Associate Professor William McLean

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RESEARCH INTERESTS

Computational mathematics;
integral equations;
nonlocal evolution equations

ADMINISTRATIVE DUTIES

School Records System Manager and Chair of the Computing Committee, Maths & Stats.

EXTERNAL

Editorial Board of SIAM Journal on Numerical Analysis and the Journal of Integral Equations and Applications.

Phone

9385 7045

E-mail

w.mclean@unsw.edu.au

Location

The School of Mathematics and Statistics University of New South Wales SYDNEY NSW 2052 The Red Centre Room 2085

Books | 2000

Mclean W, 2000, Strongly elliptic systems and boundary integral equations, Original, Cambridge University Press, UK
Book Chapters | 2019

McLean W, 2019, 'Wider Contours and Adaptive Contours', in 2017 MATRIX Annals, pp. 79 - 98, http://dx.doi.org/10.1007/978-3-030-04161-8_7

Book Chapters | 2018

McLean W, 2018, 'Exponential sum approximations for t−β', in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, Springer, pp. 911 - 930, http://dx.doi.org/10.1007/978-3-319-72456-0_40

Book Chapters | 1989

McLean W; Wendland WL, 1989, 'Trigonometric Approximation of Solutions of Periodic Pseudodifferential Equations', in The Gohberg Anniversary Collection, Birkhäuser Basel, pp. 359 - 383, http://dx.doi.org/10.1007/978-3-0348-9278-0_20

Book Chapters | 1989

McLean W; Wendland WL, 1989, 'Trigonometric Approximation of Solutions of Periodic Pseudodifferential Equations', in The Gohberg Anniversary Collection, Birkhäuser Basel, pp. 851 - 875, http://dx.doi.org/10.1007/978-3-0348-9144-8_37
Journal articles | 2024

Mustapha K; McLean W; Dick J, 2024, 'An α-Robust and Second-Order Accurate Scheme for a Subdiffusion Equation', Journal of Scientific Computing, 99, http://dx.doi.org/10.1007/s10915-024-02554-w

Journal articles | 2023

McLean W; Mustapha K, 2023, 'Error profile for discontinuous Galerkin time stepping of parabolic PDEs', Numerical Algorithms, 93, pp. 157 - 177, http://dx.doi.org/10.1007/s11075-022-01410-y

Journal articles | 2022

McLean W; Mustapha K, 2022, 'Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation', Numerical Algorithms, 89, pp. 1441 - 1463, http://dx.doi.org/10.1007/s11075-021-01160-3

Journal articles | 2021

Banz L; Ilyas M; Lamichhane BP; McLean W; Stephan EP, 2021, 'A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart–Thomas elements', Numerical Methods for Partial Differential Equations, 37, pp. 2429 - 2445, http://dx.doi.org/10.1002/num.22722

Journal articles | 2021

Liao HL; McLean W; Zhang J, 2021, 'A second-order scheme with nonuniform time steps for a linear reaction-subdiffusion problem', Communications in Computational Physics, 30, pp. 567 - 601, http://dx.doi.org/10.4208/CICP.OA-2020-0124

Journal articles | 2021

McLean W; Mustapha K; Ali R; Knio OM, 2021, 'Erratum to “Regularity theory for time-fractional advection-diffusion-reaction equations” [Comput. Math. Appl. 79 (2020) 947–961] (Computers and Mathematics with Applications (2020) 79(4) (947–961), (S0898122119304055), (10.1016/j.camwa.2019.08.008))', Computers and Mathematics with Applications, 85, pp. 82 - 83, http://dx.doi.org/10.1016/j.camwa.2021.01.008

Journal articles | 2021

McLean W, 2021, 'Numerical evaluation of Mittag-Leffler functions', Calcolo, 58, pp. 7, http://dx.doi.org/10.1007/s10092-021-00398-6

Journal articles | 2020

McLean W; Mustapha K; Ali R; Knio OM, 2020, 'Regularity theory for time-fractional advection–diffusion–reaction equations', Computers and Mathematics with Applications, 79, pp. 947 - 961, http://dx.doi.org/10.1016/j.camwa.2019.08.008

Journal articles | 2020

McLean W, 2020, 'IMPLEMENTATION of HIGH-ORDER, DISCONTINUOUS GALERKIN TIME STEPPING for FRACTIONAL DIFFUSION PROBLEMS', ANZIAM Journal, 62, pp. 121 - 147, http://dx.doi.org/10.1017/S1446181120000152

