Biography

I am working at the School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan 610068, P.R. China. I focus on the fast and parallel numerical methods (maybe temporal or/and spatial non-uniform meshes) with low storage requirement for time or/and space fractional differential equations (e.g., advection-diffusion equations, Schrödinger equation, Allen-Cahn equation, Black-Scholes Model, etc.). Discussions will be highly welcome.

Email: ylzhaofde@sina.com
Follow me: Google Scholar Researchgate GitHub
More about me: CV (under construction)

Selected publications

2021

Yong-Liang Zhao, Alexander Ostermann, Xian-Ming Gu, A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations, Journal of Computational Physics, 446 (2021) 110652. [BibTeX] [link] [slide]

@article{zhao2021low,
  title={A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations},
  author={Zhao, Yong-Liang and Ostermann, Alexander and Gu, Xian-Ming},
  journal={Journal of Computational Physics},
  pages={110652},
  year={2021},
  doi={10.1016/j.jcp.2021.110652},
  publisher={Elsevier}
}

Yong-Liang Zhao, Xian-Ming Gu, Alexander Ostermann, A preconditioning technique for an all-at-once system from Volterra subdiffusion equations with graded time steps, Journal of Scientific Computing, 88 (2021) 11. [BibTeX] [link]

@article{zhao2021preconditioning,
  title={A Preconditioning Technique for an All-at-once System from Volterra Subdiffusion Equations with Graded Time Steps},
  author={Zhao, Yong-Liang and Gu, Xian-Ming and Ostermann, Alexander},
  journal={Journal of Scientific Computing},
  volume={88},
  number={1},
  pages={1--22},
  year={2021},
  doi={10.1007/s10915-021-01527-7},
  publisher={Springer}
}

Yong-Liang Zhao, Meng Li, Alexander Ostermann, Xian-Ming Gu, An efficient second-order energy stable BDF scheme for the space fractional Cahn–Hilliard equation, BIT Numerical Mathematics, 61 (2021) 1061–1092. [BibTeX] [link]

@article{zhao2021efficient,
  title={An efficient second-order energy stable BDF scheme for the space fractional Cahn--Hilliard equation},
  author={Zhao, Yong-Liang and Li, Meng and Ostermann, Alexander and Gu, Xian-Ming},
  journal={BIT Numerical Mathematics},
  pages={1--32},
  year={2021},
  publisher={Springer}
}

Yong-Liang Zhao, Xian-Ming Gu, Meng Li, Huan-Yan Jian, Preconditioners for all-at-once system from the fractional mobile/immobile advection–diffusion model, Journal of Applied Mathematics and Computing, 65 (2021) 669–691. [BibTeX] [link]

@article{zhao2021preconditioners,
  title={Preconditioners for all-at-once system from the fractional mobile/immobile advection--diffusion model},
  author={Zhao, Yong-Liang and Gu, Xian-Ming and Li, Meng and Jian, Huan-Yan},
  journal={Journal of Applied Mathematics and Computing},
  volume={65},
  number={1},
  pages={669--691},
  year={2021},
  publisher={Springer}
}

Xian‐Ming Gu, Hai‐Wei Sun, Yanzhi Zhang, Yong‐Liang Zhao^*, Fast implicit difference schemes for time‐space fractional diffusion equations with the integral fractional Laplacian, Mathematical Methods in the Applied Sciences, 44 (2021) 441-463. [link]
Xian-Ming Gu, Yong-Liang Zhao^*, Xi-Le Zhao, Bruno Carpentieri, Yu-Yun Huang, A note on parallel preconditioning for the all-at-once solution of Riesz fractional diffusion equations, Numerical Mathematics: Theory, Methods and Applications, 14 (2021) 893-919. [link]
Xian-Ming Gu, Hai-Wei Sun, Yong-Liang Zhao, Xiangcheng Zheng, An implicit difference scheme for time-fractional diffusion equations with a time-invariant type variable order, Applied Mathematics Letters, 120 (2021) 107270. [link]
Xian-Ming Gu, Ting-Zhu Huang, Yong-Liang Zhao, Pin Lyu, Bruno Carpentieri, A fast implicit difference scheme for solving the generalized time-space fractional diffusion equations with variable coefficients, Numerical Methods for Partial Differential Equations, 37 (2021) 1136-1162. [link]
Huan-Yan Jian, Ting-Zhu Huang, Alexander Ostermann, Xian-Ming Gu, Yong-Liang Zhao, Fast IIF–WENO method on non-uniform meshes for nonlinear space-Fractional convection–diffusion–reaction equations, Journal of Scientific Computing, 89 (2021) 13. [link]

2020

Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu, Xi-Le Zhao, Huan-Yan Jian, A preconditioning technique for all-at-once system from the nonlinear tempered fractional diffusion equation, Journal of Scientific Computing, 83 (2020) 10. [BibTeX] [link]

