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Dr Quoc Le Gia
Senior Lecturer

Dr Quoc Le Gia

  • PhD in Mathematics, (Texas A&M University, 2003)
  • MS in Mathematics, (Texas A&M University, 2000)
  • BSc in Mathematics and Computer Science, UNSW, Sydney,1998. 
Science
School of Mathematics & Statistics

Dr Quoc Thong Le Gia is a Senior Lecturer in the School of Mathematics and Statistics, UNSW, Sydney. His research interests include Numerical Analysis, Approximation Theory; Partial Differential Equations; and Stochastic Processes.

Please e-mail me if you are interested in working with me
Phone
9385 7049
E-mail
qlegia@unsw.edu.au
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 2084
  • Books | 2017
    2017, Frames and Other Bases in Abstract and Function Spaces, Pesenson I; Le Gia QT; Mayeli A; Mhaskar H; Zhou D-X, (eds.), Springer International Publishing, http://dx.doi.org/10.1007/978-3-319-55550-8
    Books | 2017
    2017, Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science, Pesenson I; Le Gia QT; Mayeli A; Mhaskar H; Zhou D-X, (eds.), Springer International Publishing, http://dx.doi.org/10.1007/978-3-319-55556-0
    Books | 2017
    Pesenson I; Gia QTL; Mayeli A; Mhaskar H; Zhou D-X, 2017, Frames and Other Bases in Abstract and Function Spaces Novel Methods in Harmonic Analysis, Birkhäuser
    Books | 2017
    Pesenson I; Gia QTL; Mayeli A; Mhaskar H; Zhou D-X, 2017, Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science Novel Methods in Harmonic Analysis, Birkhäuser
    Books | 2017
    Pesenson I; Le Gia QT; Mayeli A; Mhaskar H; Zhou DX, 2017, Preface, 9783319555492
    Books | 2017
    Pesenson I; Le Gia QT; Mayeli A; Mhaskar H; Zhou DX, 2017, Preface, 9783319555553
    Books | 2015
    Hubbert S; Gia QTL; Morton TM, 2015, Preface, http://dx.doi.org/10.1525/9780520947436-001
    Books | 2015
    Hubbert S; Le Gia QT; Morton TM, 2015, Spherical Radial Basis Functions, Theory and Applications, Springer
  • Book Chapters | 2015
    Hubbert S; Lê Gia QT; Morton TM, 2015, 'Error Bounds via Duchon’s Technique', in SpringerBriefs in Mathematics, Springer International Publishing, pp. 59 - 83, http://dx.doi.org/10.1007/978-3-319-17939-1_3
    Book Chapters | 2015
    Hubbert S; Lê Gia QT; Morton TM, 2015, 'Fast Iterative Solvers for PDEs on Spheres', in SpringerBriefs in Mathematics, Springer International Publishing, pp. 97 - 119, http://dx.doi.org/10.1007/978-3-319-17939-1_5
    Book Chapters | 2015
    Hubbert S; Lê Gia QT; Morton TM, 2015, 'Motivation and Background Functional Analysis', in SpringerBriefs in Mathematics, pp. 1 - 28, http://dx.doi.org/10.1007/978-3-319-17939-1_1
    Book Chapters | 2015
    Hubbert S; Lê Gia QT; Morton TM, 2015, 'Parabolic PDEs on Spheres', in SpringerBriefs in Mathematics, pp. 121 - 138, http://dx.doi.org/10.1007/978-3-319-17939-1_6
    Book Chapters | 2015
    Hubbert S; Lê Gia QT; Morton TM, 2015, 'Radial Basis Functions for the Sphere', in SpringerBriefs in Mathematics, Springer International Publishing, pp. 85 - 95, http://dx.doi.org/10.1007/978-3-319-17939-1_4
    Book Chapters | 2015
    Hubbert S; Lê Gia QT; Morton TM, 2015, 'The Spherical Basis Function Method', in SpringerBriefs in Mathematics, Springer International Publishing, pp. 29 - 58, http://dx.doi.org/10.1007/978-3-319-17939-1_2
  • Journal articles | 2022
    Buratti Y; Dick J; Le Gia Q; Hameiri Z, 2022, 'Deep Learning Extraction of the Temperature-Dependent Parameters of Bulk Defects', ACS Applied Materials and Interfaces, vol. 14, pp. 48647 - 48657, http://dx.doi.org/10.1021/acsami.2c12162
    Journal articles | 2022