Journal articles | 2019

Le KN; McLean W; Stynes M, 2019, 'Existence, uniqueness and regularity of the solution of the time-fractional Fokker–Planck equation with general forcing', Communications on Pure and Applied Analysis, 18, pp. 2765 - 2787, http://dx.doi.org/10.3934/cpaa.2019124

Journal articles | 2019

Liao HL; McLean W; Zhang J, 2019, 'A discrete Grönwall inequality with applications to numerical schemes for subdiffusion problems', SIAM Journal on Numerical Analysis, 57, pp. 218 - 237, http://dx.doi.org/10.1137/16M1175742

Journal articles | 2019

McLean W; Mustapha K; Ali R; Knio O, 2019, 'Well-posedness of time-fractional advection-diffusion-reaction equations', Fractional Calculus and Applied Analysis, 22, pp. 918 - 944, http://dx.doi.org/10.1515/fca-2019-0050

Journal articles | 2018

Le KN; Mclean W; Mustapha K, 2018, 'A semidiscrete finite element approximation of a time-fractional Fokker Planck equation with nonsmooth initial data', SIAM Journal on Scientific Computing, 40, pp. A3831 - A3852, http://dx.doi.org/10.1137/17M1125261

Journal articles | 2017

Le KN; McLean W; Lamichhane B, 2017, 'FINITE ELEMENT APPROXIMATION of A TIME-FRACTIONAL DIFFUSION PROBLEM for A DOMAIN with A RE-ENTRANT CORNER', ANZIAM Journal, 59, pp. 61 - 82, http://dx.doi.org/10.1017/S1446181116000365

Journal articles | 2017

Le KN; McLean W; Lamichhane B, 2017, 'Finite element approximation of a time-fractional diffusion problem for a domain with a re-entrant corner', ANZIAM Journal, 59, pp. 61 - 61, http://dx.doi.org/10.21914/anziamj.v59i0.10940

Journal articles | 2017

Macnamara S; Henry B; McLean W, 2017, 'Fractional euler limits and their applications', SIAM Journal on Applied Mathematics, 77, pp. 447 - 469, http://dx.doi.org/10.1137/16M1091861

Journal articles | 2016

Le KN; McLean W; Mustapha K, 2016, 'Numerical solution of the time-fractional Fokker-Planck equation with general forcing', SIAM Journal on Numerical Analysis, 54, pp. 1763 - 1784, http://dx.doi.org/10.1137/15M1031734

Journal articles | 2015

McLean W; Mustapha K, 2015, 'Time-stepping error bounds for fractional diffusion problems with non-smooth initial data', Journal of Computational Physics, 293, pp. 201 - 217, http://dx.doi.org/10.1016/j.jcp.2014.08.050

Journal articles | 2014

Le Gia QT; McLean W, 2014, 'Solving the heat equation on the unit sphere via Laplace transforms and radial basis functions', Advances in Computational Mathematics, 40, pp. 353 - 375, http://dx.doi.org/10.1007/s10444-013-9311-6

Journal articles | 2013

Kim IS; McLean W, 2013, 'Computing the hausdorff distance between two sets of parametric curves', Communications of the Korean Mathematical Society, 28, pp. 833 - 850, http://dx.doi.org/10.4134/CKMS.2013.28.4.833

Journal articles | 2013

Mustapha K; Mclean W, 2013, 'Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations', SIAM Journal on Numerical Analysis, 51, pp. 491 - 515, http://dx.doi.org/10.1137/120880719

Journal articles | 2013

Wang K; McLean W; Kampwerth H; Wang K, 2013, 'Transient photoluminescence from silicon wafers: Finite element analysis', JOURNAL OF APPLIED PHYSICS, 114, http://dx.doi.org/10.1063/1.4826896

Journal articles | 2012

McLean W; Thomee V, 2012, 'Iterative solution of shifted positive-definite linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature', ANZIAM Journal, 53, pp. 134 - 134, http://dx.doi.org/10.21914/anziamj.v53i0.5248

Journal articles | 2012

Mclean W; Thomee V, 2012, 'Iterative solution of shifted positive-definitive linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature', ANZIAM Journal, 53, pp. 134 - 155, http://dx.doi.org/10.1017/S1446181112000107

Journal articles | 2012

Mclean W, 2012, 'Fast summation by interval clustering for an evolution equation with memory', SIAM Journal on Scientific Computing, 34, pp. A3039 - A3056, http://dx.doi.org/10.1137/120870505

