Brief History,
Research interests,
Teaching,
Administration,
Other Activities,
Publications.
William McLean
Associate Professor
 Office:
 Room 2085, Red Centre
 Phone:
 +61 2 9385 7045
 Fax:
 +61 2 9385 7123
BSc (Hons), University of Queensland, 1982;
PhD, Australian National University, 1986;
Assistant Professor, Oregon State University, 19856;
QEII Research Fellow, University of Tasmania, 19878;
UNSW since 1989.
 Partial Differential Equations
 Numerical Analysis
 Integral Equations
More details at my
Google Scholar Profile.
My timetable is available here.
 Session 1:
 Math5295 (weeks 16)
 Math2111 (weeks 712)
 Session 2
 Math2221 Higher theory and applications of differential equations
(lecture slides)
 Shev MacNamara, Bruce Henry and William McLean,
Fractional Euler
limits and their applications
SIAM J. Appl. Math. 77: 447469, 2017.
 Kim Ngan Le, William McLean and Bishnu Lamichhane
Finite element approximation
of a timefractional diffusion problem in a nonconvex polygonal
domain
arXiv:1602.00040, 2016;
SupplementaryMaterials.tgz (146KiB).
 Kim Ngan Le, William McLean and Kassem Mustapha,
Numerical solution of the
timefractional FokkerPlanck equation with general forcing
SIAM J. Numer. Anal. 54: 17631784, 2016;
Supplementary_Materials.tgz (177KiB).

William McLean and Kassem Mustapha,
Timestepping error bounds for fractional diffusion problems with
nonsmooth initial data,
J. Comp. Phys. 293: 201217, 2015.

Quoc Thong Le Gia and William McLean,
Solving the heat equation on the unit sphere via Laplace transforms
and radial basis functions,
Adv. Comput. Math. 40: 353375, 2014.

Kai Wang, William McLean and Henner Kempwerth,
Transient photoluminescence from
silicon wafers: Finite element analysis,
J. Appl. Phys. 114, 163105, 2013.

Kassem Mustapha and William McLean,
Superconvergence of a
discontinuous Galerkin method for fractional diffusion and wave equations,
SIAM J. Numer. Anal. 51: 516525, 2013.

William McLean,
Fast summation
by interval clustering for an evolution equation with memory,
SIAM J. Sci. Comput. 34: A3039A3056, 2012.

Kassem Mustapha and William McLean,
Uniform convergence
for a discontinuous Galerkin, timestepping method applied to a
fractional diffusion equation, IMA J. Numer. Anal. 32: 906925,
2012.

William McLean and Vidar Thomee,
Iterative methods for shifted positive definite linear systems and time
discretization of the heat equation,
ANZIAM J. 53: 134155, 2011.

Quoc Thong Le Gia and William McLean,
Numerical solution of a parabolic equation on the sphere using Laplace
transforms and radial basis functions,
ANZIAM J. 52: C89C102, 2011.

William McLean,
Regularity of solutions to a timefractional diffusion equation,
ANZIAM J. 52: 123138, 2010.

William McLean and Vidar Thomee, Numerical solution via Laplace transforms of a fractional
order evolution equation,
J. Integral Equations Appl 22: 5794, 2010.

William McLean and Kassem Mustapha, Convergence analysis
of a discontinuous Galerkin method for a subdiffusion equation,
Numer. Algorithms 52:6988, 2009.

Kassem Mustapha and William McLean,
Discontinuous Galerkin method for an evolution equation with a memory term
of positive type
Math. Comp. 78: 19751995, 2009.

William McLean and Kassem Mustapha, A secondorder
accurate numerical method for a fractional wave equation,
Numer. Math. 105:481510, 2007.

Ivan Graham and William McLean,
Anisotropic mesh refinement: the conditioning of Galerkin boundary element
matrices and simple preconditioners,
SIAM J. Numer. Anal. 44: 14871513, 2006.

William McLean, Ian H. Sloan and Vidar Thomee,
Time discretization via Laplace transformation of an integrodifferential
equation of parabolic type,
Numer. Math. 102: 497522, 2006.

