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Books

  1. Spherical Radial Basis Functions, Theory and Applications (with S. Hubbert and T. Morton) Pre-oder on Amazon.co.uk or Read online at Springer
  2. Frames and Other Bases in Abstract and Function Spaces: Novel Methods in Harmonic Analysis, Volume 1 (Applied and Numerical Harmonic Analysis) (editors Isaac Pesenson, Quoc Thong Le Gia, Azita Mayeli, Hrushikesh Mhaskar, Ding-Xuan Zhou)
  3. Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science: Novel Methods in Harmonic Analysis, Volume 2 (Applied and Numerical Harmonic Analysis) (editors Isaac Pesenson, Quoc Thong Le Gia, Azita Mayeli, Hrushikesh Mhaskar, Ding-Xuan Zhou)

Journal articles

  1. On approximation for time-fractional stochastic diffusion equations on the unit sphere, (with T. Alodat and I. H. Sloan), to appear in Journal of Computational and Applied Mathematics. [ DOI ] [ arXiv:2212.05690]
  2. Numerical solutions to an inverse problem for a non-linear Helmholtz equation, (with H. N. Mhaskar), ANZIAM J. Elec. Vol 64 2022. [ DOI ]
  3. Multiscale RBF method for severely ill-posed problems on spheres. (with M. Zhong, I. H. Sloan), Journal of Scientific Computing, vol. 94, 2023. [DOI]
  4. Deep Learning Extraction of the Temperature- Dependent Parameters of Bulk Defects, (with Y. Buratti, J. Dick, Z. Hameiri), ACS Applied Materials and Interfaces, vol. 14, pp. 48647 - 48657, 2022. [DOI]
  5. L2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data (with K. Hesse), J. of Comp. and App. Math., vol 408, pp. 114118 - 114118, [DOI]
  6. Elasticity equations with random domains - the shape derivative approach. (with M. Clarke, J. Dick, D. Pye), ANZIAM J. Electronic Supp. , vol. 62, pp. C256 - C272, [ DOI].
  7. A new probe of Gaussianity and Isotropy for CMB maps (with J. Hamann, I. H. Sloan, Y. G. Wang, R. S. Womersley) to appear in International J. of Modern Physics C, vol 32, 2021. [DOI], [ arXiv:1911.11442 ]
  8. Approximation of noisy data using multivariate splines and finite element methods, (with Lamichhane BP; Harris E) Journal of Algorithms and Computational Technology, vol. 15, 2021. [DOI]
  9. FaVeST: Fast Vector Spherical Harmonic Transforms, (with M. Li and Y. G. Wang), ACM Transactions on Mathematical Software, vol. 47, pp.1--24,2021. [ DOI ] [ arXiv:1908.00041 ]
  10. Extracting bulk defect parameters in silicon wafers using machine learning models (with Yoann Buratti, Josef Dick, Yan Zhu, Ziv Hameiri), (Computational Materials 6, 142(2020). [DOI]
  11. Stochastic Navier-Stokes equations on a thin spherical domain, (with Z. Brzezniak, G. Dhariwal), Applied Math. and Optimization, 2020. [DOI], [ arXiv:2002.08873 ]
  12. A spectral method to the stochastic Stokes equations on the sphere, (with Joe Peach), ANZIAM J., vol. 60, C52--C64. [ PDF ]
  13. Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere, (with I.H.Sloan, R.S.Womersley, Yu Guang Wang), Applied Computational Harmonic Analysis vol 49, issue.1, 2020, pp.257--278 [arXiv:1801.03212] [ DOI ]
  14. Higher order quasi Monte Carlo integration for Bayseian Estimation, (with J. Dick, R .N. Gantner, Ch. Schwab), Computer & Mathematics with Applications , vol.77, issue.1, 2019, pp.144--172. [arXiv:1602.07363.] [DOI]
  15. A non-uniform discretization of stochastic heat equations with multiplicative noise on the unit sphere, (with Yoshihito Kazashi), Journal of Complexity vol.50, 2019, pp.43--65. [ arXiv:1706.02838v1] [ DOI ]
