Criticality Computations in Neutron Transport Theory

Author: Scheben, F., 1 Jan 2011

Supervisor: Graham, I. (Supervisor)

Student thesis: Doctoral ThesisPhD

File

Robust solvers for large indefinite systems in seismic inversion

Author: Shanks, D., 3 Jun 2015

Supervisor: Graham, I. (Supervisor)

Student thesis: Doctoral ThesisPhD

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