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 2009

• 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
• Chair of Computing 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.
• William McLean and Kassem Mustapha, A second-order accurate numerical method for a fractional wave equation, Numer. Math. 105:481-510, 2007.
• William McLean and Kassem Mustapha, Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equations, Numer Algor 52:69-88, 2009. (DOI 10.1007/s11075-008-9258-8)

Seminar Presentations and other Talks

• Numerical Solution of a Fractional Diffusion Equation via Laplace Transformation (PRIMA Congress, Sydney, 10/07/2009).
• Numerical Solution of Fractional Diffusion Equations (Conference to Celebrate Bob Anderssen's 70th Birthday, ANU, 23/01/2009).
• The Conjugate Gradient Algorithm (16/09/2008) and its convergence theory (23/09/2008), expository talks for the Computational Maths Seminar.
• Discontinuous Galerkin method for a nonlocal evolution equation ( Computation Techniques and Applications 2008, Canberra, 13-16 July, 2008).
• 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.)
• libnpy-0.3.tgz is a small library for writing a C or Fortran array to a data file, using the NumPy binary format. A Python script can easily load such a .npy file to create a NumPy array.