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SEMINAR

OUTREACH

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Research interests

Numerical analysis and scientific computing.
Domain decomposition methods, local time-stepping.
Heterogeneous, coupled problems; flow and transport in porous media.
Exponential time integration methods.
Ocean modeling.
Numerical methods for problems in solid mechanics.

Research grants

CAREER, NSF DMS-2041884 (PI), 2021 - 2026.

NSF DMS-1912626 (PI), 2019 - 2023.

NSF DMS-1949953 (Co-PI, conference grant), 2020 - 2022.

Auburn University Intramural Grant Program (PI), 2019 - 2021.

NSF

Publications (Google Scholar profile)

(with C.-K. Doan, L. Ju and R. Lan), Convergence analysis of the dynamically regularized Lagrange multiplier method for the incompressible Navier-Stokes equations, submitted, 2025.

(with C.-K. Doan, L. Ju and R. Lan), Dynamically regularized Lagrange multiplier methods for the Cahn-Hilliard-Navier-Stokes system, Int. J. Numer. Methods Eng., 2025, to appear.

(with P.-T. Huynh, G. Zhang and F. Bao), Joint state-parameter estimation for the Reduced Fracture Model via the United Filter, J. Comput. Phys., 538, 2025.

(with C.-K. Doan and P.-T. Huynh), Noniterative localized exponential time differencing methods for hyperbolic conservation laws, Adv. Comput. Math., 51(26), 2025.

(with C.-K. Doan, L. Ju and R. Lan), Dynamically regularized Lagrange multiplier schemes with energy dissipation for the incompressible Navier-Stokes equations, J. Comput. Phys. 521 (1), 2025. https://doi.org/10.1016/j.jcp.2024.113550

(with P.-T. Huynh and Y. Cao), Monolithic and local time-stepping decoupled algorithms for transport problems in fractured porous media, IMA J. Numer. Anal., 45(1), pp. 283-328, 2025.

(with I. Yotov), A space-time mixed finite element method for the reduced fracture flow model on nonmatching grids, Math. Comp., 2024. https://doi.org/10.1090/mcom/4031

(with P.-T. Huynh and F. Bao), Parameter estimation for the reduced fracture model via a direct filter method. Journal of Machine Learning for Modeling and Computing, 2024. https://doi.org/10.1615/JMachLearnModelComput.2024056400

(with C.-K. Doan and L. Ju), Low regularity integrators for the conservative Allen-Cahn equation with a nonlocal constraint, J. Sci. Comput. 101 (57), 2024. https://doi.org/10.1007/s10915-024-02703-1

(with P.-T. Huynh and Y. Cao), Operator splitting and local time-stepping methods for transport problems in fractured porous media, Commun. Comput. Phys., 34, pp. 1215 - 1246, 2023.

(with C.-K. Doan and L. Ju), Fully discrete error analysis of first-order low regularity integrators for the Allen-Cahn equation, Numer. Methods Partial Differ. Equ., 2023. https://doi.org/10.1002/num.23017

(with C.-K. Doan, L. Ju, and K. Schratz), Low regularity integrators for semilinear parabolic equations with maximum bound principles, BIT Numer. Math., 63 (2), 2023. https://doi.org/10.1007/s10543-023-00946-2

(with P.-T. Huynh and Y. Cao), Fast and accurate domain decomposition methods for reduced fracture models with nonconforming time grids, J. Sci. Comput., 96 (23), 2023. https://doi.org/10.1007/s10915-023-02251-0

(with I.S. Pop), Iterative methods with nonconforming time grids for nonlinear flow problems in porous media, Acta Math. Vietnam., 48, pp. 29-40, 2023.

Fully implicit local time-stepping methods for advection-diffusion problems in mixed formulations, Comput. Math. Appl., 118, pp. 248-264, 2022.

Optimized Ventcel-Schwarz waveform relaxation and mixed hybrid finite element method for transport problems, Discrete Contin. Dyn. Syst. Ser. S, 2022, doi: 10.3934/dcdss.2022060.

