Peimeng Yin

Department of Mathematics | Iowa State University

  Assistant Professor
  Department of Mathematical Sciences
  The University of Texas at El Paso
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Dr. Peimeng Yin is an Assistant Professor in the Department of Mathematical Sciences at the University of Texas at El Paso (UTEP). He received his Ph.D. degree in the Department of Mathematics from Iowa State University in 2019 under the supervision of Prof. Hailiang Liu and Prof. Songting Luo. Prior to joining ORNL, he worked as a Postdoctoral Research Associate in Computer Science and Mathematics Division at Oak Ridge National Laboratory (ORNL), a Research Assistant Professor (research-track) in the Department of Radiation Oncology at the University of Kansas Medical Center, and a Post-Doc Fellow in the Department of Mathematics at Wayne State University.

He works in the area of Computational Mathematics and Applied Mathematics with the main focus on Numerical Analysis, Partial Differential Equations, Scientific Computing, and Data Science. His work reflects a strong interplay of rigorous mathematical analysis, the design and implementation of accurate and efficient numerical algorithms for partial differential equations (PDEs), and their applications to physics, astrophysics, engineering, biology, energy, and oncology. His research interests focus on advanced numerical methods for modern PDE challenges, such as high derivatives, maximum principle preserving, singularities, high dimensions and multiscale.

Research Interests

• Discontinuous Galerkin finite element methods

• Structure preserving numerical methods

• Dynamical low rank approximations

• Time integration for gradient flows

• Efficient numerical methods for multiscale problems

• Theoretical and computational methods for singular elliptic PDEs

• Mathematical theory of deep learning and PDE-based data-driven modeling.

Selected recent work

Peimeng Yin, Eirik Endeve, Cory D. Hauck and Stefan R. Schnake. A semi-implicit dynamical low-rank discontinuous Galerkin method for space homogeneous kinetic equations. Part I: emission and absorption. , arXiv preprint, arXiv:2308.05914, 2023. [arXiv]

• 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. IMA Journal of Numerical Analysis, 43:1779-1801, 2023. [PDF] [DOI] [arXiv]

• Hailiang Liu and Peimeng Yin. On the SAV-DG method for a class of fourth order gradient flows. Numerical Methods for Partial Differential Equations, 39(2):1185-1200, 2023. [PDF] [DOI] [arXiv]

• Hailiang Liu, Zhongming Wang, Peimeng Yin and Hui Yu. Positivity-preserving third order DG schemes for Poisson--Nernst--Planck equations. Journal of Computational Physics, 452:110777, 2022. [PDF] [DOI]

• Hailiang Liu and Peimeng Yin*. High order unconditionally energy stable RKDG schemes for the Swift-Hohenberg equation. Journal of Computational and Applied Mathematics, 407:114015, 2022. [PDF] [DOI]

• Hailiang Liu and Peimeng Yin*. Unconditionally energy stable DG schemes for the Cahn-Hilliard equation. Journal of Computational and Applied Mathematics, 390:113375, 2021. [PDF] [DOI]