  16. Multiscale support vector regression method on spheres with data compression, (with M. Zhong, W. Wang) [ PDF ], Applicable Analysis, vol.98, issue.8, pp.1496--1519, 2019. [ DOI ]
  17. Solving approximate cloaking problems using finite element methods (with H. Gimperlein, M. Maischak, E.P.Stephan), ANZIAM J. 58 (CTAC2016) pp C162-C174, 2017. [PDF]
  18. Application of the Newton-Raphson Method to Lifetime Spectroscopy for Extraction of Defect Parameters (with Yan Zhu, Mathias Klau,Juhl, Gianluca Coletti, Ziv Hameri), IEEE Journal of Photovoltaics, 7(4), 1092--1097, 2017. [DOI]
  19. Multilevel higher order quasi Monte Carlo Bayseian estimation, (with J.Dick, R.N.Gantner, Ch. Schwab), Mathematical Models and Methods in Applied Sciences (M3AS) 27, 953 (2017). [arXiv:1611.08324.] [ DOI ]
  20. Random attractors for the stochastic Navier--Stokes equations on the 2D unit sphere (with Z. Brzezniak, B. Goldys), Journal of Mathematical Fluid Mechanics. 20, 227-253 (2018). [PDF] [arXiv:1402.3097] [DOI]
  21. Needlet approximation for isotropic random fields on the sphere, (with Yu Guang Wang, Ian H. Sloan, Robert S. Womersley), Journal of Approximation Theory, 216 86--116, 2017. [ DOI ] [ arXiv:1512.07790.]
  22. Zooming from Global to Local: A Multiscale RBF Approach, (with I.H.Sloan and H.Wendland), Advances in Computational Mathematics 43(3).581--606, 2017. [DOI] [arXiv:1406.1333]
  23. Inverse problem for nonlinear backward space-fractional diffusion equation (with T.H.Nguyen, H.D.Nguyen, L.Le), Journal of Inverse and Ill-posed Problems, 25(4), 2015. [DOI]
  24. Fully discrete needlet approximation on the sphere (with Y.G.Wang, I.Sloan, R.Womersley), Applied Computational Harmonic Analysis, 43 (2), 2017, 292--316. DOI: 10.1016/j.acha.2016.01.003.
  25. Higher order Quasi-Monte Carlo integration for holomorphic, parametric operator equations. (with J. Dick and Ch. Schwab) SIAM J. Uncertainty Quantification 4, (2016), 48--79. [ arXiv:1409.2180]
  26. Multiscale methods with compactly supported radial basis functions for the Stokes problem on bounded domains (with A. Chernih), Advances in Computational Mathematics 42(5):1187--1208, 2016. [ DOI ]
  27. Multi-level higher order QMC Galerkin discretization for affine parametric operator equations (with J. Dick, F. Kuo, Q. T. Le Gia, and Ch. Schwab), SIAM Journal of Numerical Analysis 54(4) 2541--2568. [ arXiv:1406.4432]
  28. Fast QMC matrix-vector multiplication, (with J. Dick, F. Kuo and Ch. Schwab), SIAM J. Sci. Comput. 37 (2015), A1436--A1450. [arXiv:1501.06286]
  29. Random dynamical systems generated by stochastic Navier--Stokes equation on the rotating sphere (with Z.Brzezniak, B.Goldys), J. Mathematical Analysis and Applications [DOI] [PDF] [arXiv:1403.6571]
  30. Multiscale methods with compactly supported RBFs for Galerkin approximation of elliptic PDEs (with A. Chernih), IMA Journal of Numerical Analysis 34 (2014) , pp 569--591. [arXiv:1211.1431] [DOI]
  31. Data compression on the sphere using multiscale radial basis functions (with H. Wendland), Advances in Computational Mathematics 40 (2014), pp. 923--943 [PDF] [DOI]
  32. Solving parabolic equations on the unit sphere via Laplace transforms and radial basis functions (with W. McLean), Advances in Computational Mathematics , 20 (2014), pp 353--375. [PDF ] [DOI]
  33. Higher order QMC Galerkin discretization for parametric operator equations (with J. Dick, F. Y. Kuo, D. Nuyens, Ch. Schwab), SIAM J. Num. Analysis 52 (2014), pp. 2599--2769 DOI [ arXiv:1309.4624 ]
