University of Maryland, Baltimore County

1000 Hilltop Circle

Baltimore, MD 21250

Office : MP 438

email : tongtong.li at umbc.edu

- Numerical Analysis: numerical solution of partial differential equations, finite element methods, numerical conservation laws, high order methods
- Data Assimilation: sequential inference, ensemble learning
- Bayesian Inverse Problems: hierarchical Bayesian learning, Bayesian inference
- Applications: computational fluid dynamics, interaction of fluid flow and poroelastic media, sea ice modeling

- I attended the ICERM-SIAM Workshop on Empowering a Diverse Computational Mathematics Research Community, Brown University, July 22nd - Aug 2nd, 2024.
- Professor Anne Gelb and I are featured in the VOX article Researchers Improve Models to Predict Changes in Sea Ice.
- I gave a presentation in the North American High Order Methods Conference (NAHOMCon), Dartmouth College, June 18th, 2024.
- I gave a talk at Conference on Mathematical Models and Numerical Methods for Multiphysics Systems, University of Pittsburgh, May 3rd, 2024.
- I presented at Dartmouth-UNH Postdoctoral Research Day and won the first place award in the research presentations, Dartmouch College, March 22nd, 2024. An interview about my research is available here.

- (August 2024 - current) Assistant Professor, Department of Mathematics and Statistics, University of Maryland, Baltimore County

- (August 2021 - July 2024) Research Associate, Department of Mathematics, Dartmouth College

Supervisor : Anne Gelb

- PhD in Mathematics, University of Pittsburgh, USA, July 2021

Dissertation title : Mixed Formulations for Fluid-poroelastic Structure Interaction

Advisor : Ivan Yotov - MS in Mathematical Finance, Rutgers, the State University of New Jersey, USA, June 2016

Thesis title : Pricing Finite-maturity European Put-Heston Option with Barrier Discontinuity by FDM

Advisor : David Eliezer - BS in Economics, Huazhong Agricultural University, China, June 2014

Thesis title : Research of Chinese Agricultural Commodity Futures Market Volatility Spillover Effect Based on BEKK-GARCH Model - Taking DCE Yellow Soybean as an Example

Advisor : Guang Zeng

- Travel Award: ICERM-SIAM Workshop on Empowering a Diverse Computational Mathematics Research Community. Brown University, July - Aug. 2024.
- First Place Award for Lightning Talks: Dartmouth-UNH Postdoctoral Research Day, Dartmouth College, March 2024.
- Travel Award: Hot Topics: Recent Progress in Deterministic and Stochastic Fluid-Structure Interaction. Simons Laufer Mathematical Sciences Institute, Dec. 2023.
- Travel Award: 17th U. S. National Congress on Computational Mechanics (USNCCM17). Albuquerque, NM, July 2023.
- First Place Award (Outstanding Graduate Student Research Poster) for AWM Graduate Student Poster Competition. Seattle, WA, May 2023.
- Travel Award: AWM Workshop at SIAM Conference on Optimization (OP23). Seattle, WA, May 2023.
- Travel Award: SIAM Convening on Climate Science, Sustainability, and Clean Energy. Tysons, VA, Oct. 2022.
- Second Place Award for Poster Presentation: High Performance Computing (HPC) Day. University of Massachusetts Lowell, Sept. 2022.
- SIAM Early Career Travel Award: SIAM Conference on Mathematical Planet Earth (MPE22). Pittsburgh, PA, July 2022.
- Thomas C. Hales Distinguished Research Award, University of Pittsburgh, 2022.
- Mathematics Teaching Assistant Excellence Award, University of Pittsburgh, 2019.
- Arts and Sciences Graduate Fellowship (two times, 2020 and 2017).

