Research
Numerical analysis, Reduced order modeling, Large eddy simulations, Computational and geophysical fluid dynamics, Inverse problems
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My research interests lie around computational mathematics and numerical analysis. More specifically, I develop computational models for different physical problems (e.g., fluid-structure interaction, geophysical flows, particle transport) which are robust, accurate, and efficient through the use of different stabilization techniques like in large eddy simulations, and methods from reduced order modeling of dynamical systems.
Reduced Order Modeling:
I work on the development of reduced order models (ROMs) forfluid flow problems and fluid-structure interaction (FSI) systems, aiming to radically reduce the computational cost of their simulation while retaining essential dynamics. My research combines projection-based and data-driven techniques. A central goal is to build theoretically certified ROMs that inherit key properties of full-order models.
Large eddy simulation & filtering stabilization for geophysical flows:
My research develops filtering and stabilization techniques for geophysical fluid flows, with a focus on large eddy simulation and quasi-geostrophic ocean models, which are known to be challenging due to their convection-dominated nature. We develop methods inspired from the well-established evolve-filter-relax (EFR) algorithms. These include the design of filters through indicator functions, tuning of relaxation parameters, etc.
Finite element methods for fluid-structure interaction systems:
My research on finite element methods (FEM) for FSI systems focuses on developing and analyzing domain decomposition (DD) methods. To enforce the coupling conditions, we employ Lagrange multiplier methods which makes it easy to develop DD methods. These FSI formulations serve as the theoretical foundation for constructing structure-preserving reduced order models for multiphysics problems.
Articles:
Pre-print or in-press:
L. Besabe, H. Lee, Finite element approximation for a reformulation of a 3D fluid–2D plate interaction system, submitted (2026) arXiv:2602.05701
L. Besabe, E. Jose, A.K. Tapia, A cellular automata model for particle transport in disordered systems, submitted (2025), arXiv:2502.02298 code
Published:
L. Besabe, M. Girfoglio, A. Quaini, G. Rozza, Randomized Proper Orthogonal Decomposition for data-driven reduced order modeling of a two-layer quasi-geostrophic ocean model, Advances in Computational Science and Engineering 7 (2026) p. 1-27. doi preprint
L. Besabe, M. Girfoglio, A. Quaini, G. Rozza, Data-driven reduced order modeling of a two-layer quasi-geostrophic ocean model, Results in Engineering 25 (2025) 103691 doi preprint
L. Besabe, M. Girfoglio, A. Quaini, G. Rozza, Linear and nonlinear filtering for a two-layer quasi-geostrophic ocean model, accepted, Applied Mathematics and Computation 488 (2025) 129121. doi preprint
L. Besabe, D. Onofrei, Active control of scalar Helmholtz fields in the presence of known impenetrable obstacles. AMS Contemporary Mathematics 784 (2023) p. 189 - 206. doi
Reports (not peer-reviewed):
L. Besabe, H. Bhatt, K. Calman, J. Chen, N. de Silva, S. Dodamgodage, M. Najaf, R. Rodrigues, T. Samakhoana, H. Boateng, Randomized Matrix Sketching and Least Squares Methods for Classification Problems, SIAM Graduate Student Mathematical Modelling Camp (GSMMC) 2025. pdf
D. Auddya, L. Besabe, M. Chugunova, S. Moreno Cristobal, X. Hu, C. Hao, M. Mejia, R. Moore, T. Pothisawang, R. Rassool, S. Sattari, K. Sehgal, Maturing Homomorphic Encryption (HE) to Enable Privacy Preserving Vector Search, Mathematical Problems in Industry Workshop, 2025. pdf
Talks/Presentations:
(upcoming) SIAM Mathematics of Data Science (MDS26), November 2026
(upcoming) SIAM Mathematics of Planet Earth (MPE26), July 2026
ICERM Workshop on Simulation-Based Optimization with Applications (poster), April 2026
AMS Southeastern Sectional Meeting 2026, March 2026
Joint Mathematical Meetings 2026, January 2026
Clemson Computational Mathematics Seminar, November 2025
3rd UNCG PDE Virtual Conference, October 2025
12th Mini-Conference on Computational Mathematics, September 2025
Joint Mathematical Meetings 2025, January 2025
Reduced Order Modeling and Machine Learning for Large Eddy Simulation and Related Topics, October 2024
7th SIAM TX-LA Sectional Meeting, October 2024
Three-minute thesis event (UH College of Natural Sciences and Mathematics), October 2024
Three-minute thesis event (UH Math Department), October 2024
Joint Mathematical Meetings 2024, January 2024
6th SIAM TX-LA Sectional Meeting, November 2023.
Texas Differential Equations 2022, October 2022
SIAM Annual Meeting 2022, July 2022.
11th UPLB CAS Student-Faculty Research Conference, November 2018.
Slides:
FEM for 3D fluid-2D plate interaction system
Data-driven ROM for a two-layer quasi-geostrophic ocean model
Large Eddy Simulations for Quasi-geostrophic Equations
Active control of scalar Helmholtz fields in the presence of known impenetrable obstacles
Particle Transport in Disordered Systems using Cellular Automata
Geophysical and Environmental Applications (GEA)
I am also a contributor to Geophysical and Environmental Applications (GEA).
GEA is an open-source package which is built upon the C++ finite volume library OpenFOAM. This is aimed at providing modular codes for the finite volume-based simulation of different environmental applications such as ocean and atmospheric flows.
Some simulations from GEA:
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