Books

Spherical Radial Basis Functions, Theory and Applications
(with S. Hubbert and T. Morton)
Preoder on Amazon.co.uk
or
Read online at Springer

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, DingXuan Zhou)

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, DingXuan Zhou)
Journal articles

Multiscale RBF method for severely illposed problems on spheres.
(with M. Zhong, I. H. Sloan), Journal of Scientific Computing, vol. 94, 2023.
[DOI]

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]

L2 error estimates for polynomial discrete penalized leastsquares approximation on
the sphere from noisy data (with K. Hesse), J. of Comp. and App. Math.,
vol 408, pp. 114118  114118,
[DOI]

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].

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 ]

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]

FaVeST: Fast Vector Spherical Harmonic Transforms,
(with M. Li and Y. G. Wang),
ACM Transactions on Mathematical Software, vol. 47, pp.124,2021.
[ DOI ]
[ arXiv:1908.00041 ]

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]

Stochastic NavierStokes equations on a thin spherical domain,
(with Z. Brzezniak, G. Dhariwal), Applied Math. and Optimization, 2020.
[DOI],
[ arXiv:2002.08873 ]

A spectral method to the stochastic Stokes equations on the sphere,
(with Joe Peach), ANZIAM J., vol. 60, C52C64.
[ PDF ]

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.257278
[arXiv:1801.03212]
[ DOI ]

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.144172.
[arXiv:1602.07363.]
[DOI]

A nonuniform discretization of stochastic heat equations with multiplicative noise
on the unit sphere, (with Yoshihito Kazashi), Journal of Complexity
vol.50, 2019, pp.4365.
[ arXiv:1706.02838v1]
[ DOI ]

Multiscale support vector regression method on spheres with data compression,
(with M. Zhong, W. Wang)
[ PDF ], Applicable Analysis, vol.98, issue.8, pp.14961519, 2019.
[ DOI ]

Solving approximate cloaking problems using finite element methods
(with H. Gimperlein, M. Maischak, E.P.Stephan),
ANZIAM J. 58 (CTAC2016) pp C162C174, 2017.
[PDF]

Application of the NewtonRaphson 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), 10921097, 2017.
[DOI]

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 ]

Random attractors for the stochastic NavierStokes equations
on the 2D unit sphere
(with Z. Brzezniak, B. Goldys),
Journal of Mathematical Fluid Mechanics.
20, 227253 (2018).
[PDF]
[arXiv:1402.3097]
[DOI]

Needlet approximation for isotropic random fields on the sphere,
(with Yu Guang Wang, Ian H. Sloan, Robert S. Womersley),
Journal of Approximation Theory, 216 86116, 2017.
[ DOI ]
[ arXiv:1512.07790.]

Zooming from Global to Local: A Multiscale RBF Approach,
(with I.H.Sloan and H.Wendland),
Advances in Computational Mathematics 43(3).581606, 2017.
[DOI]
[arXiv:1406.1333]

Inverse problem for nonlinear backward spacefractional diffusion equation
(with T.H.Nguyen, H.D.Nguyen, L.Le), Journal of Inverse and Illposed Problems,
25(4), 2015.
[DOI]

Fully discrete needlet approximation on the sphere (with Y.G.Wang, I.Sloan, R.Womersley),
Applied Computational Harmonic Analysis, 43 (2), 2017, 292316.
DOI: 10.1016/j.acha.2016.01.003.

Higher order QuasiMonte Carlo integration for holomorphic, parametric operator equations.
(with J. Dick and Ch. Schwab)
SIAM J. Uncertainty Quantification 4, (2016), 4879.
[ arXiv:1409.2180]

Multiscale methods with compactly supported radial basis functions for the Stokes problem on
bounded domains (with A. Chernih),
Advances in Computational Mathematics 42(5):11871208, 2016.
[ DOI ]

Multilevel 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) 25412568.
[ arXiv:1406.4432]

Fast QMC matrixvector multiplication,
(with J. Dick, F. Kuo and Ch. Schwab),
SIAM J. Sci. Comput. 37 (2015), A1436A1450.
[arXiv:1501.06286]

