Publications


Google Scholar Profile

Research Gate Profile


Papers:

[24] V.T. Luan, T. Alhsmy
Sixth-order exponential Runge–Kutta methods for stiff systems
Applied Mathematics Letters, 15310936 (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).

DOI:https://doi.org/10.1016/j.cam.2023.115424 

[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. LuanS.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 Mathematics112, 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)