86 citations · 208 across the 25 of their papers we have counts for
29 papers
Spectral Bounds for Kernel Quadrature
A. Cloninger, Q. T. Le Gia, H. N. Mhaskar
A bottleneck in the theory of kernel methods in machine learning is the storage requirement. To ameliorate this, a standard trick is to replace the kernel with an explicit feature…
A simple modification to mitigate locking in conforming FEM for nearly incompressible elasticity
K. Mustapha, W. McLean, J. Dick +1
Due to the divergence-instability, the accuracy of low-order conforming finite element methods (FEMs) for nearly incompressible elasticity equations deteriorates as the Lamé parame…
High-order QMC nonconforming FEMs for nearly incompressible planar stochastic elasticity equations
J. Dick, T. Le Gia, W. McLean +2
In a recent work (Dick et al, arXiv:2310.06187), we considered a linear stochastic elasticity equation with random Lamé parameters which are parameterized by a countably infinite n…
Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties
M. Clarke, J. Dick, Q. T. Le Gia +2
We explore a linear inhomogeneous elasticity equation with random Lamé parameters. The latter are parameterized by a countably infinite number of terms in separated expansions. The…
Removing the mask -- reconstructing a scalar field on the sphere from a masked field
Jan Hamann, Quoc Thong Le Gia, Ian H. Sloan +1
The paper analyses a spectral approach to reconstructing a scalar field on the sphere, given only information about a masked version of the field together with precise information…
Numerical solutions to an inverse problem for a non-linear Helmholtz equation
Q. T. Le Gia, H. N. Mhaskar
In this work, we construct numerical solutions to an inverse problem of a nonlinear Helmholtz equation defined in a spherical shell between two concentric spheres centered at the o…
On approximation for time-fractional stochastic diffusion equations on the unit sphere
T. Alodat, Q. T. Le Gia, I. H. Sloan
This paper develops a two-stage stochastic model to investigate evolution of random fields on the unit sphere $\bS^2$ in . The model is defined by a time-fractional stochasti…
Approximation of noisy data using multivariate splines and finite element methods
Elizabeth Harris, Bishnu Lamichhane, Quoc Thong Le Gia
We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defi…
Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere
Quoc T. Le Gia, Ian H. Sloan, Robert S. Womersley +1
This paper discusses sparse isotropic regularization for a random field on the unit sphere in , where the field is expanded in terms of a spherical h…
A non-uniform discretization of stochastic heat equations with multiplicative noise on the unit sphere
Yoshihito Kazashi, Quoc T. Le Gia
We investigate a discretization of a class of stochastic heat equations on the unit sphere with multiplicative noises. A spectral method is used for the spatial discretization and…
Multilevel higher order Quasi-Monte Carlo Bayesian Estimation
Josef Dick, Robert N. Gantner, Quoc T. Le Gia +1
We propose and analyze deterministic multilevel approximations for Bayesian inversion of operator equations with uncertain distributed parameters, subject to additive Gaussian meas…
Higher order Quasi-Monte Carlo integration for Bayesian Estimation
Josef Dick, Robert N. Gantner, Quoc T. Le Gia +1
We analyze combined Quasi-Monte Carlo quadrature and Finite Element approximations in Bayesian estimation of solutions to countably-parametric operator equations with holomorphic d…
Needlet approximation for isotropic random fields on the sphere
Quoc T. Le Gia, Ian H. Sloan, Yu Guang Wang +1
In this paper we establish a multiscale approximation for random fields on the sphere using spherical needlets --- a class of spherical wavelets. We prove that the semidiscrete nee…
Fully discrete needlet approximation on the sphere
Yu Guang Wang, Quoc T. Le Gia, Ian H. Sloan +1
Spherical needlets are highly localized radial polynomials on the sphere , , with centers at the nodes of a suitable cubature rule.…
Fast QMC matrix-vector multiplication
Josef Dick, Frances Y. Kuo, Quoc T. Le Gia +1
Quasi-Monte Carlo (QMC) rules can be used to approximate integrals of the form $\int_{[0,1]^s} f(\boldsymbol{y} A) \,\mathrm{d} \boldsy…
Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification
Josef Dick, Quoc Thong Le Gia, Christoph Schwab
We review recent results on dimension-robust higher order convergence rates of Quasi-Monte Carlo Petrov-Galerkin approximations for response functionals of infinite-dimensional, pa…
Higher order Quasi-Monte Carlo integration for holomorphic, parametric operator equations
Josef Dick, Quoc T. Le Gia, Christoph Schwab
We analyze the convergence of higher order Quasi-Monte Carlo (QMC) quadratures of solution-functionals to countably-parametric, nonlinear operator equations with distributed uncert…
Zooming from Global to Local: A Multiscale RBF Approach
Quoc Thong Le Gia, Ian H Sloan, Holger Wendland
Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximati…
Multi-level higher order QMC Galerkin discretization for affine parametric operator equations
Josef Dick, Frances Kuo, Quoc Thong Le Gia +1
We develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably af…
Random dynamical systems generated by stochastic Navier--Stokes equation on the rotating sphere
Zdzislaw Brzeźniak, Beniamin Goldys, Quoc Thong Le Gia
In this paper we first prove the existence and uniqueness of the solution to the stochastic Navier--Stokes equations on the rotating 2-dimensional sphere. Then we show the existenc…
Numerical solutions of a boundary value problem on the sphere using radial basis functions
Quoc Thong Le Gia
Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play a…
Random attractors for the stochastic Navier--Stokes equations on the 2D unit sphere
Zdzislaw Brzeźniak, Beniamin Goldys, Quoc Thong Le Gia
In this paper we prove the existence of random attractors for the Navier--Stokes equations on 2 dimensional sphere under random forcing irregular in space and time. We also deduce…
Higher order QMC Galerkin discretization for parametric operator equations
Josef Dick, Frances Y. Kuo, Quoc T. Le Gia +2
We construct quasi-Monte Carlo methods to approximate the expected values of linear functionals of Galerkin discretizations of parametric operator equations which depend on a possi…
Multiscale methods with compactly supported radial basis functions for Galerkin approximation of elliptic PDEs
Andrew Chernih, Quoc Thong Le Gia
The aim of this work is to consider multiscale algorithms for solving PDEs with Galerkin methods on bounded domains. We provide results on convergence and condition numbers. We sho…