Hailong Guo

Hailong Guo

Senior Lecturer of Applied Mathematics

The University of Melbourne

Biography

Hailong Guo is a senior lecturer at the University of Melbourne, where he joined as a lecturer of applied mathematics in July 2018. Before that, he was a visiting assistant professor at the University of California, Santa Barbara from July 2015 to June 2018. His research interests include nonstandard finite element methods, superconvergence theory, adaptive computation, simulation of topological material, data science, and machine learning.

Interests
  • Scientific deep learning
  • Numerical solution of partial differential equations
  • Design and analysis of post-processing techniques
  • Waves in topological materials
  • Computational optics
Education

  • PhD in Mathematics, 2015

    Wayne State University

  • MS in Computational Mathematics, 2010

    Peking University

  • BSc in Information and computational science, 2007

    Hunan Normal University

Experience

 
 
 
 
 
Senior Lecturer
The University of Melbourne
Sep 2022 – Present Victoria
 
 
 
 
 
Lecturer
The University of Melbourne
Jul 2018 – Aug 2022 Victoria
 
 
 
 
 
Visiting Assistant Professor
University of California, Santa Barbara
Jul 2015 – Jun 2018 California

Recent Publications

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Jamal Adetola, Bernadin Ahounou, Gerard Awanou, Hailong Guo (2022). Low order mixed finite element approximations of the Monge-Ampère equation. Int. J. Numer. Anal. Model..

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W.-M. He, H. Guo (2022). Optimal Maximum Norm Estimates for Virtual Element Methods. SIAM J. Numer. Anal..

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H. Guo, X. Yang, Y. Zhu (2021). Unfitted Nitsche's method for computing band structures of phononic crystals with periodic inclusions. Comput. Methods Appl. Mech. Engrg..

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H. Guo, X. Yang, Y. Zhu (2021). Unfitted Nitsche's Method for Computing Wave Modes in Topological Materials. J. Sci. Comput..

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G. Dong, H. Guo (2020). Parametric polynomial preserving recovery on manifolds. SIAM J. Sci. Comput..

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H. Guo (2020). Surface Crouzeix-Raviart element for the Laplace-Beltrami equation. Numer. Math..

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H. Guo, X. Yang, Y. Zhu (2019). Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene. J. Comput. Phys..

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M. Xu, H. Guo, Q. Zou (2019). Hessian recovery based finite element methods for the Cahn-Hilliard equation. J. Comput. Phys..

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H. Guo, C. Xie, R. Zhao (2019). Superconvergent gradient recovery for virtual element methods. Math. Models Methods Appl. Sci..

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H. Guo, Z. Zhang, Q. Zou (2018). A $C^0$ linear finite element method for biharmonic problems. J. Sci. Comput..

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Teaching

  • MAST30028: Numerical Methods & Scientific Computing, The University of Melbourne, Semester 2, 2022
  • MAST90026: Computational Partial Differential Equations, The University of Melbourne, Semester 1, 2022
  • MAST30028: Numerical Methods & Scientific Computing, The University of Melbourne, Semester 2, 2021
  • MAST90064: Advanced Methods: Differential Equations, The University of Melbourne, Semester 1, 2021
  • MAST30028: Numerical Methods & Scientific Computing, The University of Melbourne, Semester 2, 2020
  • MAST90026: Computational Partial Differential Equations, The University of Melbourne, Semester 1, 2020
  • MAST30028: Numerical Methods & Scientific Computing, The University of Melbourne, Semester 2, 2019
  • MAST20029: Engineering Mathematics, The University of Melbourne, Semester 1, 2019

Recent & Upcoming Talks

Unfitted computation of edge modes in photonic graphene
May 8, 2021 — May 9, 2021 Beijing, China
Hessian recovery based finite element method for the Cahn-Hilliard equation
Jan 20, 2020 9:00 AM — 10:00 AM Beijing, China

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