Peimeng Yin

Department

Department of Mathematics

Research interest(s)/area of expertise

  • Numerical Analysis, Applied Mathematics, Scientific Computing, Partial Differential Equations, Computational Plasma Physics

Research

 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)

Education

  • 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.

Selected publications

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.
491-515.

Currently teaching

  • Winter 2020, MAT 2020, Calculus II; MAT 2030, Calculus III.

Courses taught

• 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).