Works (19)

Updated: May 8th, 2024 05:00

2024 journal article

The Carleman convexification method for Hamilton-Jacobi equations

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 159, 173–185.

By: H. Le*, T. Le n & L. Nguyen*

author keywords: Numerical methods; Carleman estimate; Hamilton-Jacobi equations; Viscosity solutions; Vanishing viscosity process
Sources: ORCID, Web Of Science, NC State University Libraries
Added: February 15, 2024

2024 journal article

The Carleman-Newton method to globally reconstruct the initial condition for nonlinear parabolic equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 445.

By: A. Abhishek*, T. Le n, L. Nguyen* & T. Khan*

author keywords: Numerical methods; Carleman estimate; Carleman-Newton; Boundary value problems; Quasilinear equations; Initial condition
Sources: ORCID, Web Of Science, NC State University Libraries
Added: February 10, 2024

2024 journal article

The Fourier-based dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 128.

By: D. Hao*, T. Le n & L. Nguyen*

author keywords: Nonlinear parabolic equations; Inverse heat conduction problem; Dimensional reduction; Truncation; Fourier series; Polynomial-exponential basis
Sources: Web Of Science, NC State University Libraries
Added: January 2, 2024

2024 journal article

The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients

Computers & Mathematics with Applications.

By: T. Le*, L. Nguyen, L. Nguyen & H. Park

UN Sustainable Development Goal Categories
13. Climate Action (OpenAlex)
Source: ORCID
Added: May 8, 2024

2023 article

A Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data

By: R. Abney, T. Le*, L. Nguyen & C. Peters

Source: ORCID
Added: January 23, 2024

2023 article

Numerical differentiation by the polynomial-exponential basis

By: P. Nguyen, T. Le*, L. Nguyen & M. Klibanov

TL;DR: This work suggests an approach that involves approximating the data by eliminating high-frequency terms from the Fourier expansion of the given data with respect to the polynomial-exponential basis, which helps to regularize the issue and ensures accuracy in the computation. (via Semantic Scholar)
Source: ORCID
Added: January 23, 2024

2023 article

Numerical verification of the convexification method for a frequency-dependent inverse scattering problem with experimental data

By: T. Le*, V. Khoa, M. Klibanov, L. Nguyen, G. Bidney & V. Astratov

Source: ORCID
Added: January 23, 2024

2023 article

The dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data

By: H. Dinh-Nho, T. Le* & L. Nguyen

Source: ORCID
Added: January 23, 2024

2023 article

The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients

By: T. Le*, L. Nguyen, L. Nguyen & H. Park

Source: ORCID
Added: January 23, 2024

2022 journal article

A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications

Computers & Mathematics with Applications, 125, 13–24.

By: T. Le*, L. Nguyen* & H. Tran*

TL;DR: A new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE by using the quasi-reversibility method with a suitable Carleman weight function is proposed. (via Semantic Scholar)
Source: ORCID
Added: January 23, 2024

2022 journal article

A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data

Journal of Inverse and Ill-Posed Problems, 30(2), 265–286.

By: T. Le* & L. Nguyen*

Contributors: T. Le* & L. Nguyen*

Source: ORCID
Added: January 23, 2024

2022 journal article

Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data

Inverse Problems, 38(4).

By: T. Le*, M. Klibanov, L. Nguyen, A. Sullivan & L. Nguyen

Contributors: T. Le*, M. Klibanov, L. Nguyen, A. Sullivan & L. Nguyen

TL;DR: It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. (via Semantic Scholar)
Source: ORCID
Added: January 23, 2024

2022 article

Global reconstruction of initial conditions of nonlinear parabolic equations via the Carleman-contraction method

ArXiv.

By: T. Le*

Contributors: T. Le*

Source: ORCID
Added: January 23, 2024

2022 article

The Carleman convexification method for Hamilton-Jacobi equations on the whole space

ArXiv.

By: H. Le, T. Le* & L. Nguyen

Contributors: H. Le, T. Le* & L. Nguyen

Source: ORCID
Added: January 23, 2024

2022 article

The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation

By: A. Abhishek, T. Le*, L. Nguyen & T. Khan

Source: ORCID
Added: January 23, 2024

2022 journal article

The Gradient Descent Method for the Convexification to Solve Boundary Value Problems of Quasi-Linear PDEs and a Coefficient Inverse Problem

Journal of Scientific Computing, 91(3).

By: T. Le* & L. Nguyen*

Contributors: T. Le* & L. Nguyen*

TL;DR: The global convergence of the gradient descent method of the minimization of strictly convex functionals on an open and bounded set of a Hilbert space is studied and proved to establish a general framework to numerically solve boundary value problems for quasi-linear partial differential equations (PDEs) with noisy Cauchy data. (via Semantic Scholar)
Source: ORCID
Added: January 23, 2024

2021 article

Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data

ArXiv. http://www.scopus.com/inward/record.url?eid=2-s2.0-85106104061&partnerID=MN8TOARS

By: M. Klibanov, T. Le, L. Nguyen, A. Sullivan & L. Nguyen

Contributors: M. Klibanov, T. Le, L. Nguyen, A. Sullivan & L. Nguyen

Source: ORCID
Added: January 23, 2024

2021 journal article

The Quasi-reversibility Method to Numerically Solve an Inverse Source Problem for Hyperbolic Equations

Journal of Scientific Computing, 87(3).

By: T. Le*, L. Nguyen*, T. Nguyen* & W. Powell*

Contributors: T. Le*, L. Nguyen*, T. Nguyen* & W. Powell*

TL;DR: A numerical method is proposed to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data by the quasi-reversibility method, and it is rigorously proved that the convergence of this method as the noise level tends to 0. (via Semantic Scholar)
Source: ORCID
Added: January 23, 2024

2020 journal article

Numerical solution of a linearized travel time tomography problem with incomplete data

SIAM Journal on Scientific Computing, 42(5), B1173–B1192.

By: M. Klibanov, T. Le* & L. Nguyen

Contributors: M. Klibanov, T. Le* & L. Nguyen

TL;DR: A new numerical method is proposed to solve the linearized problem of the travel time tomography with incomplete data using the technique of the truncation of the Fourier series. (via Semantic Scholar)
Source: ORCID
Added: January 23, 2024

Employment

Updated: October 10th, 2023 09:58

2023 - present

North Carolina State University Raleigh, North Carolina, US
Postdoctoral Research Scholar Department of Mathematics

2020 - 2023

University of North Carolina at Charlotte Charlotte, North Carolina, US
Instructor Mathematics and Statistics

2019 - 2023

University of North Carolina Charlotte, NC, US
Teaching Assistant Mathematics and Statistics

2012 - 2019

Vietnam Banking Academy Hanoi, VN
Lecturer Mathematics

Education

Updated: October 10th, 2023 09:58

2019 - 2023

University of North Carolina at Charlotte Charlotte, North Carolina, US
PhD. Applied Mathematics Mathematics and Statistics

2016 - 2018

University of North Carolina at Charlotte Charlotte, North Carolina, US
Master of Science in Mathematical Finance Mathematics & Finance & Economics

2008 - 2012

National Economics University Hanoi, VN
Bachelor in Economics - Mathematical Finance Mathematical Economics

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