Random dynamical systems generated by stochastic NavierStokes equation on the rotating sphere
(with Z.Brzezniak, B.Goldys),
J. Mathematical Analysis and Applications
[DOI]
[PDF]
[arXiv:1403.6571]
 Multiscale methods with compactly supported RBFs for Galerkin
approximation of elliptic PDEs (with A. Chernih), IMA Journal of Numerical Analysis
34 (2014) , pp 569591.
[arXiv:1211.1431]
[DOI]

Data compression on the sphere using multiscale radial basis functions (with H. Wendland),
Advances in Computational Mathematics
40 (2014), pp. 923943
[PDF]
[DOI]

Solving parabolic equations on the unit sphere via Laplace transforms and radial basis
functions (with W. McLean), Advances in Computational Mathematics ,
20 (2014), pp 353375.
[PDF ]
[DOI]

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. 25992769
DOI
[ arXiv:1309.4624 ]

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), 401412.
[PDF] 
[DOI]

Multiscale RBF collocation for solving PDEs on spheres
(with I. H. Sloan and H. Wendland), Numerische Mathematik
121 (2012), 99125.
[PDF] 
[DOI]

A pseudospectral quadrature method for NavierStokes equations on rotating
spheres, (with I. H. Sloan, M. Ganesh),
Mathematics of Computation, 80 (2011) 13971430.
[PDF] 
[DOI]

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) (83103).
DOI
or [PDF]

A radial basis Galerkin method for spherical surface Stokes equations, (with M.
Ganesh),
ANZIAM J. (E)
52 (2011), C56C71.
[PDF]

Meshless BEM and overlapping Schwarz preconditioners for exterior problems on spheroids (with A. Costea, E. P .Stephan, T. Tran)
Studia Geophysica
55 (2011), 465477.
[PDF] 
[DOI]

Stability and preconditioning for a hybrid approximation on the sphere, (with I. H. Sloan and A. J. Wathen),
Numerische Mathematik
118 (2011), 695711.
[PDF] 
[DOI]

Multiscale analysis in Sobolev spaces on the sphere, (with I. Sloan and H. Wendland),
SIAM J. on Numerical Analysis 48 (2010) 20652090.
[PDF]
 An overlapping additive Schwarz preconditioner for interpolation on
the unit sphere by spherical basis functions, (with T.Tran),
Journal of Complexity 26 (2010) 552573.
[PDF]

Preconditioners for pseudodifferential equations on the sphere
with radial basis functions, (with I. H. Sloan, E. Stephan,T. Tran),
Numerische Mathematik, 115 (1) (2010), 141163.
[PDF]
[DOI]

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), 28572871 .
[PDF]

Overlapping additive Schwarz method for elliptic PDEs on spheres,
(with T. Tran and I. H. Sloan),
Mathematics of Computation, 78 (2009),79101.
[PDF].
 Postprocessing of solutions of incompressible NavierStokes equations on rotating spheres, (with M. Ganesh),
ANZIAM J. (E)
50 (2008), C90C106.
[PDF]
 Numerical solutions to a boundary integral equation with spherical basis functions, (with D. Pham, T. Tran),
ANZIAM J. (E)
50 (2008), C266C281.
[PDF]
 Interpolation on the sphere: a fast solution technique, (with T. Tran),
ANZIAM J. (E), 50 (2008), C354C370.
[PDF]

Quadrature formulas and localized linear polynomial operators on
the sphere,(with H. Mhaskar), SIAM Numerical Analysis, 47
(2008),440466.
[PDF] .

Local radial basis function approximation on the sphere (with K. Hesse),
Bulletin of the Australian Math. Society, 77 (2008),197224.
[PDF]

Polynomial operators and local approximation of solutions of
pseudodifferential operators on the sphere
(with H. N. Mhaskar), Numerische Mathematik,
103 (2) (2006), 299322.
[PDF] .

Continuous and discrete least square error estimates on spheres
(with F. J. Narcowich, J. D. Ward, H. Wendland),
J. Approx. Theory, 143 (1) (2006), 124133.
[PDF] .