    Hesse K; Le Gia QT, 2022, 'L2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data', Journal of Computational and Applied Mathematics, vol. 408, pp. 114118 - 114118, http://dx.doi.org/10.1016/j.cam.2022.114118
    Journal articles | 2022
    Le Gia QT; Clarke M; Dick J; Pye D, 2022, 'Elasticity equations with random domains—the shape derivative approach', ANZIAM Journal, vol. 62, pp. C256 - C272, http://dx.doi.org/10.21914/anziamj.v62.16120
    Journal articles | 2021
    Brzeźniak Z; Dhariwal G; Le Gia QT, 2021, 'Stochastic Navier–Stokes Equations on a Thin Spherical Domain', Applied Mathematics and Optimization, vol. 84, pp. 1971 - 2035, http://dx.doi.org/10.1007/s00245-020-09702-2
    Journal articles | 2021
    Hamann J; Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2021, 'A new probe of Gaussianity and isotropy with application to cosmic microwave background maps', International Journal of Modern Physics C, vol. 32, http://dx.doi.org/10.1142/S0129183121500844
    Journal articles | 2021
    Lamichhane BP; Harris E; Le Gia QT, 2021, 'Approximation of noisy data using multivariate splines and finite element methods', Journal of Algorithms and Computational Technology, vol. 15, http://dx.doi.org/10.1177/17483026211008405
    Journal articles | 2021
    Le Gia QT; Li M; Wang YG, 2021, 'Algorithm 1018: FaVeST-Fast Vector Spherical Harmonic Transforms', ACM Transactions on Mathematical Software, vol. 47, pp. 1 - 24, http://dx.doi.org/10.1145/3458470
    Journal articles | 2020
    Buratti Y; Le Gia QT; Dick J; Zhu Y; Hameiri Z, 2020, 'Extracting bulk defect parameters in silicon wafers using machine learning models', npj Computational Materials, vol. 6, http://dx.doi.org/10.1038/s41524-020-00410-7
    Journal articles | 2019
    Dick J; Gantner RN; Le Gia QT; Schwab C, 2019, 'Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion', Computers and Mathematics with Applications, vol. 77, pp. 144 - 172, http://dx.doi.org/10.1016/j.camwa.2018.09.019
    Journal articles | 2019
    Gia QTL; Sloan IH; Womersley RS; Wang YG, 2019, 'Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere', Applied and Computational Harmonic Analysis, http://dx.doi.org/10.1016/j.acha.2019.01.005
    Journal articles | 2019
    Kazashi Y; Le Gia QT, 2019, 'A non-uniform discretization of stochastic heat equations with multiplicative noise on the unit sphere', Journal of Complexity, vol. 50, pp. 43 - 65, http://dx.doi.org/10.1016/j.jco.2018.09.001
    Journal articles | 2019
    Peach JJ; Le Gia QT, 2019, 'A spectral method to the stochastic Stokes equations on the sphere', ANZIAM Journal, vol. 60, pp. C52 - C64, http://dx.doi.org/10.21914/anziamj.v60i0.13987
    Journal articles | 2018
    Le Gia QT, 2018, 'Numerical solutions of a boundary value problem on the sphere using radial basis functions', Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pp. 815 - 836, http://dx.doi.org/10.1007/978-3-319-72456-0_36
    Journal articles | 2018
    Zhong M; Le Gia QT; Wang W, 2018, 'A multiscale support vector regression method on spheres with data compression', Applicable Analysis, pp. 1 - 24, http://dx.doi.org/10.1080/00036811.2018.1430783
    Journal articles | 2017
    Brzeźniak Z; Goldys B; Gia QTL, 2017, 'Random attractors for the stochastic Navier--Stokes equations on the 2D unit sphere', Journal of Mathematical Fluid Mechanics, vol. 20, pp. 227 - 253, http://dx.doi.org/10.1007/s00021-017-0351-4
    Journal articles | 2017
    Dick J; Gantner RN; Le Gia QT; Schwab C, 2017, 'Multilevel higher-order quasi-Monte Carlo Bayesian estimation', Mathematical Models and Methods in Applied Sciences, vol. 27, pp. 953 - 995, http://dx.doi.org/10.1142/S021820251750021X
