Overview

Dr. Yuan Liu is an Associate Professor of Applied Mathematics in the Department of Mathematics, Statistics, and Physics at 黑洞社区. Dr. Liu earned her PhD in Applied Math from the University of Notre Dame in 2012. She held Assistant Professorship at 黑洞社区 (2019 - 2023) and Mississippi State University (2015 - 2019). She was a Visiting Assistant Professor at Michigan State University from 2012-2015.

Dr. Liu鈥檚 research interests lie in numerical analysis, scientific computing and computational biology. Particularly, her research focus on designing, analyzing and implementing high order numerical methods for solving partial differential equations arising in physical phenomena. The numerical methods she has been working on include discontinuous Galerkin (DG) methods, (weighted) essentially non-oscillatory (ENO/WENO) methods and spectral methods.

Information

Academic Interests and Expertise
  • Numerical Analysis
  • Scientific Computing
  • Computational Biology
Areas of Teaching Interest
  • Numerical Methods
  • Numerical Linear Algebra
  • Finite Element Methods
  • Differential Equations
Publications
  • Liu, Q. Liu, Y. Liu, C.-W. Shu and M. Zhang, Locally divergence-free spectral-DG methods for ideal magnetohydrodynamic equations on cylindrical coordinates. Communications in Computational Physics, v26(3), (2019), pp.631-653.
  • Liu, Y. Cheng, S. Chen, and Y.-T. Zhang, Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations. Journal of Computational Physics, v388, (2019), pp. 90-102.
  • Du, Y. Liu, Y. Liu and Z. Xu, Well balanced discontinuous Galerkin methods for shallow water equations with constant subtraction on unstructured grids, Journal of Scientific Computing, v81, (2019), pp. 2115-2131.
  • Huang, Y. Liu, W. Guo, Z. Tao and Y. Cheng. An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form, Journal of Scientific Computing, v85(13), 2020.
  • Z. Tao, J. Huang, Y. Liu, W. Guo,  and Y. Cheng. An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations, Communications on Applied Mathematics and Computation, to appear, 2021.