Contact

  The University of Utah
          Department of Mathematics
          155 S. 1400 E., Rm 233
          Salt Lake City, UT-84112
  xia math.utah.edu

About me

I'm pursuing my PhD degree in Mathematics at the University of Utah under the supervision of Yekaterina Epshteyn. I'm expecting to defend my thesis in Spring 2019. Currently I'm preparing for job applications, which I will be submitting this fall for postdoctoral research positions. Before coming to Utah, I completed my bachelor's degree in Applied Mathematics at Central University of Finance and Economics in Beijing. Here is my CV.

Research

My PhD research focuses on numerical algorithms based on Difference Potentials Method (DPM) for PDEs in complex geometries. DPM allows us to handle complex geometries with uniform Cartesian meshes, without loss of accuracy near the irregular boundary/interface. In particular, together with my collaborators, I worked on (i) higher order accurate methods based on DPM for interface problems in 2D; and (ii) a domain decomposition method based on DPM for simulation of chemotaxis models in 3D.
I'm also interested in:
  • moving boundary/interface problems.
  • PDEs with dynamic boundary conditions (bulk-surface coupling).
  • adaptive and highly scalable parallel numerical algorithms.

Publications

  • Y. Epshteyn and Q. Xia, Upwind Difference Potentials Method for chemotaxis systems in 3D, in preparation.
  • Y. Epshteyn, K. R. Steffen, and Q. Xia, Difference Potentials Method for the Mullins-Sekerka model, in progress.
  • G. Ludvigsson, K.R. Steffen, S. Sticko, S. Wang, Q. Xia, Y. Epshteyn and G. Kreiss, High-order numerical methods for 2D parabolic problems in single and composite domains, Journal of Scientific Computing, Volume 76, Number 2, pages 812–847, January 2018 [arXiv: 1707.08459]
  • J. Albright, Y. Epshteyn and Q. Xia, High-Order Accurate Methods Based on Difference Potentials for 2D Parabolic Interface Models, Communications in Mathematical Sciences, Volume 15, Number 4, pages 985-1019, 2017. [pdf]
  • J. Albright, Y. Epshteyn, M. Medvinsky and Q. Xia, High-order numerical schemes based on difference potentials for 2D elliptic problems with material interfaces, Applied Numerical Mathematics, Volume 111, pages 64-91, January 2017. [pdf]

Teaching

Instructor
  • Math 2280: Introduction to Differential Equations -- Summer 2018
  • Math 1320: Engineering Calculus II -- Spring 2018, Fall 2018
  • Math 1311: Accelerated (Honors) Engineering Calculus I -- Fall 2017
  • Math 1220: Calculus II -- Summer 2016
  • Math 2250: Differential Equations and Linear Algebra -- Spring 2016, Spring 2017
  • Math 1060: Trigonometry -- Fall 2015
  • Math 1090: College Algebra for Business and Social Sciences -- Spring 2015
Teaching Assistant
  • Math 1320: Engineering Calculus II -- Spring 2014
  • Math 2250: Differential Equations and Linear Algebra -- Fall 2013, Fall 2014, Fall 2016