Works (19)
Updated: October 21st, 2024 14:00
2024 journal article
The Carleman convexification method for Hamilton-Jacobi equations
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 159, 173–185.
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.
author keywords: Numerical methods; Carleman estimate; Carleman-Newton; Boundary value problems; Quasilinear equations; Initial condition
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
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.
author keywords: Nonlinear parabolic equations; Inverse heat conduction problem; Dimensional reduction; Truncation; Fourier series; Polynomial-exponential basis
open access via doi.org (publisher)
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, 166, 77–90.
author keywords: Time reduction; Carleman contraction mapping; Initial condition; Damping coefficient
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
13. Climate Action
(OpenAlex)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: May 8, 2024
2023 article
A Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data
Source: ORCID
Added: January 23, 2024
2023 article
Numerical differentiation by the polynomial-exponential basis
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
Source: ORCID
Added: January 23, 2024
2023 article
The dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data
Source: ORCID
Added: January 23, 2024
2023 article
The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients
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.
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
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data
Inverse Problems, 38(4).
Contributors: * , 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.
Source: ORCID
Added: January 23, 2024
2022 article
The Carleman convexification method for Hamilton-Jacobi equations on the whole space
ArXiv.
Source: ORCID
Added: January 23, 2024
2022 article
The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation
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).
Contributors: * & 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
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).
Contributors: * , 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
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.
Contributors: T. Le * & L. Nguyen *
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.
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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