William McLean

Senior Lecturer

Office:

Room 2085, Red Centre

Phone:

+61 2 9385 7045

Fax:

+61 2 9385 7123

Email:

w.mclean@unsw.edu.au

Mail:

School of Mathematics
The University of New South Wales
Sydney 2052, Australia

Brief History

Research Interests

• Partial Differential Equations
• Numerical Analysis
• Integral Equations

Teaching for 2008

• Math1151/1251 Computing component week 0 talk
• Math3101/Math5305 Computational Mathematics
• Math3311/Math5335 Mathematical Computing for Finance

Administration

• Associate Editor, Journal of Integral Equations and Applications
• Member of Computing Committee and Academic Committee.

Selected Publications

• William McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, 2000. (errata file)
• Mark Ainsworth and William McLean, Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes, Numer. Math. (2003) 93:387--413.
• William McLean and Vidar Thomee, Time discretization of an evolution equation via Laplace transforms, IMA J. Numer. Anal. 24:439-463, 2004.
• William McLean, Ian H. Sloan and Vidar Thomee, Time discretization via Laplace transformation of an integro-differential equation of parabolic type, Numer. Math. 102: 497-522, 2006.

Seminar Presentations and other Talks

• A second-order accurate scheme for a fractional wave equations (NA07, 22nd Biennial Conference on Numerical Analysis, University of Dundee, Scotland, 26-29 June, 2007).
• Python for scientific computing with example programs in pyscicomp_progs.tgz. (Talk for masters students, Dept. of Mathematical Sciences, University of Bath, 21 March, 2007.)
• Numerical solution of a fractional diffusion equation (Numerical analysis seminar, Dept. of Mathematical Sciences, University of Bath, 2 February, 2007.)
• Numerical methods for some fractional-order partial differential equations (International Symposium on Fractional Calculus, Dunedin, 9-13 January, 2006)
• Conditioning of Boundary Element Equations (Symposium in honour of Mike Osborne, ANU, Canberra, 21-23 September, 2005)
• Lectures on Boundary Integral Equations (Boundary Integral Methods and Applications, Reading, 14-18 September, 2004)
• Quadrature for Boundary Element Methods.

Software

• fosc.m is a Matlab GUI illustrating forced oscillations.
• sake-0.3.tgz is a Fortran 95 library that generates special-purpose, 4D quadrature rules used in boundary element computations for integral equations on surfaces.
• gaussquad-2.4.tgz provides a Fortran 95 module that generates all of the classical Gauss quadrature rules, including the Radau and Lobatto variants. The package includes test programs and bindings for C and Python. (The latter require a fortran compiler, such as g95, that supports a few of the interoperability features in the f2003 standard.)