Papers:
[24] V.T. Luan, T. Alhsmy
Sixth-order exponential Runge–Kutta methods for stiff systems
Applied Mathematics Letters, 153, 10936 (2024).
DOI: https://doi.org/10.1016/j.aml.2024.109036
[23] V.T. Luan, N. V. Hoang, J.O. Ehigie,
Efficient exponential methods for genetic regulatory systems
Journal of Computational and Applied Mathematics, 436, 115424 (2024).
[22] L.T. Tuyen, V.T. Luan
A representation theorem for set-valued submartingales
Stochastic Analysis and Applications (published online, 12/2023).
DOI: https://doi.org/10.1080/07362994.2023.2296528
[21] V.T. Luan, T. Alhsmy
Adaptive time-stepping exponential Runge-Kutta methods for stiff PDEs
(Preprint, 07/2023)
[20]J.O. Ehigie, V.T. Luan
Efficient high-order two-derivative DIRK methods with optimized phase errors
Preprint, 2023
[19] V. T. Luan, R. Chinomona, D.R. Reynolds
Multirate exponential Rosenbrock methods
SIAM Journal on Scientific Computing 44 (5), A3265–A3289 (2022).
DOI: https://doi.org/10.1137/21M1439481
[18]J.O. Ehigie, V.T. Luan, S.A. Okunugaa, X. You
Exponentially fitted two-derivative DIRK methods for oscillatory differential equations
Applied Mathematics and Computation, 418, 126770 (2022).
DOI: https://doi.org/10.1016/j.amc.2021.126770
[17] V.T. Luan, D.L. Michels
Efficient exponential time integration for simulating nonlinear coupled oscillators
Journal of Computational and Applied Mathematics, 391, 113429 (2021).
DOI: https://doi.org/10.1016/j.cam.2021.113429
[16] V.T. Luan
Efficient exponential Runge–Kutta methods of high order: construction and implementation
BIT Numerical Mathematics, 61, 535–560 (2021).
DOI: https://doi.org/10.1007/s10543-020-00834-z
[15] V.T. Luan, D.L. Michels
Exponential Rosenbrock methods and their application in visual computing
Invited chapter in book “Rosenbrock-Wanner-Type Methods: Theory and Applications”
(Eds. T. Jax, A. Bartel, M. Ehrhardt, M. Günther, G. Steinebach), Springer (2021)
DOI: https://doi.org/10.1007/978-3-030-76810-2_3
[14] V.T. Luan, D.R. Reynolds, R. Chinomona,
A new class of high-order methods for multirate differential equations
SIAM Journal on Scientific Computing, 42(2), A1245–A1268 (2020).
DOI: https://doi.org/10.1137/19M125621X
[13] V.T. Luan, J. A. Pudykiewicz, D.R. Reynolds
Further development of efficient and accurate time integration schemes for meteorological models
Journal of Computational Physics, Vol. 376, 817-837 (2019).
DOI: https://doi.org/10.1016/j.jcp.2018.10.018
[12] D.L. Michels, V.T. Luan, and M. Tokman
A stiffly accurate integrator for elastodynamic problems
ACM Transactions on Graphics, Vol. 36, No. 4, Article 116 (2017).