Youngmok Jeon and William McLean, A new boundary
element method for the biharmonic equation with Dirichlet boundary
conditions, Adv. Comput. Math. 102: 497522, 2003.

Mark Ainsworth and William McLean,
Multilevel diagonal scaling preconditioners for boundary element equations
on locally refined meshes,
Numer. Math. 93:387413, 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: 271286, 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: 19011932, 1999.

W. McLean and S. Proessdorf,
Boundary element collocation methods using splines with multiple knots,
Numer. Math. 74: 419451, 1996.
 W. McLean and I. H. Sloan, A fully discrete and
symmetric boundary element method,
IMA J. Numer. Anal. 14: 311345, 1994.

William McLean, Numerical evaluation of some trigonometric series,
Math. Comp. 63: 271275, 1994.

W. McLean, S. Proessdorf and W. L. Wendland, A fullydiscrete trigonometric collocation method,
J. Integral Equations Appl. 5: 103129, 1993.

W. McLean and V. Thomee, Numerical solution of an evolution equation with a positivetype
memory term,
J. Austral. Math. Soc Ser. B 35: 2370, 1993.

Martin Costabel and William McLean, Spline
collocation for strongly elliptic equations on the torus,
Numer. Math. 62: 511538, 1992.

William McLean, Local and global descriptions
of periodic pseudodifferential equations,
Math. Nachr. 150: 151161, 1991.

W. McLean,
Asymptotic error expansions for numerical solutions of integral equations,
IMA J. Nuerm. Anal. 9: 373384, 1989.

William McLean, Solutions in Hölder spaces of singular
integral equations on Lipschitz contours", Technical Report No.~266, Department of
Mathematics, University of Tasmania, 1988.

W. McLean and D. Elliott, On the pnorm of the truncated Hilbert trasform,
Bull. Austral. Math. Soc. 38: 413420, 1988.

W. McLean, A spectral Galerkin method for a boundary integral equation,
Math. Comp. 47: 597607, 1986.
 Subdiffusion in a nonconvex polygon,
Monash Workshop on Numerical PDEs, February 2016, and
MAFELAP, June 2016, Brunel University.
 Numerical solution of fractional PDEs,
(1.8MB) 10 lectures at the Beijing Computational Mathematics Research Center,
November 2015.
 A simple finite element code written in Julia,
Australia and New Zealand Mathematics Convention 2014, University of Melbourne,
812 December, 2014.
 Error bounds for time stepping fractional
diffusion problems with nonsmooth initial data, Department of Mathematics and Statistics,
University of Otago, Dunedin, 6 May, 2014.
 Julia: a programming language for
scientific computing, Computational Maths Seminar, UNSW, 19 November,
2013. (Code examples)
 Discontinuous Galerkin timestepping and
fast summation for fractional diffusion and wave equations,
International Symposium on Fractional PDEs, Newport, 35 June, 2013.
 Fast summation for an evolution equation
with memory, SCPDE11, Hong Kong, 59 December, 2011.
 Iterative methods for positive definite linear
systems with a complex shift, Workshop on Laplace transform methods and
their applications, NIMS, Daejeon, Korea, 15 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, 1316 July, 2008).
 A secondorder accurate scheme for a
fractional wave equations (NA07, 22nd Biennial Conference on
Numerical Analysis, University of Dundee, Scotland, 2629 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 fractionalorder partial
differential equations
(International
Symposium on Fractional Calculus, Dunedin, 913 January, 2006)
 Conditioning of Boundary Element Equations
(Symposium in
honour of Mike Osborne, ANU, Canberra, 2123 September, 2005)
 Lectures on Boundary Integral Equations
(Boundary Integral
Methods and Applications, Reading, 1418 September, 2004)
 Quadrature for Boundary Element Methods.

fosc.m is a Matlab GUI illustrating forced oscillations.

sake0.3.tgz is a Fortran 95 library that
generates specialpurpose, 4D quadrature rules used in
boundary element computations for integral equations on surfaces.

gaussquad2.5.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.)

libnpy0.5.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.

blocktstsolver0.1.tgz provides an FFT based solver
for block tridiagonal symmetric Toeplitz matrices.
Return to
Numerical analysis research group ,
School of Mathematics,
UNSW.