Journal articles | 2012

Mustapha K; Mclean W, 2012, 'Uniform convergence for a discontinuous Galerkin, time-stepping method applied to a fractional diffusion equation', IMA Journal of Numerical Analysis, 32, pp. 906 - 925, http://dx.doi.org/10.1093/imanum/drr027

Journal articles | 2011

Le Gia QT; Mclean W, 2011, 'Numerical solution of a parabolic equation on the sphere using Laplace transforms and radial basis functions', ANZIAM Journal, pp. C89 - C102

Journal articles | 2011

McLean W, 2011, 'Regularity of solutions to a time-fractional diffusion equation', ANZIAM Journal, 52, pp. 123 - 138, http://dx.doi.org/10.1017/S1446181111000617

Journal articles | 2011

Mclean W; Mustapha K, 2011, 'Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation', Numerical Algorithms, 56, pp. 159 - 184, http://dx.doi.org/10.1007/s11075-010-9379-8

Journal articles | 2010

Mclean W; Thomee V, 2010, 'Maximum-norm error analysis of a numerical solution via Laplace transformation and quadrature of a fractional-order evolution equation', IMA Journal of Numerical Analysis, 30, pp. 208 - 230, http://dx.doi.org/10.1093/imanum/drp004

Journal articles | 2010

Mclean W; Thomee V, 2010, 'Numerical solution via Laplace transforms of a fractional order evolution equation', Journal of Integral Equations and Applications, 22, pp. 57 - 94, http://dx.doi.org/10.1216/JIE-2010-22-1-57

Journal articles | 2009

Mustapha K; Mclean W, 2009, 'Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation', Numerical Algorithms, 52, pp. 69 - 88

Journal articles | 2009

Mustapha KA; Mclean W, 2009, 'Discontinuous galerkin method for an evolution equation with a memory term of positive type', Mathematics of Computation, 78, pp. 1975 - 1995

Journal articles | 2007

Mclean W; Mustapha K, 2007, 'A second-order accurate numerical method for a fractional wave equation', Numerische Mathematik, 105, pp. 481 - 510

Journal articles | 2006

Graham IG; Mclean W, 2006, 'Anisotropic mesh refinement: the conditioning of Galerkin boundary element matrices and simple preconditioners', SIAM Journal on Numerical Analysis, 44, pp. 1487 - 1513

Journal articles | 2005

Mclean W; Sloan IH; Thomee V, 2005, 'Time discretization via Laplace transformation of an integro-differential equation of an integro-differential equation of parabolic type', Numerische Mathematik, 102, pp. 497 - 522

Journal articles | 2004

Mclean W; Thomee V, 2004, 'Time discretization of an evolution equation via Laplace transforms', IMA Journal of Numerical Analysis, 24, pp. 439 - 463

Journal articles | 2003

Ainsworth M; Mclean W, 2003, 'Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes', Numerische Mathematik, 93, pp. 387 - 413

Journal articles | 2003

Jeon Y; Mclean W, 2003, 'A new boundary element method for the biharmonic equation with Dirichlet boundary conditions', Advances in Computational Mathematics, 19, pp. 339 - 365

Journal articles | 2000

Ainsworth M; Mclean W; Tran T, 2000, 'Diagonal scaling of stiffness matrices in the Galerkin boundary element method', Journal of Australian Mathematical Society B, pp. 141 - 150

Journal articles | 1999

Ainsworth M; Mclean W; Tran T, 1999, 'The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling', SIAM Journal on Numerical Analysis, pp. 1901 - 1932

Journal articles | 1999

Mclean W; Steinbach O, 1999, 'Boundary element preconditioners for a hypersingular integral equation on an interval', Advances in Computational Mathematics, 11, pp. 271 - 286

Journal articles | 1997

Mclean W; Thomee V, 1997, 'Asymptotic behaviour of numerical solutions of an evolution equation with memory', Asymptotic Analysis, 14, pp. 257 - 276

Journal articles | 1997

Mclean W; Tran T, 1997, 'A preconditioning strategy of boundary element Galerkin methods', Numerical Methods for Partial Differential Equations, 13, pp. 283 - 301

Journal articles | 1996

Mclean W; Prossdorf S, 1996, 'Boundary element collocation methods using splines with multiple knots', Numerische Mathematik, pp. 419 - 451

