Dr. Paul Harris.

I have worked at the University of Brighton since 1992. My main interests are in applied mathematics and the use of numerical methods for solving practical problems which arise in science and engineering. I am the leader of the finite element and boundary element research group which forms part of the Computational Maths group.

My teaching interests are towards applied and/or methods type courses. Modules that I have taught over the last few years include Mathematics for the first year B.Eng. Mechanical Engineering, Mathematics for Sports Science first year, a module on the calculus of functions of several variables and a module on the finite elements method.

Research projects that I am currently involved with include the mathematical modelling of the motion of the gas bubbles which results from an underwater explosion bubble, and studying the diffusion which occurs in gels used in radiation dose experiments. Some of this work has been carried out in collaboration with The Defence Evaluation and Research Agency, The University of Birmingham, The University of Wollongong, The National University of Singapore, The Royal Sussex County Hospital, Queensland University of Technology and The Princess Royal Hospital, Haywards Heath.

Research Interests.

Frequency Domain Acoustics.          In collaboration with Prof. Ke. Chen at the University of Liverpool.
Time Domain Acoustics.                   In collaboration with Dr. Gary Geaves at B&W Group Ltd.
Causes Of Syringomyelia.                In collaboration with C. Hardwidge at The Princess Royal Hospital, Haywards Heath.

See the COMPUTATIONAL MATHEMATICS group’s page for further details.

Potential Ph.D. Projects

High Frequency Acoustics                Developing special boundary integral methods for dealing with the rapidly oscillating solutions which can occur.
Time Domain Acoustics                    Developing the integral convolution method and comparing it to conventional retarded potential methods.
Syringomyelia                                    Developing a finite element model of the growth of the voids in the spinal cord.


Recent Publications

Efficient preconditioners for iterative solution of the boundary element equations of the three-dimensional Helmholtz equation.

J. Appl. Numer. Math., 36, pp 475-489, (2001).

(With K. Chen).

On preconditioned iterative solution of the coupled block linear system arising from the three-dimensional fluid-structure interation problem.

Proceedings of the Third UK Conference on Boundary Integral Methods, Ed. P. J. Harris, pp 139-148, (2001).

(With K. Chen).

Boundary integral method applied to the bubble structure interaction problem.

Proceedings of the Third UK Conference on Boundary Integral Methods, Ed. P. J. Harris, pp 23-26, (2001).

(With A Salhan and R. Chakrabarti).

On efficient preconditioners for iterative solution of a Galerkin boundary element equation for the three dimensional exterior Helmholtz problem.

The Journal of Computational and Applied Mathematics, 156, pp. 303-318, (2003).

(With K. Chen)

Modelling transient acoustic radiation using the retarded potential integral equation method.

Proc. Fourth UK Conference on Boundary Integral Methods (ed. S. Amini), University of Salford. pp 57-66. (2003).

(With H. Wang, R. Chakrabarti and D. Henwood).

An investigation into the use of the boundary integral method to model the motion of a single gas or vapour bubble in a liquid.

Proc. Fourth UK Conference on Boundary Integral Methods (ed. S. Amini), University of Salford. pp 37-46. (2003).

Easily inverted approximation type preconditioners for matrices arising from wavelet discretisations of boundary integral equations.

Proc. Fourth UK Conference on Boundary Integral Methods (ed. S. Amini), University of Salford. pp 165-174. (2003).

(With K. Chen and S. Hawkins).

A discontinuous linear boundary element method for solving the three-dimensional exterior Helmholtz problem.

Proc. Fourth UK Conference on Boundary Integral Methods (ed. S. Amini), University of Salford. pp 57-66. (2003).

(With K. Chen).

An investigation into the use of the boundary integral method to model the motion of a single gas or vapour bubble in a liquid.

Engineering Analysis with Boundary Elements, 28, Issue 4, Pages 325-332, 2004.

A method for modelling non-harmonic periodic acoustic radiation from a loudspeaker.

Proceedings of Integral Methods in Science and Engineering 2002, Ed. C. Constanda, Birkhauser, Boston. (2004).

(With R. Chakrabarti, D. Henwood and H. Wang).

An investigation into the effects of heat transfer on the motion of a spherical bubble.

ANZAM J 45, pp361-371 (2004).

(With W. K. Soh and H. Al-Awadi).

A Weakly Singular  Boundary Integral Formulation of the External Helmholtz Problem Valid For All Wavenumbers.

Proceedings of Integral Methods in Science and Engineering 2004, ed. C. Constanda, Birkhauser, Boston. (2005).

(With K. Chen and J. Cheng).

Stability analysis of the collocation method for the retarded potential integral equation.

J. of Computational Acoustics, Vol 13, Part 2, pp 287 – 299, (2005).

(With H. Wang, R. Chakrabarti and D. Henwood).

Some Results on  Modelling High Frequency Acoustic Radiation.

Proc. Fifth UK Conference on Boundary Integral Methods (ed. K. Chen), University of Liverpool. (2005).

(With K. Chen).

On The Significance of Fluid-Structure Coupling for Non-Harmonic Periodic Acoustic Radiation.

Proc. Fifth UK Conference on Boundary Integral Methods (ed. K. Chen), University of Liverpool. (2005).

(With D. Chappell, D. Henwood and R. Chakrabati).

An operator splitting preconditioner for matrices arising from a wavelet boundary element method for the Helmholtz equation.

Int. J. of Wavelets, Multiresolution and Information Processing, Vol. 3, No. 4,  pp 601-620, (2005).

(With S. C.Hawkins and K. Chen).

On Methods For Modelling Non-Harmonic Sound Fields Radiated By A Loudspeaker.

Submitted to Int. J. Numer. Meth. Engng.

(With H. Wang, R. Chakrabarti, D. Henwood and G. Geaves).

An efficient weakly singular formulation of the Helmholtz boundary integral equation valid for all real and positive wavenumbers.

Submitted to IMA J. App. Math.

(With K. Chen and J. Cheng)

Other Mathematical Interests

I am currently Treasurer of the Mathematical Association, a charitable organisation dedicated to promoting better teaching and
learning in mathematics. Their web-site can be found by following this link: Mathematical Association.


Railways

Below are some of my railway movies. These files are large and may take a long time to download.

Paddington (9.27Mb)
Exeter St. Davids (10.80Mb)
Norwich (4.78Mb)
Wymondham (6.03Mb)
Sheffield Park (13.5Mb)
Glasgow Central 1 (10.2Mb)
Glasgow Central 2 (9.0 Mb)
Fort William (23.1 Mb)

Disclaimer

This page is maintained by Dr. Harris. Pages of individuals do not necessarily reflect the official position of the University.