Department of Mathematics
Research interest(s)/area of expertise
Numerical Analysis, Applied Mathematics, Scientific Computing, Partial Differential Equations, Computational Plasma Physics
My main research interests lie in the field of Numerical analysis, applied mathematics and scientific computing,
• Design and Analysis of numerical methods
– Direct discontinuous Galerkin methods, Mixed discontinuous Galerkin methods, finite element methods, Finite diffrente methods, Graded meshes
• Numerical solution of nonlinear Partial Differential Equations, such as Elliptic equations (e.g.,Poisson-Boltzmann equation, Biharmonic equation), time-dependent PDEs ( Swift-Hohenberg equation, and Cahn-Hilliard equation), singular problems
• Asymptotic method for Kinetic equations (e.g., Bhatnagar-Gross-Krook (BGK) equation)
- 2019.08. Ph.D., Applied Mathematics, Iowa State University. Advisor: Hailiang Liu & Songting Luo
Awards and grants
1. Spring 2019, Mario Gutierrez Fund for International Graduate Students, International Students and Scholars Office, Iowa State University.
2. Fall 2017, Wolfe Research Fellowship: one semester free of teaching duties for focusing on research awarded for Spring 2018, Iowa State University.
1. (With Hailiang Liu.) Unconditionally energy stable SAV-DG schemes for the Swift-Hohenberg
equation. in preparation.
2. (With Henguang Li, etc.) Finite Element Method for Laplace Equation in Two-dimensional Do-
mains with a Singular Fracture. in preparation.
3. Hailiang Liu and Peimeng Yin. Unconditionally energy stable DG schemes for the Cahn-Hilliard
equation. Submitted to J. Comput. Phys.
4. Hailiang Liu, James Ralston and Peimeng Yin. General Superpositions of Gaussian beams and
propagation errors. Math. Comp. 89 (2020), pp. 675-697.
5. Hailiang Liu and Peimeng Yin. Unconditionally energy stable DG schemes for the Swift-
Hohenberg equation. Submitted to J. Sci. Comput. 81-2 (2019), pp. 789-819.
6. Hailiang Liu and Peimeng Yin. A mixed discontinuous Galerkin method without interior penalty
for time-dependent fourth order problems. J. Sci. Comput., 77-1 (2018), pp. 467-501.
7. Peimeng Yin, Yunqing Huang and Hailiang Liu. Error estimates for the iterative discontinuous
Galerkin method to the nonlinear Poisson-Boltzmann equation. Commun. Comput. Phys., 23-1
(2018), pp. 168-197.
8. Peimeng Yin, Yunqing Huang and Hailiang Liu. An iterative discontinuous Galerkin method
for solving the nonlinear Poisson-Boltzmann equation. Commun. Comput. Phys., 16 (2014), pp.
Winter 2020, MAT 2020, Calculus II; MAT 2030, Calculus III.
• Instructor at Wayne State University:
– Winter 2020, MAT 2020, Calculus II; MAT 2030, Calculus III.
– Fall 2019, MAT 2020, Calculus II.
• Instructor at Iowa State University:
– Summer 2016, MATH 166, Calculus II.
– Summer 2015, MATH 492, Undergraduate Seminar (Numerical Analysis).
• Recitation Leader at Iowa State University:
– Fall 2016 / Fall 2017 / Fall 2018, MATH 143, Precalculus (6 sections).
– Spring 2016 / Spring 2017, MATH 267, ODEs and Laplace Transforms (6 sections).
– Spring 2015, MATH 166, Calculus II (3 sections).