    Journal articles | 2017
    Dinh Nguyen Duy H; Nguyen Huy T; Le Dinh L; Quoc Thong Le G, 2017, 'Inverse problem for nonlinear backward space-fractional diffusion equation', Journal of Inverse and Ill-Posed Problems, vol. 25, pp. 423 - 443, http://dx.doi.org/10.1515/jiip-2015-0065
    Journal articles | 2017
    Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2017, 'Needlet approximation for isotropic random fields on the sphere', Journal of Approximation Theory, vol. 216, pp. 86 - 116, http://dx.doi.org/10.1016/j.jat.2017.01.001
    Journal articles | 2017
    Le Gia QT; Sloan IH; Wendland H, 2017, 'Zooming from global to local: a multiscale RBF approach', Advances in Computational Mathematics, vol. 43, pp. 581 - 606, http://dx.doi.org/10.1007/s10444-016-9498-4
    Journal articles | 2017
    Wang YG; Le Gia QT; Sloan IH; Womersley RS, 2017, 'Fully discrete needlet approximation on the sphere', Applied and Computational Harmonic Analysis, vol. 43, pp. 292 - 316, http://dx.doi.org/10.1016/j.acha.2016.01.003
    Journal articles | 2017
    Zhu Y; Le Gia QT; Juhl MK; Coletti G; Hameiri Z, 2017, 'Application of the Newton–Raphson method to lifetime spectroscopy for extraction of defect parameters', IEEE Journal of Photovoltaics, vol. 7, pp. 1092 - 1092, http://dx.doi.org/10.1109/JPHOTOV.2017.2695666
    Journal articles | 2016
    Chernih A; Le Gia QT, 2016, 'Multiscale methods with compactly supported radial basis functions for the Stokes problem on bounded domains', Advances in Computational Mathematics, vol. 42, pp. 1187 - 1208, http://dx.doi.org/10.1007/s10444-016-9458-z
    Journal articles | 2016
    Dick J; Kuo FY; Le Gia QT; Schwab C, 2016, 'Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations', SIAM Journal on Numerical Analysis, vol. 54, pp. 2541 - 2568, http://dx.doi.org/10.1137/16M1078690
    Journal articles | 2016
    Dick J; Le Gia QT; Schwab C, 2016, 'Higher order quasi-monte carlo integration for holomorphic, parametric operator equations', SIAM-ASA Journal on Uncertainty Quantification, vol. 4, pp. 48 - 79, http://dx.doi.org/10.1137/140985913
    Journal articles | 2015
    Brzeźniak Z; Goldys B; Le Gia QT, 2015, 'Random dynamical systems generated by stochastic Navier-Stokes equations on a rotating sphere', Journal of Mathematical Analysis and Applications, vol. 426, pp. 505 - 545, http://dx.doi.org/10.1016/j.jmaa.2015.01.054
    Journal articles | 2015
    Dick J; Kuo FY; Gia QTL; Schwab C, 2015, 'Fast QMC matrix-vector multiplication', SIAM Journal on Scientific Computing, vol. 37, pp. A1436 - A1450, http://dx.doi.org/10.1137/151005518
    Journal articles | 2014
    Chernih A; Le Gia QT, 2014, 'Multiscale methods with compactly supported radial basis functions for Galerkin approximation of elliptic PDEs', IMA Journal of Numerical Analysis, vol. 34, pp. 569 - 591, http://dx.doi.org/10.1093/imanum/drt004
    Journal articles | 2014
    Dick J; Kuo FY; Le Gia QT; Nuyens D; Schwab C, 2014, 'Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs', SIAM Journal on Numerical Analysis, vol. 52, pp. 2676 - 2702, http://dx.doi.org/10.1137/130943984
    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, vol. 40, pp. 353 - 375, http://dx.doi.org/10.1007/s10444-013-9311-6
    Journal articles | 2014
    Le Gia QT; Wendland H, 2014, 'Data compression on the sphere using multiscale radial basis function approximation', Advances in Computational Mathematics, vol. 40, pp. 923 - 943, http://dx.doi.org/10.1007/s10444-013-9334-z
    Journal articles | 2012
