Peimeng Yin

I am a Postdoctoral Research Associate in Computer Science and Mathematics Division at Oak Ridge National Laboratory (ORNL). I received my Ph.D. 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, I worked as a Post-Doc Fellow in the Department of Mathematics at Wayne State University, a Research Assistant Professor (research-track) in the Department of Radiation Oncology at the University of Kansas.

I work in the area of Computational Mathematics and Applied Mathematics with the main focus on Numerical Analysis, Partial Differential Equations, and Scientific Computing. My work reflects a strong interplay of rigorous mathematical analysis, the design and implementation of accurate and efficient numerical algorithms for partial differential equations, and their applications to physics, astrophysics, engineering, biology, energy, and medicine.

I am a Mathematical Reviews/MathSciNet Reviewer, and a referee for many journals, such as Journal of Scientific Computing, Journal of Computational and Applied Mathematics, Numerical Algorithms, etc.

Research Interests

• Discontinuous Galerkin finite element method - FEM, DG, DDG, IPDG, Mixed DG, penalty free DG, etc.

• Numerical methods for gradient flows - BDFk, CN, RK; stabilized, (convex) splitting, IEQ, SAV, etc.

• Structure preserving numerical methods - Positive/Maximum principle preserving, mass, energy, etc.

• Theories and numerical methods for PDEs with singularities - FEM/Adaptive FEM/$C^0$ IPDG, Poisson/Stokes/biharmonic/triharmonic equations.

• Dynamical low-rank method for transport and kinetic equations - Application in medical problems, astrophysics, etc.

• Mathematical theory of deep learning.