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.

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## Projects 2009 2021

### Fast solvers for frequency-domain wave-scattering problems and applications

Graham, I., Gazzola, S. & Spence, E.

1/01/19 → 31/12/21

Project: Research council

### Bifurcation Theory, Numerical Linear Algebra and Applications

Freitag, M. & Graham, I.

1/05/13 → 30/09/13

Project: UK charity

### Numerical Analysis of Stochastic Partial Differential Equations

1/05/12 → 12/09/12

Project: UK charity

### Adaptive Multiscale Methods for Approximation and Preconditioning

Engineering and Physical Sciences Research Council

1/05/10 → 31/07/11

Project: Research council

### EPSRC LMS Durham Symposia

Engineering and Physical Sciences Research Council

1/03/10 → 30/11/10

Project: Research council

## Research Output 1994 2019

### Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients

Gilbert, A. D., Graham, I. G., Kuo, F. Y., Scheichl, R. & Sloan, I. H., 1 Aug 2019, In : Numerische Mathematik. 142, 4, p. 863-915 53 p.Research output: Contribution to journal › Article

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

Bonazzoli, M., Dolean, V., Graham, I., Spence, E. & Tournier, P-H., 30 May 2019, In : Mathematics of Computation (MCOM).Research output: Contribution to journal › Article

### The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances

Graham, I., Pembery, O. & Spence, E., 5 Mar 2019, In : Journal of Differential Equations. 266, 6, p. 2869-2923 55 p.Research output: Contribution to journal › Article

### 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 journal › Article

### 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 proceeding › Chapter

## Thesis

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

Author: Millward, R., 1 May 2011Supervisor: Graham, I. (Supervisor)

Student thesis: Doctoral Thesis › PhD

## Asymptotic and numerical methods for high-frequency scattering problems

Author: Kim, T., 31 Mar 2012Supervisor: Graham, I. (Supervisor) & Smyshlyaev, V. (Supervisor)

Student thesis: Doctoral Thesis › PhD

## Domain Decomposition Methods for Nuclear Reactor Modelling with Diffusion Acceleration

Author: Blake, J., 29 Jul 2016Supervisor: Graham, I. (Supervisor), Spence, A. (Supervisor) & Smith, P. (External person) (Supervisor)

Student thesis: Doctoral Thesis › PhD

## Iterative Methods for Criticality Computations in Neutron Transport Theory

Author: Scheben, F., 1 Jan 2011Supervisor: Graham, I. (Supervisor)

Student thesis: Doctoral Thesis › PhD

## Robust solvers for large indefinite systems in seismic inversion

Author: Shanks, D., 3 Jun 2015Supervisor: Graham, I. (Supervisor)

Student thesis: Doctoral Thesis › PhD