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Publications
1.
V.T.
Luan, T. Trky
Derivation of sixth-order exponential Runge–Kutta methods for stiff systems
Applied Mathematics Letters, 153, 10936 (2024).
2.
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).
3.
L.T. Tuyen, V.T.
Luan
A representation theorem for set-valued submartingales
Stochastic Analysis and Applications, 1-20 (2023).
4.
V.T. Luan, T. Alhsmy
Adaptive time-stepping exponential Runge-Kutta methods for stiff PDEs
(Preprint, to be submitted to Journal of
Scientific Computing)
5.
J.O. Ehigie, V.T. Luan
Efficient high-order two-derivative DIRK
methods with optimized phase errors
(Preprint, to be submitted to Numerical Algorithms).
6.
V.
T. Luan, R. Chinomona, D.R. Reynolds
Multirate exponential Rosenbrock methods
SIAM Journal
on Scientific Computing, 44 (5),
A3265–A3289 (2022).
7.
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).
8.
V.T.
Luan, D.L. Michels
Efficient exponential time integration for
simulating nonlinear coupled oscillators
Journal of Computational and Applied
Mathematics, 391, 113429 (2021).
9.
V.T.
Luan
Efficient exponential Runge–Kutta methods of high order: construction and
implementation
BIT Numerical Mathematics, 61, 535–560 (2021).
10. 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).
11. V.T. Luan, D.R. Reynolds, R. Chinomona
A new class of high-order for multirate
differential equations,
SIAM Journal
on Scientific Computing, 42(2), A1245–A1268 (2020).
12. 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).
13. D.L. Michels, V.T. Luan, M. Tokman
A stiffly accurate integrator for elastodynamic
problems,
ACM Transactions on Graphics, Vol. 36, No. 4, Article 116 (2017).
14. V.T. Luan, M. Tokman, G.
Rainwater
Preconditioned implicit-exponential integrators (IMEXP) for stiff PDEs,
Journal of Computational Physics, Vol. 335, 846-864 (2017).
15. V.T. Luan
Fourth-order two-stage explicit exponential integrators for time-dependent
PDEs,
Applied Numerical Mathematics, 112, 91–103 (2017).
16. V.T. Luan, A. Ostermann
Parallel exponential Rosenbrock methods,
Computers and mathematics with Applications, 71(5), 1137–1150 (2016).
17. V.T. Luan, A. Ostermann
Stiff order conditions for exponential Runge-Kutta
methods of order five,
Modeling, Simulation and Optimization of Complex Processes- HPSC (H.G. Bock et
al. eds.), 133-143 (2014).
18. 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).
19. V.T. Luan, A. Ostermann
Exponential Rosenbrock methods of order five-derivation, analysis and numerical
comparisons,
Journal of Computational and Applied Mathematics, 255, 417-431 (2014).
20. V.T. Luan, A. Ostermann
Exponential B-series: The stiff case,
SIAM Journal on Numerical Analysis, 51(6), 3431-3445 (2013).
21. Q.A. Dang, V.T. Luan
Iterative method for solving a nonlinear fourth-order boundary value problem,
Computers and mathematics with Applications, 60(1), 112-121 (2010).
22. 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).
23. 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).
24. V.T. Luan, Dang Q. A
On influence aspect of parameter in scattered data approximation problems using
multiquadric RBF function,
Journal of Computer Science and Cybernetics, 25(1), 33-42 (2009).
Theses:
1.
V.T. Luan, High-order exponential integrators
Ph.D. thesis, University of Innsbruck (2014).
2.
V.T. Luan, Some methods of unitary integration and applications (in
Vietnamese)
MSc. thesis, HUS-Vietnam National University
(2008).
3.
V.T. Luan, Using vector methods in solving geometry problems (in
Vietnamese)
BSc. thesis, Hanoi National University of Education (2005)
Poster presentations:
1.
Huy Pham, V. T.
Luan
Exponential Nyström integrators for stiff and
highly oscillatory problems
NSF CompMath PI
meeting, University of Utah, Salt Lake City, UT, May 8-9, 2025
2.
Hoang Nguyen, V. T.
Luan
Two-derivative exponential methods for stiff
PDEs,
NSF CompMath PI meeting, University of Utah, Salt Lake
City, UT, May 8-9, 2025
3.
Hoang Nguyen, V. T.
Luan, J. Ehigie
Efficient exponential methods for genetic regulatory systems,
NSF CompMath PI meeting, University of Washington,
Seattle, UW, July 15 -16, 2024
4.
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.
5.
R. Raderstof, V.
T. Luan, and Hoang Nguyen
Innovative Time Integration for Epidemiological Models,
Undergraduate Research Showcase, Mississippi State University, August 4, 2022.
6.
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.
7.
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.
Software/Codes
1.
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 (freely licensed) at https://github.com/drreynolds/Phipm_simul_iom
2.
MERK: Multirate Expontential Runge-Kutta methods for
the additively split multirate problems. Released Spring
2019 (freely licensed) at https://github.com/rujekoc/merk_v1
3.
MERB: Multirate Expontential Rosenbrock methods for the additively split multirate problems. Released Summer 2022 (freely licensed)
at https://github.com/rujekoc/merbrepo