@article{zhao2020preconditioning,
  title={A preconditioning technique for all-at-once system from the nonlinear tempered fractional diffusion equation},
  author={Zhao, Yong-Liang and Zhu, Pei-Yong and Gu, Xian-Ming and Zhao, Xi-Le and Jian, Huan-Yan},
  journal={Journal of Scientific Computing},
  volume={83},
  number={1},
  pages={10},
  year={2020},
  doi={10.1007/s10915-020-01193-1},
  publisher={Springer}
}

Yong-Liang Zhao, Ting-Zhu Huang, Xian-Ming Gu, Wei-Hua Luo, A fast second-order implicit difference method for time-space fractional advection-diffusion equation, Numerical Functional Analysis and Optimization, 41 (2020) 257-293. [BibTeX] [link] [slide]

@article{zhao2020fast,
  title={A fast second-order implicit difference method for time-space fractional advection-diffusion equation},
  author={Zhao, Yong-Liang and Huang, Ting-Zhu and Gu, Xian-Ming and Luo, Wei-Hua},
  journal={Numerical Functional Analysis and Optimization},
  volume={41},
  number={3},
  pages={257--293},
  year={2020},
  publisher={Taylor \& Francis}
}

Meng Li, Chengming Huang, Yongliang Zhao, Fast conservative numerical algorithm for the coupled fractional Klein-Gordon-Schrödinger equation, Numerical Algorithms, 84 (2020) 1081-1119. [link]

2019

Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu, Xi-Le Zhao, Jianxiong Cao, A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time–space fractional diffusion equation, Journal of Computational and Applied Mathematics, 362 (2019) 99-115. [BibTeX] [link] [slide]

@article{zhao2019limited,
  title={A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time--space fractional diffusion equation},
  author={Zhao, Yong-Liang and Zhu, Pei-Yong and Gu, Xian-Ming and Zhao, Xi-Le and Cao, Jianxiong},
  journal={Journal of Computational and Applied Mathematics},
  volume={362},
  pages={99--115},
  year={2019},
  publisher={Elsevier}
}

Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu, Xi-Le Zhao, A second-order accurate implicit difference scheme for time fractional reaction-diffusion equation with variable coefficients and time drift term, East Asian Journal on Applied Mathematics, 9 (2019) 723-754. [BibTeX] [link]

@Article{zhao2019EAJAM,
author = {Zhao, Yong-Liang and Zhu, Pei-Yong and Gu, Xian-Ming and Zhao, Xi-Le},
title = {A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term},
journal = {East Asian Journal on Applied Mathematics},
year = {2019},
volume = {9},
number = {4},
pages = {723--754},
}

2018

Yong-Liang Zhao, Pei-Yong Zhu, Wei-Hua Luo, A fast second-order implicit scheme for non-linear time-space fractional diffusion equation with time delay and drift term, Applied Mathematics and Computation, 336 (2018) 231-248. [BibTeX] [link]

@article{zhao2018fast,
  title={A fast second-order implicit scheme for non-linear time-space fractional diffusion equation with time delay and drift term},
  author={Zhao, Yong-Liang and Zhu, Pei-Yong and Luo, Wei-Hua},
  journal={Applied Mathematics and Computation},
  volume={336},
  pages={231--248},
  year={2018},
  publisher={Elsevier}
}

Meng Li, Yong-Liang Zhao^*, A fast energy conserving finite element method for the nonlinear fractional Schrödinger equation with wave operator, Applied Mathematics and Computation, 338 (2018) 758-773. [link]

Experiences

2021.07-Now: School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan 610068, P.R. China; staff.
2017.09-2021.06: School of Mathematical Sciences, University of Electronic Science and Technology of China (UESTC), Chengdu, Sichuan 611731, P.R. China; PhD student in Mathematics. (Supervisor: Prof. Pei-Yong Zhu)
2019.09-2020.09: Numerical Analysis group, University of Innsbruck, Technikerstraße 13, 6020 Innsbruck, Austria; visiting PhD student supported by CSC. (Supervisor: Prof. Alexander Ostermann)
2015.09-2017.06: School of Mathematical Sciences, University of Electronic Science and Technology of China (UESTC), Chengdu, Sichuan 611731, P.R. China; Master student in Computational Mathematics. (Supervisor: Prof. Ting-Zhu Huang)
2011.09-2015.06: School of Information Engineering, Lanzhou City University, Lanzhou, Gansu 730070, P.R. China; Bachelor student in Mathematics and Applied Mathematics

Talks

Fourth-order finite difference scheme with boundary value methods for space fractional diffusion equation (Contributed talk, 25 min) - The IMACS 2016 World Congress (IMACS 2016), Xiamen University, Xiamen, China, December, 2016. [Slide]
A second-order implicit difference method for time-space advection-diffusion equation, invited report in Neijiang Normal University, November 12, 2016. [Slide]
A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations (25分钟口头报告) - 第一届川渝地区分数阶微分方程会议（线上），西南财经大学，2020年11月。[Slide]

Projects

Member of the UESTC-Math Test Matrix Library, please see https://www.researchgate.net/project/UESTC-Math-Test-Matrix-Library. See also https://github.com/Hsien-Ming-Ku/SWUFE-Math.