Department of Mathematics
27 N Main Street
Hanover, NH 03755
Office : 200 Kemeny Hall
email : tongtong.li at dartmouth.edu
I am currently a postdoctoral researcher at the Department of Mathematics, Dartmouth College.
My research interests lie in the broad areas of computational and applied mathematics, including numerical analysis and solution of partial differential equations (PDEs), data assimilation and Bayesian inverse problems. On one hand, I focus on the development, theoretical analysis and computational implementation of numerical methods that approximate solutions of PDEs arising from complex systems in various fields, including environmental sciences, petroleum engineering, hydrology and biomechanics engineering. While PDEs serve as an essential tool to understand and predict dynamics, judicious treatment of data is crucial due to the structural complexity and computational intensity within these dynamics. In this regard, I am interested in the study of computational methods that enhance the information we can extract from existing data and knowledge by employing data assimilation and Bayesian approaches. My research aims to design rigorous and comprehensive methods for meaningful descriptions and novel treatments of systems in scientific and engineering applications, by leveraging advanced tools developed in areas including numerical analysis, data assimilation and Bayesian inference, understanding the underlying philosophies of each area, and forging connections between them.
I received my PhD in Mathematics under the supervision of Professor Ivan Yotov at the University of Pittsburgh.
Numerical Analysis: numerical solution of partial differential equations, finite element methods, numerical conservation laws, high order methods
Data Assimilation: sequential inference, ensemble learning
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: 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).
Jack E. Friedman (together with Anne Gelb), 2022 - 2023
David J. Appleton (together with Anne Gelb), 2022 - 2023
Graduate student directed reading
Jessica Rattray (Numerical Solution of PDEs), Spring 2023
University of Pittsburgh
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
Teaching Fellow / Teaching Assistant
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.