  34. Multiscale approximation for functions in arbitrary Sobolev spaces by scaled radial basis functions on the unit sphere (with I.H.Sloan, H. Wendland), Applied Computational Harmonic Analysis 32 (2012), 401-412. [PDF] | [DOI]
  35. Multiscale RBF collocation for solving PDEs on spheres (with I. H. Sloan and H. Wendland), Numerische Mathematik 121 (2012), 99-125. [PDF] | [DOI]
  36. A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres, (with I. H. Sloan, M. Ganesh), Mathematics of Computation, 80 (2011) 1397-1430. [PDF] | [DOI]
  37. Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions, (with E.P.Stephan, T.Tran), Advances in Computational Math. 34 (2011) (83--103). DOI or [PDF]
  38. A radial basis Galerkin method for spherical surface Stokes equations, (with M. Ganesh), ANZIAM J. (E) 52 (2011), C56-C71. [PDF]
  39. Meshless BEM and overlapping Schwarz preconditioners for exterior problems on spheroids (with A. Costea, E. P .Stephan, T. Tran) Studia Geophysica 55 (2011), 465-477. [PDF] | [DOI]
  40. Stability and preconditioning for a hybrid approximation on the sphere, (with I. H. Sloan and A. J. Wathen), Numerische Mathematik 118 (2011), 695-711. [PDF] | [DOI]
  41. Multiscale analysis in Sobolev spaces on the sphere, (with I. Sloan and H. Wendland), SIAM J. on Numerical Analysis 48 (2010) 2065-2090. [PDF]
  42. An overlapping additive Schwarz preconditioner for interpolation on the unit sphere by spherical basis functions, (with T.Tran), Journal of Complexity 26 (2010) 552-573. [PDF]
  43. Preconditioners for pseudodifferential equations on the sphere with radial basis functions, (with I. H. Sloan, E. Stephan,T. Tran), Numerische Mathematik, 115 (1) (2010), 141-163. [PDF]| [DOI]
  44. Boundary integral equations on the sphere with radial basis functions: error analysis, (with I. H. Sloan, E. Stephan,T. Tran), Applied Numerical Mathematics, 59 (11) (2009), 2857-2871 . [PDF]
  45. Overlapping additive Schwarz method for elliptic PDEs on spheres, (with T. Tran and I. H. Sloan), Mathematics of Computation, 78 (2009),79-101. [PDF].
  46. Post-processing of solutions of incompressible Navier-Stokes equations on rotating spheres, (with M. Ganesh), ANZIAM J. (E) 50 (2008), C90-C106. [PDF]
  47. Numerical solutions to a boundary integral equation with spherical basis functions, (with D. Pham, T. Tran), ANZIAM J. (E) 50 (2008), C266-C281. [PDF]
  48. Interpolation on the sphere: a fast solution technique, (with T. Tran), ANZIAM J. (E), 50 (2008), C354-C370. [PDF]
  49. Quadrature formulas and localized linear polynomial operators on the sphere,(with H. Mhaskar), SIAM Numerical Analysis, 47 (2008),440-466. [PDF] .
  50. Local radial basis function approximation on the sphere (with K. Hesse), Bulletin of the Australian Math. Society, 77 (2008),197-224. [PDF]
  51. Polynomial operators and local approximation of solutions of pseudo-differential operators on the sphere (with H. N. Mhaskar), Numerische Mathematik, 103 (2) (2006), 299-322. [PDF] .
  52. Continuous and discrete least square error estimates on spheres (with F. J. Narcowich, J. D. Ward, H. Wendland), J. Approx. Theory, 143 (1) (2006), 124-133. [PDF] .
  53. Approximation of parabolic PDEs on spheres using collocation method, Adv. Comput. Math., 22 (2005), 377-397. [PDF] .
  54. Galerkin approximation of elliptic PDEs on spheres, J. Approx. Theory , 130 (2004), 125-149. [PDF] .
  55. The uniform norm of hyperinterpolation on the unit sphere in an arbitrary number of dimensions (with Ian H. Sloan), Constructive Approximation 17:249-265, 2001. [PDF] [DOI]