Journal articles | 1996

Mclean W; Thomee V; Wahlbin LB, 1996, 'Discretization with variable time steps of an evoloution equation with a positive type memory term', Journal of Computational and Applied Mathematics, pp. 49 - 69

Journal articles | 1994

MCLEAN W, 1994, 'NUMERICAL EVALUATION OF SOME TRIGONOMETRIC SERIES', MATHEMATICS OF COMPUTATION, 63, pp. 271 - 275, http://dx.doi.org/10.2307/2153573

Journal articles | 1994

McLEAN W, 1994, 'Numerical evaluation of some trigonometric series', Mathematics of Computation, 63, pp. 271 - 274, http://dx.doi.org/10.1090/S0025-5718-1994-1240661-6

Journal articles | 1994

McLean W, 1994, 'Fully-discrete collocation methods for an integral equation of the first kind', Journal of Integral Equations and Applications, 6, pp. 537 - 571, http://dx.doi.org/10.1216/jiea/1181075835

Journal articles | 1994

Mclean W; Sloan IH, 1994, 'A fully discrete and symmetric boundary element method', IMA Journal of Numerical Analysis, 14, pp. 311 - 345, http://dx.doi.org/10.1093/imanum/14.3.311

Journal articles | 1993

MCLEAN W; THOMEE V, 1993, 'NUMERICAL-SOLUTION OF AN EVOLUTION EQUATION WITH A POSITIVE-TYPE MEMORY TERM', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 35, pp. 23 - 70, http://dx.doi.org/10.1017/S0334270000007268

Journal articles | 1993

McLean W; Prössdorf S; Wendland WL, 1993, 'A fully-discrete trigonometric collocation method', Journal of Integral Equations and Applications, 5, pp. 103 - 129, http://dx.doi.org/10.1216/jiea/1181075730

Journal articles | 1992

Costabel M; McLean W, 1992, 'Spline collocation for strongly elliptic equations on the torus', Numerische Mathematik, 62, pp. 511 - 538, http://dx.doi.org/10.1007/BF01396241

Journal articles | 1991

McLean W, 1991, 'Local and Global Descriptions of Periodic Pseudodifferential Operators', Mathematische Nachrichten, 150, pp. 151 - 161, http://dx.doi.org/10.1002/mana.19911500112

Journal articles | 1990

MCLEAN W, 1990, 'AN INTEGRAL-EQUATION METHOD FOR A PROBLEM WITH MIXED BOUNDARY-CONDITIONS', SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 21, pp. 917 - 934, http://dx.doi.org/10.1137/0521051

Journal articles | 1989

McLean W; Prößdorf SB; Wendland WL, 1989, 'Pointwise error estimates for the trigonometric collocation method applied to singular integral equations and periodic Pseudodifferential equations', Journal of Integral Equations and Applications, 2, pp. 125 - 146, http://dx.doi.org/10.1216/JIE-1989-2-1-125

Journal articles | 1989

Mclean W, 1989, 'Asymptotic error expansions for numerical solutions of integral equations', IMA Journal of Numerical Analysis, 9, pp. 373 - 384, http://dx.doi.org/10.1093/imanum/9.3.373

Journal articles | 1988

McLean W; Elliott D, 1988, 'On the p-norm of the truncated Hilbert transform', Bulletin of the Australian Mathematical Society, 38, pp. 413 - 420, http://dx.doi.org/10.1017/S0004972700027799

Journal articles | 1988

McLean W, 1988, 'Hölder estimates for the Cauchy integral on a Lipschitz contour', Journal of Integral Equations and Applications, 1, pp. 435 - 451, http://dx.doi.org/10.1216/JIE-1988-1-3-435

Journal articles | 1986

MCLEAN W, 1986, 'A SPECTRAL GALERKIN METHOD FOR A BOUNDARY INTEGRAL-EQUATION', MATHEMATICS OF COMPUTATION, 47, pp. 597 - 607, http://dx.doi.org/10.2307/2008175

Journal articles | 1986

McLean W, 1986, 'A spectral Galerkin method for a boundary integral equation', Mathematics of Computation, 47, pp. 597 - 607, http://dx.doi.org/10.1090/S0025-5718-1986-0856705-2
Preprints | 2024

Dick J; Gao H; McLean W; Mustapha K, 2024, Time-fractional diffusion equations with randomness, and efficient numerical estimations of expected values

