Tongtong Li

Tongtong Li

Department of Mathematics
Dartmouth College
27 N Main Street
Hanover, NH 03755

Office : 200 Kemeny Hall
email : at

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.

Research Interests





My CV is available for download here [link]

Journal papers and preprints


Dartmouth College


Undergraduate student research mentoring

Graduate student directed reading

University of Pittsburgh


Teaching Fellow / Teaching Assistant

PDE solvers

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 Codes

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.

If you are interested in a MATLAB program for data assimilation, you can check the following book by Law, Stuart and Zygalakis, which contains MATLAB codes