Research Interests:

My research interests focus on the construction, analysis, and application of numerical methods to solve partial differential equations that arise in emerging fields, especially those governed by hyperbolic conservation laws and those involving moving or complicated geometries. In addition to conducting rigorous analysis of the proposed methods and developing related computational tool in parallel computing environments, I collaborate with various research groups from across the world on problems like tumor growth modeling, simulation of virotherapy, river meandering study, and reduced-order models of complex flows. Last but not the least, I work on high-performance computing challenges related to these problems.

My current research topics include:

- A inherently superconvergent hybrid-variable (HV) discretization framework for hyperbolic and parabolic partial differential equations.

- Mathematical and numerical investigation of time-delayed PDE model of biological systems such as immune cell infiltration in tumor dynamics and virus infection of skin cells.

- A shifted boundary method (SBM) for compressible flows on complicated or moving boundaries, and related reduced order models (ROM).

- An ALE-EBM method that enables embedded boundary computation of multi-material flows on moving grids, with particular interest in shock hydrodynamics and fluid-structure interactions.

- Mathematical and numerical investigation of meandering instability in various fluid-like systems, with model validation with field observation and experimental data.

Xianyi Zeng

Assistant Professor

Department of Mathematics

Lehigh University

Bethlehem, PA 18015

Office: Chandler-Ullmann Hall 247

Phone: 610-758-3745

Email: xyzeng(at)lehigh(dot)edu

Brief Biography:

In the summer of 2002, I won a gold medal in the 43rd IMO held at Glasgow, United Kindom, which earned me the acceptance to the School of Mathematical Sciences at Peking University, China. I received my B.S. in mathematics in 2006; and I worked with Dr. Maozhi Xu on my undergraduate thesis on constructing high degree prime polynomials on the binary field with applications in modern cryptography. During the same period, I received a second B.S. in economics from China Center for Economic Research (now known as National School of Development).

I spent my graduate years (2006-2012) in the the Institute for Computational & Mathematical Engineering at Stanford University; and I earned my Ph.D. in the June of 2012. My thesis work was about high-order embedded boundary methods for fluid-structure interactions with large structural motions, advised by Dr. Charbel Farhat. Subsequently I left Farhat Research Group for Duke University, and became the first lab member of Dr. Guglielmo Scovazzi as a postdoctoral scholar.

While at Stanford University, I also completed many courses in statistics and stochastic differential equations, which earned me a Master degree in financial mathematics (2007-2010).

Starting the Fall semester of 2016, I am an assistant professor at the Department of Mathematical Sciences and Computational Science Program at the University of Texas at El Paso. In the Spring semester of 2022, my tenure promotion was approved by the University of Texas System, and then I moved to the Department of Mathematics at Lehigh University as an assistant professor for family reasons.