By Dr Quoc Thong Le Gia

Journal articles

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, 32, pp. 401 - 412, http://dx.doi.org/10.1016/j.acha.2011.07.007

Chernih A; Le Gia QT, 2012, 'Multiscale methods with compactly supported radial basis functions for elliptic partial differential equations on bounded domains', Proceedings of the 16th Computational Techniques and Applications Conference, published in ANZIAM Journal, 54, pp. C137 - C152, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6304

Le Gia QT; Sloan IH; Wendland H, 2012, 'Multiscale RBF collocation for solving PDEs on spheres', Numerische Mathematik, 121, pp. 99 - 125, http://dx.doi.org/10.1007/s00211-011-0428-6

Ganesh M; Le Gia QT; Sloan IH, 2011, 'A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres', Mathematics of Computation, 80, pp. 1397 - 1430, http://dx.doi.org/10.1090/S0025-5718-2010-02440-8

Ganesh M; Le Gia QT, 2011, 'A redial basis Galerkin method for spherical surface Stokes equations', ANZIAM Journal, pp. C56 - C71

Le Gia QT; Tran T, 2011, 'Additive Schwartz preconditioners for interpolation of divergence-free vector fields on spheres', The ANZIAM Journal, pp. C742 - C758

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, 55, pp. 465 - 477

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

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, 34, pp. 83 - 103, http://dx.doi.org/10.1007/s10444-010-9145-4

Le Gia QT; Sloan IH; Wathen AJ, 2011, 'Stability and preconditioning for a hybrid approximation on the sphere', Numerische Mathematik, 118, pp. 695 - 711, http://dx.doi.org/10.1007/s00211-011-0369-0

Ganesh M; Le Gia QT, 2010, 'A radial basis Galerkin method for spherical surface Stokes equations', ANZIAM Journal, 52

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, 26, pp. 552 - 573

Le Gia QT; Sloan IH; Wendland H, 2010, 'Multiscale analysis in Sobolev spaces on the sphere', SIAM Journal on Numerical Analysis, 48, pp. 2065 - 2090, http://dx.doi.org/10.1137/090774550

Tran T; Le Gia QT; Sloan IH; Stephan EP, 2010, 'Preconditioners for pseudodifferential equations on the sphere with radial basis functions', Numerische Mathematik, 115, pp. 141 - 163

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, 59, pp. 2857 - 2871

Le Gia QT; Sloan IH; Tran T, 2009, 'Overlapping additive schwarz preconditioners for elliptic pdes on the unit sphere', Mathematics of Computation, 78, pp. 79 - 101

Le Gia QT; Tran T, 2008, 'Interpolation on the sphere: a fast solution technique', ANZIAM Journal, pp. 354 - 370

Le Gia QT; Hesse K, 2008, 'Local radial basis function approximation on the sphere', Bulletin of the Australian Mathematical Society, 77, pp. 197 - 224

Le Gia QT; Mhaskar H, 2008, 'Localized linear polynomial operators and quadrature formulas on the sphere', SIAM Journal on Numerical Analysis, 47, pp. 440 - 466

Le Gia QT; Pham TD; Tran T, 2008, 'Numerical solutions to a boundary integral equation with spherical radial basis functions', ANZIAM Journal, pp. 266 - 281

Le Gia QT; Ganesh M, 2008, 'Post-processing of solutions of incompressible Navier-Stokes equations on rotating spheres', ANZIAM Journal, pp. 90 - 106

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, 143, pp. 124 - 133

Le Gia QT; Mhaskar H, 2006, 'Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere', Numerische Mathematik, 103, pp. 299 - 322

Le Gia QT, 2005, 'Approximation of parabolic PDEs on spheres using spherical basis functions', Advances in Computational Mathematics, 22, pp. 377 - 397, http://dx.doi.org/10.1007/s10444-003-3960-9

Le Gia QT, 2005, 'Approximation of parabolic PDEs on spheres using collocation method', Advances in Computational Mathematics, 22, pp. 377 - 397

Le Gia QT, 2004, 'Galerkin approximation of elliptic PDEs on spheres', Journal of Approximation Theory, 130, pp. 125 - 149

Conference Papers

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

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', in Conference Record of the IEEE Photovoltaic Specialists Conference, Institute of Electrical and Electronics Engineers (IEEE), Chicago, USA, pp. 3070 - 3073, presented at 46th IEEE photovoltaic specialists conference, Chicago, USA, 17 June 2019 - 21 June 2019, http://dx.doi.org/10.1109/PVSC40753.2019.8980717

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, Australian Mathematical Publishing Association, 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

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, Springer Nature, 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

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

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

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, Gatlinburg, Tennessee, presented at 11th International Conference in Approximation Theory, Gatlinburg, Tennessee, 18 May 2004 - 22 May 2004

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, presented at 11th European Workshop on Knowledge Acquisition, Management and Modelling, Schloss Dagstuhl Gaermany, 26 May 1999 - 29 May 1999

Conference Presentations

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

Working Papers

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

Gia QTL; Sloan IH; Womersley RS; Wang YG; Le Gia Q, 2018, Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere, http://dx.doi.org

Preprints

Hamann J; Gia QTL; Sloan IH; Womersley RS, 2023, Removing the mask -- reconstructing a scalar field on the sphere from a masked field, http://dx.doi.org/10.1137/23M1603157

Gia QTL; Mhaskar HN, 2023, Numerical solutions to an inverse problem for a non-linear Helmholtz equation, http://arxiv.org/abs/2302.01475v1

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