William McLean

Senior Lecturer

Office:

Room 2085, Red Centre

Phone:

+61 2 9385 7045

Fax:

+61 2 9385 7123

Brief History

Research Interests

• Partial Differential Equations
• Numerical Analysis
• Integral Equations

Teaching for 2012

• AMSI Course: conjugate gradients.
  • lecture slides
  • exercises
  • example programs
• Math3101/Math5305 Computational Mathematics
  • Course handout
  • Lecture slides
  • Programs from lectures
  • Example library
  • Lab questions
  • Tutorial problems
• Math5175 Finite Element Methods
  • fem.pdf
  • problems.pdf

Administration

• Associate Editor, Journal of Integral Equations and Applications
• Manager of the Student Record System.

Selected Publications

• William McLean, Fast summation by interval clustering for an evolution equation with memory, Preprint, 2012.
• William McLean and Vidar Thomee, Iterative methods for shifted positive definite linear systems and time discretization of the heat equation, Preprint, 2011.
• William McLean, Regularity of solutions to a time-fractional diffusion equation, ANZIAM J. 52: 123-138, 2010.
• William McLean and Vidar Thomee, Numerical solution via Laplace transforms of a fractional order evolution equation, J. Integral Equations Appl 22: 57-94, 2010.
• William McLean and Kassem Mustapha, Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation, Numer. Algorithms 52:69-88, 2009.
• Kassem Mustapha and William McLean, Discontinuous Galerkin method for an evolution equation with a memory term of positive type Math. Comp. 78: 1975-1995, 2009.
• William McLean and Kassem Mustapha, A second-order accurate numerical method for a fractional wave equation, Numer. Math. 105:481-510, 2007.
• Ivan Graham and William McLean, Anisotropic mesh refinement: the conditioning of Galerkin boundary element matrices and simple preconditioners, SIAM J. Numer. Anal. 44: 1487-1513, 2006.
• 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.
• Youngmok Jeon and William McLean, A new boundary element method for the biharmonic equation with Dirichlet boundary conditions, Adv. Comput. Math. 102: 497-522, 2003.
• Mark Ainsworth and William McLean, Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes, Numer. Math. 93:387-413, 2003.
• William McLean, Strongly Elliptic Systems and Boundary Integral Equations Cambridge University Press, 2000. (errata file)
• W. McLean and O. Steinback, Boundary element preconditioners for a hypersingular integral equation on an interval", Adv. Comput. Math. 11: 271-286, 1999.
• Mark Ainsworth, William McLean and Thanh Tran, The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling, SIAM J. Numer. Anal. 36: 1901-1932, 1999.
• W. McLean and S. Proessdorf, Boundary element collocation methods using splines with multiple knots, Numer. Math. 74: 419-451, 1996.
• W. McLean and I. H. Sloan, A fully discrete and symmetric boundary element method, IMA J. Numer. Anal. 14: 311-345, 1994.
• William McLean, Numerical evaluation of some trigonometric series, Math. Comp. 63: 271-275, 1994.
• W. McLean, S. Proessdorf and W. L. Wendland, A fully-discrete trigonometric collocation method, J. Integral Equations Appl. 5: 103-129, 1993.
• W. McLean and V. Thomee, Numerical solution of an evolution equation with a positive-type memory term, J. Austral. Math. Soc Ser. B 35: 23-70, 1993.
• Martin Costabel and William McLean, Spline collocation for strongly elliptic equations on the torus, Numer. Math. 62: 511-538, 1992.
• William McLean, Local and global descriptions of periodic pseudodifferential equations, Math. Nachr. 150: 151-161, 1991.
• W. McLean, Asymptotic error expansions for numerical solutions of integral equations, IMA J. Nuerm. Anal. 9: 373-384, 1989.
• W. McLean and D. Elliott, On the p-norm of the truncated Hilbert trasform, Bull. Austral. Math. Soc. 38: 413-420, 1988.
• W. McLean, A spectral Galerkin method for a boundary integral equation, Math. Comp. 47: 597-607, 1986.

Seminar Presentations and other Talks

• Fast summation for an evolution equation with memory, SCPDE11, Hong Kong, 5-9 December, 2011.
• Iterative methods for positive definite linear systems with a complex shift, Workshop on Laplace transform methods and their applications, NIMS, Daejeon, Korea, 1-5 November, 2011.
• Discontinuous Galerkin methods for fractional diffusion problems, Max Planck Institute fur Mathematik in den Naturwissenschaften, Leipzig, 07/10/2010.
• 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-0.5.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.
• blocktstsolver-0.1.tgz provides an FFT based solver for block tridiagonal symmetric Toeplitz matrices.