(with H. Kunwar and H. Lee), Nonconforming time discretization based on Robin transmission conditions for the Stokes-Darcy system, Appl. Math. Comput., 413, 2022, https://doi.org/10.1016/j.amc.2021.126602.

(with H. Lee), A Global-in-time Domain Decomposition Method for the Coupled Nonlinear Stokes and Darcy Flows, J. Sci. Comput., 87 (22), 2021, https://doi.org/10.1007/s10915-021-01422-1.

(with X. Li and L. Ju), Overlapping Localized Exponential Time Differencing Methods for Semilinear Parabolic Equations, BIT Numer. Math., 2021, DOI: 10.1007/s10543-020-00817-0.

(with X. Meng, Z. Wang and L. Ju), Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study, Commun. Comput. Phys., 29, pp. 80 - 110, 2021.

(with L. Ju and Z. Wang), Exponential Time Differencing and Nonoverlapping Domain Decomposition for Diffusion Problems, J. Sci. Comput., 82 (2), 2020, DOI: 10.1007/s10915-020-01136-w.

(with T.H. Ong), Optimized Schwarz and Finite Element Cell-Centered Method for Heterogeneous Anisotropic Diffusion Problems, Appl. Numer. Math. 151, pp. 380 - 401, 2020.

(with L. Ju, W. Leng and Z. Wang), High-order Explicit Local Time-Stepping Algorithms For Hyperbolic Conservation Laws, Math. Comp., 89 (324), pp. 1807 - 1842, 2020.

(with W. Leng, L. Ju, Z. Wang and K. Pieper), Conservative Explicit Local Time-Stepping Schemes for Shallow Water Equations, J. Comput. Phys. 382, pp. 152 - 176, 2019.

(with L. Ju and Z. Wang), Overlapping Localized Exponential Time Differencing Methods for Diffusion Problems, Comm. Math. Sci. 16 (6), pp. 1531 - 1555, 2018.

(with D.C.H. Vo and T.H. Ong). A Low-Order Finite Element Method for Three Dimensional Linear Elasticity Problems with General Meshes, Comput. Math. Appl. 74 (6), pp. 1379 - 1398, 2017.

(with C. Japhet, M. Kern and J.E. Roberts), Space-Time Domain Decomposition For Advection-Diffusion Problems in Mixed Formulations, Math. Comput. Simulat. 137, pp. 366 - 389, 2017.

(with C. Japhet, M. Kern and J.E. Roberts), Space-Time Domain Decomposition For Reduced Fracture Models in Mixed Formulation, SIAM J. Numer. Anal. 54 (1), pp. 288 - 316, 2016.

(with C. Japhet, M. Kern and J.E. Roberts), Ventcell Conditions with Mixed Formulations for Flow in Porous Media. In T. Dickopf, M.J. Gander, L. Halpern, R. Krause, L.F. Pavarino (eds.), Domain Decomposition Methods in Science and Engineering XXII, Lecture Notes in Computational Science and Engineering, vol. 104, pp. 531 - 540, Springer, 2016.

(with T.H. Ong, S.P.A. Bordas and H. Nguyen-Xuan), A staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity on general meshes, SIAM J. Numer. Anal. 53 (4), pp. 2051 - 2073, 2015.

(with J. Jaffré, C. Japhet, M. Kern and J.E. Roberts), Space-Time Domain Decomposition For Mixed Formulations of Diffusion Equations. In J. Erhel, M.J. Gander, L. Halpern, G. Pichot, T. Sassi, O. Widlund (eds.), Domain Decomposition Methods in Science and Engineering XXI, Lecture Notes in Computational Science and Engineering, vol. 98, pp. 257 - 264, Springer, 2014.

(with J. Jaffré, C. Japhet, M. Kern and J.E. Roberts), Space-Time Domain Decomposition For Diffusion Problems in Mixed Formulations, SIAM J. Numer. Anal. 51 (6), pp. 3532 - 3559, 2013.

Doctoral dissertation

Space-Time Domain Decomposition Methods for Mixed Formulations of Flow and Transport Problems in Porous Media, Ph.D. thesis, Université Pierre et Marie Curie, Paris, France, 2013.

Thi-Thao-Phuong Hoang, Auburn University