Conference papers

  1. Q. T. Le Gia, Numerical solutions of a boundary value problem on the sphere using radial basis functions, in J. Dick et al. (eds.), Contemporary Computational Mathematics: A Celebration of the 80th Birthday of Ian Sloan, [DOI] [ arXiv:1402.3353 ]
  2. J. Dick, Q. T. Le Gia, Ch. Schwab, Higher Order Quasi Monte-Carlo integration in uncertainty quantification (in ICOSAHOM 2014 proceedings )
  3. Q. T. Le Gia, H.T.Nguyen, T.Tran Solving the backward heat equation on the unit sphere, ANZIAM J. (E) 56 (2016), pp. C262--C278. [URL]
  4. Multiscale methods with compactly supported radial basis functions for elliptic partial differential equations on bounded domains (with A. Chernih), ANZIAM J. (E) 54 (2012), C137--C152 [PDF]
  5. Fast iterative solvers for boundary value problems on a local spherical region (with T. Tran), ANZIAM J. (E) 54 (2012), C492--C507 [PDF]
  6. Q. T. Le Gia, A QMC-spectral method for elliptic PDEs with random coefficients on the unit sphere [PDF], Monte Carlo and Quasi-Monte Carlo Methods 2012, pp 517--534, eds J. Dick, F. Kuo, G. Peters, I.H. Sloan.
  7. Additive Schwarz preconditioners for interpolation of divergence-free vector fields on spheres (with T. Tran), ANZIAM J. (E) 52 (2011), C742--C758. [PDF]
  8. Numerical solution of a parabolic equation on the sphere using Laplace transforms and RBFs, (with W. McLean), ANZIAM J. (E) 52 (2011), C89-C102. [PDF]
  9. A. Costea, Q. T. Le Gia, E. P .Stephan, T. Tran, Meshless boundary element methods for exterior problems on spheroids [PDF] , Proceeding of the XI International Conference on Boundary Element and Meshless Techniques, Berlin, Germany, 12-14 July 2010.
  10. The L^2(S^n) error estimates for the Galerkin method for elliptic PDEs on spheres [PS] , Proceeding of the Eleventh International Conference in Approximation Theory, Gatlinburg, USA, May 18-22, 2004.
  11. The bivariate contouring problem, IMA Workshop for Graduate Students , University of Minnesota, July 19-28, 2000. [ Slides]
  12. A Test Bed for Study of Distributed Denial of Service Attacks,  IEEE Systems, Man, and Cybernetics  Information Assurance and Security Workshop, June 6-7, 2000 at West Point, New York.
  13. FMR: an incremental knowledge acquisition system for fuzzy domains, European Knowledge Acquisition Workshop . EKAW 1999 [PS]
  14. A trade-off between domain knowledge and problem-solving method, Eleventh Workshop on Knowledge Acquisition, Modeling and Management (KAW'98), Banff, Alberta, Canada, 1998. [HTMLversion]
  15. From Multiple Classification RDR to Configuration RDR, Proceedings of 3rd AKAW, UNSW, Sydney, 1998, pp.6.1-6.14. [Abstract]

Submitted articles

  1. J. Dick, Q.T. Le Gia, W. McLean, K. Mustapha, T. Tran, High-order QMC nonconforming FEMs for nearly incompressible planar stochastic elasticity equations, [ arXiv:2402.11545]
  2. J. Dick. Q. T. Le Gia, K. Mustapha, T. Tran, Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties, [ arXiv:2310.06187 ]
  3. J. Hamann, Q.T. Le Gia, I. H. Sloan, R. Womersley, Removing the mask -- reconstructing a scalar field on the sphere from a masked field, [ arXiv:2309.14815 ]
  4. Z. Brzezniak, Gaurav Dhariwal and Q. T. Le Gia, Stochastic Navier--Stokes equations on a 3D thin domain, [arXiv:2008.07394]
  5. A. Costea, Q. T. Le Gia, D. Pham, E. Stephan, T. Tran, Solving the Dirichlet-to-Neumann map on an oblate spheroid by a mesh-free method [PDF]

Theses

Notes