The University of Utah
Department of Mathematics
155 S. 1400 E., Rm 233
Salt Lake City, UT-84112
I successfully defended my PhD thesis in April 2019, under the supervision of Prof. Yekaterina Epshteyn. Starting in July 2019, I will be a Postdoctoral Research Associate working on computational nanophotonics at Department of Mathematical Sciences at Rensselaer Polytechnic Institute. 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.
ResearchMy 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 have worked on (i) high-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 am also interested in:
- moving boundary/interface problems.
- PDEs with dynamic boundary conditions (bulk-surface coupling).
- adaptive and highly scalable parallel numerical algorithms.
- Y. Epshteyn and Q. Xia, Efficient Numerical Algorithms based on Difference Potentials for Chemotaxis Systems in 3D, Journal of Scientific Computing, Volume 80, Issue 1, pages 26-59, July 2019. [DOI] [arXiv:1811.03557]
- 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. [DOI] [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. [DOI] [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. [DOI] [pdf]
- Y. Epshteyn and Q. Xia, Difference Potentials Method for Models with Dynamic Boundary Conditions and Bulk-Surface Problems, submitted, 2019. [pdf] [arXiv:1904.08362]
- Y. Epshteyn, K. R. Steffen, and Q. Xia, Difference Potentials Method for the Mullins-Sekerka model, in progress.
- Math 2280: Introduction to Differential Equations -- Summer 2018
- Math 1320: Engineering Calculus II -- Spring 2018, Fall 2018, Spring 2019
- 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
- Math 1320: Engineering Calculus II -- Spring 2014
- Math 2250: Differential Equations and Linear Algebra -- Fall 2013, Fall 2014, Fall 2016