Dr. Martyn Hughes's Home Page

On a 777 en route to 

Welcome! (Huan ying!)

I am an Honorary Research Fellow and Teacher in the Department of Mathematical Sciences at the University of Liverpool. I also assist with the department's IT facilities. In March and April 2009 I was on secondment to our partner university, XJTLU (Xi'an Jiaotong - Liverpool University), in Suzhou, China, teaching the second year course Introduction to the Methods of Applied Mathematics.

In the current semester at Liverpool I am giving tutorials for the first year course MATH111 (Mathematical IT Skills). I have previously taught the third year course MATH322 (Chaos Theory), the second year courses MATH283 (Field Theory and PDE's) and MATH201 (Ordinary Differential Equations), the first year course MATH122 (Dynamic Modelling), and the foundation courses MATH015 (Mathematical Applications of Computers) and MATH014 (Differential Equations and Applications to Mechanics) (the latter with special responsibility for international students). I have also previously taught the second year course MTH213 (Numerical Methods) at XJTLU in China, using Skype to deliver the lectures from Liverpool. In connection with IT, I assist with maintenance and problem-solving for the departmental hardware and software from time to time. I also assist at Open Days and Applicant Discovery Days.

I completed my PhD at Liverpool in September 2004. My project involved research on fast iterative methods for solving the linear systems of equations arising from underwater acoustics and, in particular, the interaction of an acoustic field with a submerged structure. My supervisor was Prof. Ke Chen and I was supported by EPSRC, with additional support from QinetiQ.

The linear systems that I dealt with were derived by coupling a boundary element analysis of the acoustic field and finite element analysis of the structure. Potentially fast modern iterative solvers such as the Krylov subspace methods like GMRES and CG do not converge for these systems without some sort of preconditioning. My research involved developing sophisticated sparse approximate inverse preconditioners, using a priori patterns based on the diagonal blocks of the system matrices, which proved to be very effective for this problem. The programs to produce the linear systems, generate the preconditioners, and solve the systems, which can be run on the university’s powerful parallel computing facilities, were written in Fortran, but much of my experimental work was carried out using Matlab. This is ideally suited to this work since it enables experimental programs to be written quickly and easily, while at the same time having very powerful and sophisticated features for carrying out the necessary matrix and vector calculations.

Since completing my PhD, I have investigated the parallel implementation of the programs developed during my research in more detail and have incorporated the results in a published paper. I have also worked on novel 2-sided preconditioners with Prof. Chen.

I am particularly pleased to have done my PhD research at Liverpool, and now to be working here, because, besides being an excellent university, my family originate from the Wirral, although I grew up near Bury, receiving my secondary education at Bury Grammar School.

As you might be able to tell from the photo, I was a mature PhD student (in terms of age at least!). I was previously a chartered surveyor and I obtained my undergraduate degree in maths from the Open University while running my own surveying and technical consultancy practice in Shrewsbury. I also used to write website reviews for New Scientist magazine. I did the "hippy trail" (now known as taking a gap year) in the late 1960s, including working as a surveyor in an iron ore mine near Pine Creek in the Northern Territory in Australia, which reopened in 2007 after a 33 year break as a result of rising demand from China (but has now closed again as a result of falling demand and prices!). The mine appeared in one of the last episodes of the Top Gear programme to be made for the BBC before they fell out with Jeremy Clarkson. I was fortunate enough to be able to revisit the mine on the way back from my secondment in China in 2009. If you fancy a drive through the bush at Pine Creek, click here.

During the course of my PhD research, I presented a poster and gave talks at various conferences:

1. "Fast iterative solution of coupled 3-dimensional fluid-structure interaction problems". Poster at IUTAM Symposium on Asymptotics, Singularities, and Homogenisation in Problems of Mechanics, University of Liverpool, 8-11th July 2002.

2. "Improved preconditioners for the iterative solution of coupled 3-dimensional fluid-structure interaction problems". Talk at 20th Biennial Conference on Numerical Analysis, University of Dundee, 24-27th June 2003.

3. "Effective sparse preconditioners of the two-level deflation type for fast solution of the Helmholtz equation and related problems". Talk at 4th UK Conference on Boundary Integral Methods, University of Salford, 15-16th September 2003.

I also attended a European Mathematical Society summer school at Charles University in Prague in August 2001.

In my spare time, besides studying mathematics, computing and science, I enjoy exploring old railways and their archaeology (including in Australia, given the chance). This enables me to combine my interest in railways with interests in photography and collecting maps and books. I do a lot of my exploration by cycling, which is another of my hobbies. I am a volunteer worker on the East Lancashire Railway at Bury, helping to repair and maintain diesel and steam locomotives, including rebuilding rare historic steam locomotives. I also enjoy keeping up with current affairs, watching cricket, listening to music, DIY and fixing things generally, and doing crossword puzzles.

On the way back from my secondment in China in 2009 I was able to fulfil an ambition to travel from Darwin to Adelaide on the famous Ghan train. I also saw some impressive freight trains in the Northern Territory and here is an example. This is a shortened (in all senses) version. Here is the full version if you really like trains. I also saw some equally impressive trains in China. Here is a long but slow mixed passenger/freight train and here is an express passenger train (if you listen carefully at the end you can hear the contrast between the modern smooth-running train and an old vehicle put-putting its way across the road bridge that I was standing on). Note the new 380 km/hour (240 miles/hour) Shanghai-Nanjing high-speed railway line under construction alongside the existing line. This line opened in July 2010.

I have paid a further three visits to China in connection with the courses I have been teaching using Skype and I have been able to see the new high-speed line in action. Here is some typical action, with trains on the new and old lines, near the new station serving the district in which XJTLU is situated.


Martyn D Hughes and K Chen, "Efficient parallelization of the iterative solution of a coupled fluid-structure interaction problem", Concurrency and Computation: Practice and Experience, Vol. 19, Issue 10 (2007), pp 1423 - 1445.

Martyn D Hughes, "Iterative Solution of Coupled 3-dimensional Fluid-Structure Interaction Problems", PhD Thesis, University of Liverpool, 2004.

M D Hughes and K Chen, "An efficient preconditioned iterative solver for solving a coupled fluid structure interaction problem", International Journal of Computer Mathematics, Vol. 81, No. 5 (2004), pp. 583-594.

K Chen, S C Hawkins and M D Hughes, "Effective sparse preconditioners of the two-level deflation type for fast solution of the Helmholtz equation and related problems", in 4th UK Conference on Boundary Integral Methods, S Amini (Ed.), September 2003, University of Salford, pp. 147-156.

M D Hughes and K Chen, "Fast iterative solution of coupled 3-dimensional fluid-structure interaction problems", in Proceedings of IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, A B Movchan (Ed.), July 2002, University of Liverpool, pp. 595-604.

Contact information


Office: 0151 794 4047
Mobile: 07973247965



Postal address

Dr. Martyn D Hughes
Department of Mathematical Sciences
University of Liverpool
L69 7ZL

Last modified 22/09/2019