Preprints | 2024

Mustapha K; McLean W; Dick J, 2024, An $\alpha$-robust and second-order accurate scheme for a subdiffusion equation, , http://dx.doi.org/10.48550/arxiv.2401.04946

Preprints | 2022

McLean W; Mustapha K, 2022, Error Profile for Discontinuous Galerkin Time Stepping of Parabolic PDEs, , http://arxiv.org/abs/2208.03846v2

Preprints | 2022

McLean W, 2022, Numerical Evaluation of Mittag-Leffler Functions, http://dx.doi.org/10.1007/s10092-021-00398-6

Preprints | 2020

McLean W; Mustapha K, 2020, Uniform stability for a spatially-discrete, subdiffusive Fokker-Planck equation, , http://dx.doi.org/10.48550/arxiv.2012.13860

Preprints | 2019

Le K-N; McLean W; Stynes M, 2019, Existence, uniqueness and regularity of the solution of the time-fractional Fokker-Planck equation with general forcing, , http://dx.doi.org/10.48550/arxiv.1902.02564

Preprints | 2019

Le KN; McLean W; Mustapha K, 2019, A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial data, , http://dx.doi.org/10.48550/arxiv.1902.03204

Preprints | 2019

McLean W; Mustapha K; Ali R; Knio OM, 2019, Regularity theory for time-fractional advection-diffusion-reaction equations, , http://dx.doi.org/10.48550/arxiv.1902.00850

Preprints | 2018

McLean W; Mustapha K; Ali R; Knio O, 2018, Well-posedness of time-fractional, advection-diffusion-reaction equations, , http://dx.doi.org/10.48550/arxiv.1810.04836

Preprints | 2016

Le KN; McLean W; Lamichhane B, 2016, Finite element approximation of a time-fractional diffusion problem in a non-convex polygonal domain, , http://dx.doi.org/10.48550/arxiv.1602.00040

Patents | 2015

Kampwerth H; Wang KW; MCLEAN , 2015, A method and apparatus for testing the performance of a semiconductor material, Patent No. , Patent Agent:Griffithhack

Preprints | 2015

Le KN; McLean W; Mustapha K, 2015, Numerical solution of the time-fractional Fokker-Planck equation with general forcing, , http://dx.doi.org/10.48550/arxiv.1507.05706

Preprints | 2014

McLean W; Mustapha K, 2014, Time-stepping error bounds for fractional diffusion problems with non-smooth initial data, , http://dx.doi.org/10.48550/arxiv.1405.2140

Conference Papers | 2013

wang K; Kampwerth H; McLean W, 2013, 'Time-resolved Photoluminescence of Silicon Wafers for Illumination Source with High Repetition Rate: Finite Element Solution', http://dx.doi.org/10.4229/28theupvsec2013-2cv.3.52

Preprints | 2012

Mustapha K; McLean W, 2012, Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations, , http://dx.doi.org/10.48550/arxiv.1206.2686

Preprints | 2011

McLean W; Thomée V, 2011, Iterative methods for shifted positive definite linear systems and time discretization of the heat equation, , http://dx.doi.org/10.48550/arxiv.1111.5105

Conference Papers | 2010

Le Gia QT; Mclean W, 2010, 'Numerical solution of a parabolic equation on the sphere using Laplace transforms and radial basis functions', in ANZIAM Journal, Australian Mathematics Publishing Association Inc, Canberra, ACT, Australia, pp. C89 - C102, presented at CTAC 2010, UNSW, Sydney, 28 November 2010 - 01 December 2010

Conference Papers | 1995

McLean W; Prossdorf S, 1995, 'Boundary element collocation methods with reduced inter-element smoothness', in Morino L; Wendland WL (ed.), IABEM SYMPOSIUM ON BOUNDARY INTEGRAL METHODS FOR NONLINEAR PROBLEMS, KLUWER ACADEMIC PUBL, ITALY, PONTIGNANO, pp. 155 - 160, presented at IABEM Symposium on Boundary Integral Methods for Nonlinear Problems, ITALY, PONTIGNANO, 28 May 1995 - 03 June 1995, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1997BJ28U00024&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1984

McLean W, 1984, 'EFFECT OF APPROXIMATING THE GEOMETRY FOR A SIMPLE BOUNDARY INTEGRAL EQUATION.', pp. 277 - 288

My Teaching

Math3101/5305 Computational Mathematics
Math3371/5371 Numerical Linear Algebra

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Associate Professor William McLean