Fengyan Li

Professor, Mathematical Sciences

Dr. Fengyan Li received her BS and MS degrees in Computational Mathematics from Peking University in 1997 and 2000, respectively, and her PhD degree in Applied Mathematics from Brown University in 2004. Before she joined RPI in 2006, she held a postdoc position at University of South Carolina.

Dr. Li's research interests and activities are mainly in Numerical Analysis and Scientific Computing. Her research focuses on the design and analysis of robust and highly accurate computational methods, especially discontinuous Galerkin finite element methods, with applications such as in wave propagation, fluid dynamics, rarefied gas dynamics, plasma physics, astrophysics, and nonlinear optics. Dr. Li received a Stella Dafermos Award at Brown University in 2004, and was a recipient of Alfred P. Sloan Research Fellowship in 2008. In 2009, she was granted an NSF-CAREER award for her research in high order methods and their applications. Dr. Li. was a plenary speaker a the 2015 Annual Meeting of Computational Mathematics in China (Guangzhou, China) , and at the International Conference on Spectral and High Order Methods (ICOSAHOM, London, UK) in 2018. Currently, Dr. Li is serving on the editorial board of SIAM Journal of Numerical Analysis, CSIAM Transaction on Applied Mathematics, and Applied Mathematics and Mechanics (English Edition). She was an associate editor for SIAM Journal of Numerical Computing during 2014-2019.

Dr. Li has been actively involved in Association for Women in Mathematics (AWM) and Women in Numerical Analysis and Scientific Computing (WINASC) Research Network. In 2015, she co-organized a mini-symposium and served as a career panelist at the 8th International Congress on Industrial and Applied Mathematics (ICIAM) in Beijing (China), she was also an invited speaker at the workshop, Women in Applied Maths & Soft Matter Physics, in Mainz (Germany); She has been serving as a mentor through AWM Mentor Network since 2011, and as a faculty advisor of the AWM Student Chapter at RPI since 2016. Dr. Li is currently a member of the Steering Committee of WINASc.

Education

Ph.D. in Applied Mathematics, Brown University, 2004

M.S. in Computational Mathematics, Peking University, 2000

B.S. in Computational Mathematics, Peking University, 1997

Research Focus
  • Discontinuous Galerkin methods; Finite element methods
  • High order methods for MHD, Hamilton-Jacobi, Maxwell's equations in linear and nonlinear media, Vlasov-Maxwell equations, multi-scale kinetic transport models, fluid models
  • High order structure-preserving methods: divergence-free, well-balanced, energy stable/conservative, positivity preserving, asymptotic preserving
  • Model order reduction: numerical algorithms and analysis
Contact Information
Select Works
  • Z. Peng and F. Li, Asymptotic preserving IMEX-DG-S schemes for linear kinetic transport equations based on Schur complement, SIAM Journal on Scientific Computing, accepted (2020)
  • Z. Peng, Y. Cheng, J.-M. Qiu, F. Li, Stability-enhanced AP IMEX1-LDG method: energy-based stability and rigorous AP property, SIAM Journal on Numerical Analysis, accepted (2020)
  • Z. Peng, Y. Cheng, J.-M. Qiu, F. Li, Stability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scaling, Journal of Computational Physics, v415 (2020), pp.109485
  • Z. Peng, V.A. Bokil, Y. Cheng, F. Li, Asymptotic and positivity preserving methods for Kerr-Debye model with Lorentz dispersion in one dimension, Journal of Computational Physics, v402 (2020), 109101
  • D. Appelo, V.A. Bokil, Y. Cheng, F. Li, Energy stable SBP-FDTD methods for Maxwell-Duffing models in nonlinear photonics, IEEE Journal on Multiscale and Multiphysics Computational Techniques, v4 (2019), pp.329-336
  • Y. Jiang, P. Sakkaplangkul, V.A. Bokil, Y. Cheng, F. Li, Dispersion analysis of finite difference and discontinuous Galerkin schemes for Maxwell's equations in linear Lorentz media, Journal of Computational Physics, v394 (2019), pp.100-135
  • A. Chen, F. Li, Y. Cheng, An ultra-weak discontinuous Galerkin method for Schrodinger equation in one dimension, Journal of Scientific Computing, v78 (2019), pp.772-815
  • P. Fu, Y. Cheng, F. Li, Y Xu, Discontinuous Galerkin methods with optimal L2 accuracy for one dimensional linear PDEs with high order spatial derivatives, Journal of Scientific Computing, v78 (2019), pp.816-863