    Le Gia QT; Sloan IH; Wendland H, 2012, 'Multiscale RBF collocation for solving PDEs on spheres', Numerische Mathematik, vol. 121, pp. 99 - 125, http://dx.doi.org/10.1007/s00211-011-0428-6
    Journal articles | 2012
    Le Gia QT; Sloan IH; Wendland H, 2012, 'Multiscale approximation for functions in arbitrary Sobolev spaces by scaled radial basis functions on the unit sphere', Applied and Computational Harmonic Analysis, vol. 32, pp. 401 - 412, http://dx.doi.org/10.1016/j.acha.2011.07.007
    Journal articles | 2011
    Costea A; Le Gia Q; Stephan E; Tran T, 2011, 'Meshless BEM and overlapping Schwarz preconditioners for exterior problems on spheroids', Studia Geophysica et Geodaetica, vol. 55, pp. 465 - 477, http://dx.doi.org/10.1007/s11200-011-0027-0
    Journal articles | 2011
    Ganesh M; Le Gia QT; Sloan IH, 2011, 'A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres', Mathematics of Computation, vol. 80, pp. 1397 - 1430, http://dx.doi.org/10.1090/S0025-5718-2010-02440-8
    Journal articles | 2011
    Le Gia QT; Sloan IH; Wathen AJ, 2011, 'Stability and preconditioning for a hybrid approximation on the sphere', Numerische Mathematik, vol. 118, pp. 695 - 711, http://dx.doi.org/10.1007/s00211-011-0369-0
    Journal articles | 2011
    Le Gia QT; Stephan EP; Tran T, 2011, 'Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions', Advances in Computational Mathematics, vol. 34, pp. 83 - 103, http://dx.doi.org/10.1007/s10444-010-9145-4
    Journal articles | 2010
    Le Gia QT; Sloan IH; Wendland H, 2010, 'Multiscale analysis in Sobolev spaces on the sphere', SIAM Journal on Numerical Analysis, vol. 48, pp. 2065 - 2090, http://dx.doi.org/10.1137/090774550
    Journal articles | 2010
    Le Gia QT; Tran T, 2010, 'An overlapping additive Schwarz preconditioner for interpolation on the unit sphere with spherical radial basis functions', Journal of Complexity, vol. 26, pp. 552 - 573, http://dx.doi.org/10.1016/j.jco.2010.06.003
    Journal articles | 2010
    Tran T; Le Gia QT; Sloan IH; Stephan EP, 2010, 'Preconditioners for pseudodifferential equations on the sphere with radial basis functions', Numerische Mathematik, vol. 115, pp. 141 - 163, http://dx.doi.org/10.1007/s00211-009-0269-8
    Journal articles | 2009
    Le Gia QT; Sloan IH; Tran T, 2009, 'Overlapping additive schwarz preconditioners for elliptic pdes on the unit sphere', Mathematics of Computation, vol. 78, pp. 79 - 101, http://dx.doi.org/10.1090/S0025-5718-08-02150-9
    Journal articles | 2009
    Le Gia QT; Tran T; Sloan IH; Stephan EP, 2009, 'Boundary integral equations on the sphere with radial basis functions: error analysis', Applied Numerical Mathematics, vol. 59, pp. 2857 - 2871, http://dx.doi.org/10.1016/j.apnum.2008.12.033
    Journal articles | 2008
    Le Gia QT; Ganesh M, 2008, 'Post-processing of solutions of incompressible Navier-Stokes equations on rotating spheres', ANZIAM Journal, vol. 50, pp. 90 - 106
    Journal articles | 2008
    Le Gia QT; Hesse K, 2008, 'Local radial basis function approximation on the sphere', Bulletin of the Australian Mathematical Society, vol. 77, pp. 197 - 224, http://dx.doi.org/10.1017/S0004972708000087
    Journal articles | 2008
    Le Gia QT; Mhaskar H, 2008, 'Localized linear polynomial operators and quadrature formulas on the sphere', SIAM Journal on Numerical Analysis, vol. 47, pp. 440 - 466, http://dx.doi.org/10.1137/060678555
    Journal articles | 2008
    Le Gia QT; Pham TD; Tran T, 2008, 'Numerical solutions to a boundary integral equation with spherical radial basis functions', ANZIAM Journal, vol. 50, pp. 266 - 281
    Journal articles | 2008
    Le Gia QT; Tran T, 2008, 'Interpolation on the sphere: a fast solution technique', ANZIAM Journal, vol. 50, pp. 354 - 370