[highlighted at SIGGRAPH 2017]
DOI: https://doi.org/10.1145/3072959.3073706
[11] V.T. Luan, M. Tokman, G. Rainwater
Preconditioned implicit-exponential integrators (IMEXP) for stiff PDEs
Journal of Computational Physics 335, 846-864 (2017)
DOI: https://doi.org/10.1016/j.jcp.2017.01.054
[10] V.T. Luan
Fourth-order two-stage explicit exponential integrators for time-dependent PDEs
Applied Numerical Mathematics, 112, 91–103 (2017)
DOI: https://doi.org/10.1016/j.apnum.2016.10.008
[9] V.T. Luan, A. Ostermann
Parallel exponential Rosenbrock methods
Computers & Mathematics with Applications, 71(5), 1137–1150 (2016)
DOI: https://doi.org/10.1016/j.camwa.2016.01.020
[8] V.T. Luan, A. Ostermann
Stiff order conditions for exponential Runge-Kutta methods of order five
in book: Modeling, Simulation and Optimization of Complex Processes – HPSC 2012 (H.G. Bock et al. eds.), 133-143 (2014)
DOI: https://doi.org/10.1007/978-3-319-09063-4_11
[7] V.T. Luan, A. Ostermann
Exponential Runge-Kutta methods of high-order for parabolic problems
Journal of Computational and Applied Mathematics, 256, 168-179 (2014)
DOI: https://doi.org/10.1016/j.cam.2013.07.027
[6] V.T. Luan, A. Ostermann
Exponential Rosenbrock methods of order five-derivation- construction, analysis, and numerical comparisons
Journal of Computational and Applied Mathematics, 255, 417-431 (2014)
DOI: https://doi.org/10.1016/j.cam.2013.04.041
[5] V.T. Luan, A. Ostermann
Exponential B-series: The stiff case,
SIAM Journal on Numerical Analysis, 51(6), 3431-3445 (2013)
DOI: https://doi.org/10.1137/130920204
[4] Q.A. Dang, V.T. Luan
Iterative method for solving a nonlinear fourth-order boundary value problem
Computers & Mathematics with Applications, 60(1), 112-121 (2010)
DOI: https://doi.org/10.1016/j.camwa.2010.04.037
[3]. Q.A. Dang, V.T. Luan, D.Q. Long
Iterative method for solving a fourth-order differential equation with nonlinear boundary condition
Applied Mathematical Sciences, Vol. 4, no. 70, 3467-3481 (2010)
[2]. Q.A. Dang, V.T. Luan
Iterative method for solving a nonlinear fourth-order boundary value problem arising in the study of transverse vibrations of a hinged beam
Publishing House of Natural Science and Technology, Hanoi, pp. 383-399 (in Vietnamese) (2010)
[1] V.T. Luan, Dang Quang A
On influence aspect of parameter in scattered data approximation problems using multiquadric radial basis function
Journal of Computer Science and Cybernetics, 25(1), 33-42 (2009)
Codes:
Phipm_simul_iom, written in MATLAB (a C version is being developed): Simultaneously compute all linear combinations of matrix exponential or phi- functions evaluated at some scaling of a matrix A, t*A, acting on a set of input vectors. Released fall 2017 at https://github.com/drreynolds/Phipm_simul_iom
Poster presentations:
[4] A. Payne, V. T. Luan, and Hoang Nguyen
Advanced time integrators for reaction-diffusion systems in pattern formation,
Undergraduate Research Showcase, Mississippi State University, August 2, 2023.
[3] C. R. Raderstof, V. T. Luan, and Hoang Nguyen
Innovative Time Integration for Epidemiological Models,
Undergraduate Research Showcase, Mississippi State University, August 4, 2022.
[2] V.T. Luan, M. Ritter, W. Benger, and G. Ritter
Visualization of the Solution of Advection-Diffusion-Reaction Equations Extended to 3D,
DK+ Computational Interdisciplinary Modelling, March 03-06, 2013, Obergurgl, Austria.
[1] V.T. Luan, M. Ritter, and G. Ritter
Visualization of the Solution of Advection-Diffusion-Reaction Equations,
DK+ Computational Interdisciplinary Modelling, January 28 – February 1, 2012, Obergurgl, Austria.
Theses:
V.T. Luan
High-order exponential integrators
Ph.D. thesis, University of Innsbruck (2014) (classification: Excellent)
V.T. Luan
Some methods of unitary integration and applications (in Vietnamese)
MSc. thesis, HUS-Vietnam National University (2007) (classification: Excellent)
V.T. Luan
Using vector methods in solving geometry problems (in Vietnamese)
BSc. thesis, Hanoi National University of Education, Vietnam (2005) (classification: Excellent)