BSc (Nankai University); PhD (Peking University)

Academic background

I completed my PhD in computational mathematics in 2017 at Peking University. My PhD thesis is mainly concerned with the structure-preserving discretisation of multiphysics systems, particularly the magnetohydrodynamics (MHD) equations that arise from plasma physics.

During the last two years of my PhD, I had an extended visit to the Department of Mathematics, University of Oslo. During this time and later postdoctoral experiences at Oslo (2017-2018) and Minnesota (2018-2021), my research was more focused on the theory of the finite element exterior calculus (FEEC), a cohomological approach for numerical partial differential equations. During the time at Minnesota, I am also a member of the Simons collaboration exploring localisation of waves. Along with these positions, I enjoyed visits to other institutes, including Penn State University, the University of Illinois at Urbana-Champaign, ETH Zürich, Isaac Newton Institute, and the University of Vienna.

Currently, I am a Hooke Research Fellow at the Mathematical Institute, University of Oxford, and a Postdoctoral Research Fellow at Christ Church.

Research interests

I am a numerical analyst by training. My current research is on numerical methods for PDEs that preserve certain topological, geometric and physical structures.

Recently I have been excited about the development and applications of differential complexes and the Bernstein-Gelfand-Gelfand (BGG) machinery from Lie algebra and representation theory. This tool was used to tackle elasticity problems by Arnold, Falk and Winther in the FEEC context. The BGG machinery seems to provide many connections between numerical PDEs, analysis (e.g., Korn inequalities), continuous and discrete differential geometry (e.g., Riemannian and conformal geometry), continuum mechanics (microstructures, defects), and general relativity. In particular, I am interested in solving the Einstein equations numerically.

Featured publications

1. Finite Element Systems for vector bundles : elasticity and curvature; Snorre H. Christiansen and Kaibo Hu, accepted, Foundations of Computational Mathematics (2021) arXiv:1906.09128
2. A family of finite element Stokes complexes in three dimensions; Kaibo Hu, Qian Zhang and Zhimin Zhang, accepted, SIAM Journal on Numerical Analysis (2021) arXiv:2008.03793
3. Complexes from complexes; Douglas N. Arnold and Kaibo Hu, Foundations of Computational Mathematics (2021)
4. Helicity-conservative finite element discretization for incompressible MHD systems; Kaibo Hu, Young-Ju Lee and Jinchao Xu, Journal of Computational Physics (2021)
5. A discrete elasticity complex on three-dimensional Alfeld splits; Snorre H. Christiansen, Jay Gopalakrishnan, Johnny Guzmán, Kaibo Hu (2020) arXiv:2009.07744
6. Simple curl-curl-conforming finite elements in two dimensions; Kaibo Hu, Qian Zhang and Zhimin Zhang, SIAM Journal of Scientific Computing (2020)
7. A characterization of supersmoothness of multivariate splines; Michael S. Floater and Kaibo Hu, Advances in Computational Mathematics (2020)
8. Well-conditioned frames for high order finite element methods; Kaibo Hu and Ragnar Winther, Journal of Computational Mathematics (2020)
9. Poincaré path integrals for elasticity; Snorre H. Christiansen, Kaibo Hu and Espen Sande; Journal de Mathématiques Pures et Appliquées (2019)
10. Generalized Gaffney inequality and discrete compactness for discrete differential forms; Juncai He, Kaibo Hu and Jinchao Xu; Numerische Mathematik (2019)
11. Generalized Finite Element Systems for smooth differential forms and Stokes problem; Snorre H. Christiansen and Kaibo Hu; Numerische Mathematik (2018)
12. Structure-preserving finite element methods for stationary MHD models; Kaibo Hu and Jinchao Xu; Mathematics of Computation (2018)
13. Nodal finite element de Rham complexes; Snorre H. Christiansen, Jun Hu and Kaibo Hu; Numerische Mathematik (2018)
14. Robust Preconditioners for Incompressible MHD Models; Yicong Ma, Kaibo Hu, Xiaozhe Hu and Jinchao Xu; Journal of Computational Physics, (2016)
15. Stable Finite Element Methods Preserving ∇ · B = 0 Exactly for MHD Models; Kaibo Hu, Yicong Ma and Jinchao Xu; Numerische Mathematik (2016)

For a full list of publications, please see Google Scholar ( https://scholar.google.com/citations?user=44CVm40AAAAJ&hl=en&oi=ao ).

Other interests and activities

I enjoy travel, reading, music (listening, so far), and swimming (especially open water).