    Journal articles | 2006
    Le Gia QT; Mhaskar H, 2006, 'Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere', Numerische Mathematik, vol. 103, pp. 299 - 322, http://dx.doi.org/10.1007/s00211-006-0676-z
    Journal articles | 2006
    Le Gia QT; Narcowich FJ; Ward JD; Wendland H, 2006, 'Continuous and discrete least-squares approximation by radial basis functions on spheres', Journal of Approximation Theory, vol. 143, pp. 124 - 133, http://dx.doi.org/10.1016/j.jat.2006.03.007
    Journal articles | 2005
    Le Gia QT, 2005, 'Approximation of parabolic PDEs on spheres using collocation method', Advances in Computational Mathematics, vol. 22, pp. 377 - 397
    Journal articles | 2005
    Le Gia QT, 2005, 'Approximation of parabolic PDEs on spheres using spherical basis functions', Advances in Computational Mathematics, vol. 22, pp. 377 - 397, http://dx.doi.org/10.1007/s10444-003-3960-9
    Journal articles | 2004
    Le Gia QT, 2004, 'Galerkin approximation of elliptic PDEs on spheres', Journal of Approximation Theory, vol. 130, pp. 125 - 149, http://dx.doi.org/10.1016/j.jat.2004.07.008
  • Working Papers | 2019
    Hamann J; Gia QTL; Sloan IH; Wang YG; Womersley RS, 2019, A New Probe of Gaussianity and Isotropy applied to the CMB Maps, http://dx.doi.org, http://arxiv.org/abs/1911.11442v2
    Working Papers | 2018
    Gia QTL; Sloan IH; Womersley RS; Wang YG, 2018, Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere, http://dx.doi.org, http://arxiv.org/abs/1801.03212v1
  • Preprints | 2023
    Gia QTL; Mhaskar HN, 2023, Numerical solutions to an inverse problem for a non-linear Helmholtz equation, http://arxiv.org/abs/2302.01475v1
    Conference Papers | 2019
    Buratti Y; Dick J; Le Gia Q; Hameiri Z, 2019, 'A machine learning approach to defect parameters extraction: Using random forests to inverse the shockley-read-hall equation', Chicago, USA, presented at 46th IEEE photovoltaic specialists conference, Chicago, USA, 17 June 2019 - 21 June 2019
    Conference Papers | 2019
    Buratti Y; Dick J; Le Gia Q; Zhu Y; Hameiri Z, 2019, 'Inversion of the Shockley-Read-Hall equation using random forests', Canberra, presented at Asia Pacific Solar Research Conference, Canberra, 03 December 2019
    Conference Papers | 2016
    Le Gia QT; Gimperlein H; Maischak M; Stephan EP, 2016, 'Solving approximate cloaking problems using finite element methods', in Droniou J; Clarke S; Page M (eds.), Proceedings Computational Techniques and Applications Conference, Computational Techniques and Applications Conference, Monash University, Melbourne, presented at Computational Techniques and Applications Conference, Monash University, Melbourne, 27 November 2016 - 30 November 2016, http://dx.doi.org/10.21914/anziamj.v58i0.11729
    Conference Papers | 2014
    Dick J; Le Gia QT; Schwab CH, 2014, 'Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification', in Kirby RM; Berzins M; Hesthaven JS (eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Salt Lake City, Utah, USA, pp. 445 - 453, presented at ICOSAHOM conference, Salt Lake City, Utah, USA, 23 June 2014 - 27 June 2014, http://dx.doi.org/10.1007/978-3-319-19800-2_41
    Conference Papers | 2014
    Le Gia QT; Tran, T ; Nguyen HT, 2014, 'Solving the backward heat equation on the unit sphere', in ANZIAM Journal : Electronic Supplement, Australian Mathematical Society, ANU, pp. C262 - C278, presented at Computational Techniques and Applications Conference, ANU, 01 December 2014 - 03 December 2014, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/9346
    Conference Papers | 2012
