Research Interests:

I work on both the theoretical and the practical sides of scientific computing and partial differential equations. One of my research focuses is nonlinearly stable and high-order numerical methods for nonlinear hyperbolic systems, including those appear in continuum mechanics and biological systems. Another one of my research topics is stabilized methods for very stiff problems, such as transient dynamics of nearly incompressible materials. Finally, I have continuous interest in fluid-structure interactions and multi-phase flow simulations.

Currently, my research focuses are:

- A new hybrid-variable (HV) discretization framework for hyperbolic and parabolic partial differential equations, which delivers higher order accuracy in comparison with conventional methods given the same computational costs.

- Numerical methods for infiltration dynamics of differential-equations based tumor growth models, including both partial differential equations and stochastic partial differential equations.

- A simple, stable, and accurate finite element method for solid dynamics of materials that are: linear or nonlinear, elastic or inelastic, compressible or nearly incompressible, and isotropic or anisotropic.

- An embedded boundary method (EBM) combined with arbitrary Lagrangian-Eulerian (ALE) flow computations for multi-material flows in the context of shock hydrodynamics or fluid-structure interactions.

Xianyi Zeng

Assistant Professor

Department of Mathematical Sciences

Computational Science Program

University of Texas at El Paso

El Paso, TX 79968

Office: Bell Hall 202

Phone: 915-747-6759

Email: xzeng(at)utep(dot)edu

Brief Biography:

I received B.S. in mathematics from the School of Mathematical Sciences at Peking University, China, in 2006. 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.