- T. Li and A. Gelb, A Bayesian framework for spectral reprojection. Arxiv. Submitted. [link]
- T. Li, A. Gelb, and Y. Lee, A structurally informed data assimilation approach for nonlinear partial differential equations. Arxiv. Submitted. [link]
- S. Caucao, A. Dalal, T. Li and I. Yotov, Mixed finite element methods for the Navier-Stokes-Biot model. In: Ivan Lirkov, Svetozar Margenov (eds) Large-Scale Scientific Computations. 14th International Conference, LSSC 2023, Sozopol, Bulgaria, June 5–9, 2023, Revised Selected Papers. Springer, Cham. DOI: 10.1007/978-3-031-56208-2. [link]
- T. Li, A. Gelb, and Y. Lee, Improving numerical accuracy for the viscous-plastic formulation of sea ice. J. Comput. Phys., 487: 112184, 2023. DOI: 10.1016/j.jcp.2023.112184. [link]
- T. Li, S. Caucao and I. Yotov, An augmented fully mixed formulation for the coupling of the quasi-static Navier-Stokes and Biot models. IMA J. Numer. Anal, 2023. [link]
- S. Caucao, T. Li and I. Yotov, A multipoint stress-flux mixed finite element method for the Stokes-Biot model. Numer. Math., 2022. DOI: 10.1007/s00211-022-01310-2. [link]
- T. Li, X. Wang and I. Yotov, Non-Newtonian and poroelastic effects in simulations of arterial flows. Arxiv. Preprint. [link]
- T. Li and I. Yotov, A mixed elasticity formulation for fluid-poroelastic structure interaction. ESAIM Math. Model. Numer. Anal., 56(1): 1-40, 2022. DOI: 10.1051/m2an/2021083. [link]
- S. Caucao, T. Li and I. Yotov, A cell-centered finite volume method for the Navier-Stokes/Biot model. In: Klofkorn R., Keilegavlen E., Radu F., Fuhrmann J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. DOI: 10.1007/978-3-030-43651-3_29. [link]

- 2024 Fall - Math 225 Introduction to Differential Equations (Undergraduate Level)

- 2024 Spring - Math 23 Differential Equations (Undergraduate Level)
- 2023 Summer - Math 117 First Year Graduate Seminar (Data Assimilation, Graduate Level, One Week Voluntary)
- 2023 Winter - Math 116 Applied Mathematics (Numerical Linear Algebra, Graduate Level)
- 2022 Spring - Math 76/146 Applied Mathematics (Finite Element Method, Mixed Undergraduate and Graduate Levels)

- Ethan M. Baird, Summer 2024
- Mason F. King, Summer 2024
- Gary Jiang, Summer 2024
- Jack E. Friedman, 2022 - 2023
- David J. Appleton, 2022 - 2023

- Jessica Rattray (Numerical Solution of PDEs), Spring 2023

- 2021 Summer - Math 0230 Analytic Geometry and Calculus 2
- 2020 Summer - Math 0290 Applied Differential Equations
- 2017 Summer - Math 0220 Analytic Geometry and Calculus 1

- 2020 Fall - Math 0240 Analytic Geometry and Calculus 3 (2 sections)
- 2020 Spring - Math 0220 Analytic Geometry and Calculus 1
- 2019 Fall - Math 0230 Analytic Geometry and Calculus 2 (3 sections)
- 2019 Spring - Math 0413 Intro to Theoretical Mathematics (2 sections)
- 2018 Fall - Math 0240 Analytic Geometry and Calculus 3 (3 sections)
- 2018 Spring - Math 0450 UHC Intro to Analysis
- 2017 Fall - Math 0220 Analytic Geometry and Calculus 1 (3 sections)

It is a good exercise to develop your own PDE solvers based on what you have learned in Numerical Analysis. However, for practical research computations, it is strongly recommended to use PDE solvers developed and refined by many researchers. There are many PDE solvers freely available online. Among others, I recommend the following PDE solvers - AMReX @ LBL and PETSc @ Argonne - for robust and efficient computations. Check out the following links.

Data assimilation combines a numerical forecast model with observational data to improve the prediction skill. If you are interested in testing/running data assimilation, please check the following programs.