Approximation of parabolic PDEs on spheres using collocation method,
Adv. Comput. Math., 22 (2005), 377397.
[PDF] .

Galerkin approximation of elliptic PDEs on spheres,
J. Approx. Theory , 130 (2004), 125149.
[PDF] .

The uniform norm of hyperinterpolation on the unit sphere in an arbitrary
number of dimensions (with
Ian H. Sloan),
Constructive Approximation 17:249265, 2001.
[PDF]
[DOI]
Conference papers
 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 ]
 J. Dick, Q. T. Le Gia, Ch. Schwab,
Higher Order Quasi MonteCarlo integration in uncertainty
quantification
(in ICOSAHOM 2014 proceedings )
 Q. T. Le Gia, H.T.Nguyen, T.Tran
Solving the backward heat equation on the unit sphere,
ANZIAM J. (E) 56 (2016), pp. C262C278.
[URL]

Multiscale methods with compactly supported radial basis functions for elliptic partial differential equations on bounded domains (with A. Chernih), ANZIAM J. (E) 54
(2012), C137C152
[PDF]
 Fast iterative solvers for boundary value problems on a local
spherical region (with T. Tran), ANZIAM J. (E) 54
(2012), C492C507
[PDF]
 Q. T. Le Gia, A QMCspectral method for elliptic PDEs with random coefficients on the
unit sphere [PDF],
Monte Carlo and QuasiMonte Carlo Methods 2012, pp 517534,
eds J. Dick, F. Kuo, G. Peters, I.H. Sloan.

Additive Schwarz preconditioners for interpolation of divergencefree vector
fields on spheres (with T. Tran), ANZIAM J. (E) 52
(2011), C742C758.
[PDF]
 Numerical solution of a parabolic equation on the sphere using Laplace transforms and RBFs, (with W. McLean),
ANZIAM J. (E)
52 (2011), C89C102.
[PDF]

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, 1214 July 2010.

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 1822, 2004.
 The bivariate contouring problem,
IMA Workshop for Graduate Students ,
University of Minnesota,
July 1928, 2000. [
Slides]

A Test Bed for Study of Distributed Denial of Service Attacks, IEEE
Systems, Man, and Cybernetics Information Assurance and Security
Workshop, June 67, 2000 at West Point, New York.

FMR: an incremental knowledge acquisition system for fuzzy domains, European
Knowledge Acquisition Workshop .
EKAW
1999
[PS]

A tradeoff between domain knowledge and problemsolving method, Eleventh
Workshop on Knowledge Acquisition, Modeling and Management
(KAW'98), Banff, Alberta, Canada, 1998. [HTMLversion]

From Multiple Classification RDR to Configuration RDR, Proceedings of
3rd AKAW, UNSW, Sydney, 1998, pp.6.16.14.
[Abstract]
Submitted articles

Q. T. Le Gia, H. N. Mhaskar,
Numerical solutions to an inverse problem for a nonlinear Helmholtz equation,
[ arXiv:2302.01475]

T. Alodat, Q. T. Le Gia, I. H. Sloan,
On approximation for timefractional stochastic diffusion equations on the unit sphere,
[ arXiv:2212.05690]

Z. Brzezniak, Gaurav Dhariwal and Q. T. Le Gia,
Stochastic NavierStokes equations on a 3D thin domain,
[arXiv:2008.07394]
 A. Costea, Q. T. Le Gia, D. Pham, E. Stephan, T. Tran,
Solving the DirichlettoNeumann map on an oblate spheroid by a meshfree method
[PDF]
Theses
Notes

Behaviour of an interpolation norm on the sphere.
[GZipped]

The Jordan curve theorem. [DVI],

The space of holomorphic functions and the Bergman kernel.
[DVI],

A proof of C^2 = C, where C is an infinite cardinal number.
[DVI],

Some worked out problems in real analysis.
[DVI]

The StrangFix condition in finite element method.
[DVI],

Numerical solution for PDE using wavelet approximations.
[
GZipped ]

An interative process to generate refinable functions.
[ PS ]
 Finite element method for elliptic PDEs in 2D
[PS]