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Peng Wei

Peng Wei

As described in my application letter, a majority of my research interests focuses on the analysis, approximation and simulation of partial differential equations (PDEs) involving fractional diffusion operators. The latter gained recent popularity for their ability to model non-local phenomenons in material science, finance, fluid dynamics, and imaging to name a few.

A typical example is the electro-convection effect in thin liquid crystal film for which a small quantity of charged fluid can be put in rotational motion using an electric potential difference. The complexity of the resulting system of equations prevents accurate approximation, even with modern computing techniques. My work focused on a model reduction approach leading to fractional operators. Both, mathematically and computationally, the intriguing part of this research is the coupling of nonlinear effects with nonlocal operators.

Currently, I am working on a manuscript discussing the mathematical and approximation properties of the charge equation. At the same time, I am at the testing stage of the parallel algorithm I have implemented for the electro-convection system. Upon completion of this phase, I am planning to compare my numerical simulation with laboratory experiments.

I attended the annual Finite Element Rodeo 2017 held at University of Houston in March 2017. I will attend the Nonlocal School on Fractional Equations held at Iowa State University in August. The summer school topics include Modeling, Regularity Theory, and Numerical Analysis for fractional nonlocal PDEs.

My HEEP Fellowship funding allowed me to focus on my research. I deepened my knowledge and experience in numerical analysis, approximation theory while improving my scientific programming abilities. It also offered me the opportunity to learn from and work with worldwide top experts in these areas, which in turn bolstered my confidence of seeking researching position in academia after my graduation.

Mr. Wei was not able to collaborate with Faculty Fellow Dr. Ingrid Daubechies this past year as originally planned due to a schedule change.  However, he is hopeful to collaborate with her when she comes to Texas A&M at a later time.

Major

Applied Mathematics

Graduation Year

August 2019

Degree Type

Ph.D.

Fellowship Year(s)

'16-'17

Previous Education

M.S. in Computational Mathematics - China University of Mining and Technology - '11
B.S. in Information and Computing Science - China University of Mining and Technology - '08

Advisor

Andrea Bonito

Presentations

Finite Element Rodeo 2017 held at University of Houston. No conference paper.

Personal Webpage

http://www.math.tamu.edu/~weip/