    Chernih A; Le Gia QT, 2012, 'Multiscale methods with compactly supported radial basis functions for elliptic partial differential equations on bounded domains', in McCue S; Moroney T (ed.), Proceedings of the 16th Computational Techniques and Applications Conference, published in ANZIAM Journal, Australian Mathematical Society, Australia, pp. C137 - C152, presented at The 16th Biennial Computational Techniques and Applications Conference, Brisbane, 23 September 2012 - 26 September 2012, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6304
    Conference Papers | 2012
    Le Gia QT, 2012, 'A QMC spectral method for elliptic PDEs with random coefficients on the unit sphere', in Dick J; Kuo FY; Peters GW; Sloan IH (eds.), Monte Carlo and Quasi-Monte Carlo Methods 2012, Sydney, Australia, pp. 517 - 534, presented at MCQMC 2012, Sydney, Australia, 13 February 2012 - 17 February 2012, http://dx.doi.org/10.1007/978-3-642-41095-6_26
    Conference Papers | 2012
    Le Gia QT; Tran T, 2012, 'Fast iterative solvers for boundary value problems on a local spherical region', in McCue S; Moroney T (ed.), Proceedings of the 16th Computational Techniques and Applications Conference, published in ANZIAM Journal, Australian Mathematical Society, Australia, pp. C492 - C507, presented at CTAC-2012, QUT, Brisbane, 23 September 2012 - 26 September 2012, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6303/1730
    Conference Papers | 2010
    Ganesh M; Le Gia QT, 2010, 'A radial basis Galerkin method for spherical surface Stokes equations', in ANZIAM Journal
    Conference Papers | 2010
    Ganesh M; Le Gia QT, 2010, 'A redial basis Galerkin method for spherical surface Stokes equations', in ANZIAM Journal, Australian Mathematics Publishing Association Inc, Canberra, ACT, Australia, pp. C56 - C71, presented at CTAC 2010, UNSW, Sydney, 28 November 2010 - 01 December 2010
    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 | 2010
    Le Gia QT; Tran T, 2010, 'Additive Schwartz preconditioners for interpolation of divergence-free vector fields on spheres', in The ANZIAM Journal, Australian Mathematical Society, Australia, pp. C742 - C758, presented at CTAC 2010, UNSW, Sydney, 28 November 2010 - 01 December 2010
    Conference Papers | 2010
    Stephan EP; Costea A; Le Gia QT; Tran T, 2010, 'Meshless boundary element methods for exterior problems on spheroids', in Advances in Boundary Element Techniques XI, EC Ltd, UK, London, pp. 455 - 461, presented at Boundary Element Techniques XI, Berlin, Germany, 12 July 2010 - 14 July 2010
    Conference Presentations | 2004
    Le Gia QT, 2004, 'Galerkin method for elliptic PDEs on spheres: the L2(Sn) error estimates', presented at 11th International Conference in Approximation Theory, Gatlinburg, Tennessee, 18 May 2004 - 22 May 2004
    Conference Papers | 2004
    Le Gia QT, 2004, 'The L2(Sn) error estimate for the Galerkin method for elliptic PDEs on spheres', in Eleventh International Conference on Approximation Theory XI, 11th International Conference in Approximation Theory, Gatlinburg, Tennessee, presented at 11th International Conference in Approximation Theory, Gatlinburg, Tennessee, 18 May 2004 - 22 May 2004
    Conference Papers | 1999
    Martinez-Bejar R; Ibanez-Cruz F; Treadgold NK; Cao TM; Compton PJ, 1999, 'FMR: An Incremental Knowledge Acquisition System for Fuzzy Domains', in 11th European Workshop on Knowledge Acquisition, Management and Modelling, Schloss Dagstuhl Gaermany, pp. 349 - 354, presented at 11th European Workshop on Knowledge Acquisition, Management and Modelling, Schloss Dagstuhl Gaermany, 26 May 1999 - 29 May 1999

