Fangyan Yao

Hung Hom, Hong Kong

fangyan.yao[AT]polyu.edu.hk

I am currently a Research Assistant Professor (RAP) in the Department of Applied Mathematics at The Hong Kong Polytechnic University (PolyU). My research focuses on numerical analysis and scientific computing, with particular interests in the design and analysis of algorithms for nonlinear dispersive equations, including:

Nonlinear Schrödinger equations
Korteweg-de Vries equations
Nonlinear wave equations

I completed both my Ph.D. degrees at South China University of Technology, where I worked under the guidance of Prof. Yongsheng Li and Prof. Yifei Wu on Low-regularity integrators and derivation from mean-field limit of some nonlinear Schrödinger equations. During this time, I was awarded the CSC scholarship as a joint training Ph.D. student at the University of Innsbruck, Austria, where I had the opportunity to work with Prof. Alexander Ostermann. Afterward, I joined PolyU as a postdoctoral fellow, collaborating with Prof. Buyang Li on developing low-regularity integrators for nonlinear dispersive equations.

I’m enthusiastic about connecting with fellow researchers and students. If you’re interested in collaborating on exciting numerical PDE projects, feel free to reach out!

news

Jun 24, 2025	I will be attending the 30th Biennial Numerical Analysis Conference hosted by the University of Strathclyde.

selected publications

Convergence of a moving window method for the Schrödinger equation with potential on R^d

Arieh Iserles , Buyang Li, and Fangyan Yao

2024

Preprint

Bib

@unpublished{Iserles-Li-Yao,
  author = {Iserles, Arieh and Li, Buyang and Yao, Fangyan},
  title = {Convergence of a moving window method for the Schr\"odinger equation with potential on R^d},
  note = {Preprint},
  url = {https://arxiv.org/abs/2408.09463},
  year = {2024},
}

SIAM J. Numer. Anal.

Numerical approximation of discontinuous solutions of the semilinear wave equation

Jiachuan Cao , Buyang Li, Yanping Lin, and Fangyan Yao

SIAM Journal on Numerical Analysis, 2024

DOI Bib

@article{Cao-Li-Lin,
  author = {Cao, Jiachuan and Li, Buyang and Lin, Yanping and Yao, Fangyan},
  title = {Numerical approximation of discontinuous solutions of the semilinear wave equation},
  journal = {SIAM Journal on Numerical Analysis},
  year = {2024},
  doi = {10.1137/24M1635879},
  dimensions = {true},
  url = {https://arxiv.org/abs/2312.10392},
}

Math. Comp.

A first-order Fourier integrator for the nonlinear Schrödinger equation on T without loss of regularity

Yifei Wu, and Fangyan Yao

Mathematics of Computation, 2022

DOI Bib

@article{Wu-Yao,
  author = {Wu, Yifei and Yao, Fangyan},
  title = {A first-order Fourier integrator for the nonlinear Schrödinger equation on T without loss of regularity},
  journal = {Mathematics of Computation},
  year = {2022},
  volume = {91},
  doi = {10.1090/mcom/3705},
  number = {335},
  dimensions = {true},
  pages = {1212--1235},
  url = {https://www.ams.org/journals/mcom/2022-91-335/S0025-5718-2021-03705-9/home.html},
}

A fully discrete low-regularity integrator for the nonlinear Schrödinger equation

Alexander Ostermann, and Fangyan Yao

Journal of Scientific Computing, 2022

DOI Bib

@article{Ostermann-Yao,
  author = {Ostermann, Alexander and Yao, Fangyan},
  title = {A fully discrete low-regularity integrator for the nonlinear Schr\"odinger equation},
  journal = {Journal of Scientific Computing},
  year = {2022},
  volume = {91},
  number = {1},
  pages = {9},
  dimensions = {true},
  doi = {10.1007/s10915-022-01786-y},
  url = {https://link.springer.com/10.1007/s10915-022-01786-y},
}