Research

Research interests

I work in the area of Computational Mathematics and Applied Mathematics with the main focus on Numerical Analysis, Partial Differential Equations, Optimal transport, Optimization, and Scientific Computing. I am interested in the design and implementation of accurate and efficient numerical algorithms for partial differential equations, and their applications to physics, engineering, and biology. 

Journals Publications

  1. A dynamic mass transport method for Poisson-Nernst-Planck equations  (with H. Liu), Journal of Computational Physics, 2023
  2.  Efficient, positive, and energy stable schemes for multi-D Poisson–Nernst–Planck Systems (with H. Liu), Journal of Scientific Computing, 2021
  3. Positive and free energy satisfying schemes for diffusion with interaction potentials  (with H. Liu), Journal of Computational Physics , 2020
  4. Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system  (with H. Liu), Communications In Computational Physics , 2019
  5. Fourth-Order Finite Difference Approach for Numerical Solution of Burgers Equation(with Kayser, Nurmemet),  2010 International Conference on Multimedia Information Networking and Security-2010

Conference Talks

  1. Positive and free energy satisfying second order schemes for Poisson-Nernst-Planck Equations— at The 5th Annual Meeting of SIAM Central States Section, Iowa State University, IA. October 2019 (Invited)
  2. Positivity-preserving Schemes for Poisson-Nernst-Planck Equations— at SIAM Conference on Computational Science and Engineering, Spokane, WA. February 2019
  3. Positive and free energy satisfying schemes for diffusion with interaction potentials— at The 4th Annual Meeting of SIAM Central States Section, University of Oklahoma, OK. October 2018
  4. A free energy satisfying discontinues Galerkin method for one-dimensional Poisson-Nernst-Planck systems— at The Midwest Numerical Analysis Day 2017, University of Nebraska, NE. April 2017

Seminar Talks

  1. A dynamic mass transport method for Poisson-Nernst-Planck equations— at Optimal transport and mean field games at University of California Los Angeles, IA, September 2021
  2. Efficient, positive, and energy stable schemes for multi-D Poisson-Nernst-Planck systems— at CAM seminar at Iowa State University, IA, October 2020
  3. Fisher information regularization schemes for Wasserstein Gradient Flows— at Analysis Seminar, Iowa State University, IA, September 2019
  4. Positive and free energy satisfying schemes for diffusion with interaction potentials— at SIAM Seminar, Iowa State University, IA, November 2018
  5. Positive and energy stable schemes for gradient flow structure— at CAM seminar at Iowa State University, IA. March 2018

Conference Attendance

  1. SIAM Conference on Analysis of Partial Differential Equations, La Quinta, CA, Dec 2019
  2. The 5th Annual Meeting of SIAM Central States Section, Iowa State University, IA. Oct 2019
  3. The Midwest Numerical Analysis Day 2019, Illinois Institute of Technology, IL. April 2019
  4. SIAM Conference on Computational Science and Engineering, Spokane, WA. February 2019
  5. The 4th Annual Meeting of SIAM Central States Section, University of Oklahoma, OK. Oct 2018
  6. The Midwest Numerical Analysis Day 2018, university of Kansas, KS. April 2018
  7. Recent Advances and Challenges in Discontinues Gallerkin Methods and Related Approaches, University of Minnesota, MN. June 2017
  8. The Midwest Numerical Analysis Day 2017, University of Nebraska, NE. April 2017
  9. Kinetic Discriptin of Chemical and biological Systems: Models, Analysis and Numerics, Iowa State University, IA. March 2017