Peimeng Yin

Department

Department of Mathematics

Research interest(s)/area of expertise

  • My main research interests lie in the field of Numerical analysis, applied mathematics and scientific
    computing,
    • Design and Analysis of numerical methods
    – Time discretization: Explicit/implicit method, Crank-Nicolson method, convex splitting
    method, Invariant Energy Quadratization (IEQ) apprach, scalar auxiliary variable (SAV)
    approach, Runge-Kutta (RK) methods.
    – Discontinuous Galerkin methods (DDG, IEQ-DG, RK-IEQ-DG, SAV-DG), Mixed DG ( with or without interior penalty);
    – Finite element methods, Mixed FEM methods, including graded meshes.
    • Numerical solution of nonlinear Partial Differential Equations
    – Elliptic equations (e.g., Poisson-Boltzmann equation, Biharmonic equation), Elliptic/Biharmonic
    problems (with singularities).
    – Time-dependent PDEs (e.g., Swift-Hohenberg equation, Cahn-Hilliard equation).
    • Asymptotic method for Kinetic equations (e.g., Bhatnagar-Gross-Krook (BGK) equation)

Education

  • 2019.08. Ph.D., Applied Mathematics, Iowa State University. Advisors: 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

 

2020

[11] Hailiang Liu and Peimeng Yin. On the high order IEQ-DG method for a class of fourth order gradient flows. , preprint.
[10] Hengguang Li, Peimeng Yin and Zhimin Zhang. High order $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain. , preprint.
[9] Hengguang Li, Peimeng Yin* and Zhimin Zhang. A $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain. SIAM Journal on Numerical Analysis, submitted.
[8] Hailiang Liu and Peimeng Yin. On the SAV-DG method for a class of fourth order gradient flows. Numerical Methods for Partial Differential Equations, submitted.
[7] Hengguang Li, Xiang Wan, Peimeng Yin* and Lewei Zhao. Regularity and finite element approximation for two-dimensional elliptic equations with line Dirac sources. Journal of Computational and Applied Mathematics, submitted.
[6] Hailiang Liu and Peimeng Yin*. Unconditionally energy stable DG schemes for the Cahn-Hilliard equation. Journal of Computational and Applied Mathematics, submitted.
[5] Hailiang Liu, James Ralston and Peimeng Yin. General Superpositions of Gaussian beams and propagation error. Mathematics of Computation, 89 (2020), pp. 675-697.

2019

[4] Hailiang Liu and Peimeng Yin. Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Journal of Scientific Computing, 81-2 (2019), pp. 789–819.

2018

[3] Hailiang Liu and Peimeng Yin. A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Journal of Scientific Computing, 77 (2018), pp. 467-501.
[2] Peimeng Yin, Yunqing Huang and Hailiang Liu. Error estimates for the iterative discontinuous Galerkin method to the nonlinear Poisson-Boltzmann equation. Communications in Computational Physics, 23 (2018), pp. 168-197.

2014

[1] Peimeng Yin, Yunqing Huang and Hailiang Liu. An iterative discontinuous Galerkin method for solving the nonlinear Poisson-Boltzmann equation. Communications in Computational Physics, 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).