Department of Mathematics
Research interest(s)/area of expertise
- Numerical methods for PDEs with high order spatial derivatives - FEM, DG, DDG, Mixed DG, penalty free DG.
- Numerical methods for Gradient flows - BDF1, BDF2, CN, convex splitting, IEQ, SAV, RK, etc.
- Theories and numerical methods for PDEs with singularities.
- Maximum principle preserving numerical methods.
- Computational high frequency wave propagation.
- Computational biology - (Poisson-Boltzmann, Poisson-Nernst-Planck)
- Mathematical theory of deep learning.
More details, please view
- 2019.08. Ph.D., Applied Mathematics, Iowa State University. Advisors: Hailiang Liu & Songting Luo
Awards and grants
1. April 2021, Postdoctoral Trainee Research Award, Wayne State University.
2. Spring 2019, Mario Gutierrez Fund for International Graduate Students, International Students and Scholars Office, Iowa State University.
3. Fall 2017, Wolfe Research Fellowship: one semester free of teaching duties for focusing on research awarded for Spring 2018, Iowa State University.
13. Hengguang Li and Peimeng Yin. A $C^0$ finite element method for the six order problem with the simply supported boundary conditions in a polygonal domain. , preprint.
12. Hailiang Liu, Zhongming Wang, Peimeng Yin and Hui Yu. Positivity-preserving third order DG schemes for Poisson--Nernst--Planck equations. Journal of Computational Physics, submitted, arXiv preprint, arXiv:2102.00101, 2021.
11. Hailiang Liu and Peimeng Yin. Energy stable Runge-Kutta discontinuous Galerkin schemes for a class of fourth order gradient flows. , submitted, arXiv preprint, arXiv:2101.00152, 2021.
10. Hengguang Li and Peimeng Yin. Optimal high order $C^0$ finite element method for the biharmonic problem with hinged boundary conditions. , preprint.
9. 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. arXiv preprint, arXiv:2008.11877, 2020.
8. 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, in revision, arXiv:2012.12374, 2020.
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,, 393:113518, 2021.
 Hailiang Liu and Peimeng Yin*. Unconditionally energy stable DG schemes for the Cahn-Hilliard equation. Journal of Computational and Applied Mathematics, 390:113375, 2021.
 Hailiang Liu, James Ralston and Peimeng Yin. General Superpositions of Gaussian beams and propagation error. Mathematics of Computation, 89 (2020), pp. 675-697.
 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.
 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.
 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.
 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.
- Winter 2021, MAT 2020, Calculus II.
• Instructor at Wayne State University:
– Winter 2021, MAT 2020, Calculus II.
– Fall 2020, MAT 2010, Calculus I (2 sections).
– 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).