  • ARC Discovery Project DP220101811, "Novel mathematics and efficient computational techniques for human vision", $412K (2022-2024).
  • ARC Discovery Project DP180100506, "Uncertainty on spheres and shells: mathematics and methods for applications", $387K (2018-2020).

L. F. Guseman Prize in Mathematics, Texas A\&M University, April, 2003.

Research Interests

  • Approximation of functions on the unit sphere
  • Numerical methods for partial differential equations on spheres and surfaces
  • Numerical methods for stochastic partial differential equations
  • Partial differential equations with random coefficients
  • Machine learning/ Data science

External

My Research Supervision

Past Ph.D students

My Teaching

Undergraduate courses

MATH2301: Mathematical Computing

MATH3371/5371: Numerical linear algebra

Master students

  • Yuyang Li, Numerical methods for option pricing, UNSW, Feb--Aug 2020.
  • Yijia Ma, Numerical methods for Asian options, UNSW, Feb--Aug 2020.
  • Pengyun Zhang, Numerical methods for the multi-asset Black-Scholes equation. UNSW, Jun--Dec 2019.
  • Fan Li, Pricing options with finite difference methods, UNSW, Feb--Aug 2019.
  • Yujia Liu, Numerical solutions of the Black-Scholes-Merton equation, UNSW, Feb--Aug 2019.
  • Xiongwen Ke, Learning with imbalanced data, UNSW, Mar-June 2018 (joint advisor).

Honours students

  • Brock Sherlock, Oncolytic virus treatment of human breast cancer cells: modelling therapy efficacy, UNSW, Feb-2021 -- Nov-2021 (joint advisor).
  • Callum Scott, Solving partial differential equations using neural networks, UNSW, Feb-2021 -- Nov-2021.
  • Michelle Qiu, Machine learning techniques for imbalanced data with an application in finance, UNSW, Feb-2021 -- Nov-2021.
  • Chris Lee, Machine learning techniques applied to COVID-19 literature clustering, UNSW, Feb-2020 -- Nov-2020
  • James Hortle, Alzheimer's disease detection via machine learning, UNSW, July 2016--July 2017.