Dr Kaibo Hu

PhD

Status

Research Fellow

Hooke Research Fellow, Mathematical Institute

Christ Church

email: kaibo.hu [at] maths.ox.ac.uk

Contact form

+44 1865 615307

Research groups

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Teaching

2021: MSc in Mathematical Modelling and Scientific Computing (MMSC), dissertation project

2021 Michaelmas Term: Finite element exterior calculus, notes

2022 Hilary Term: MMSC Case Studies (Modelling) on Turing mechanism. notes slides

Research interests

I work on theoretical numerical analysis in a broad sense, in particular, structure-preserving methods and finite element exterior calculus.

The vision of my current research includes:

1) connections between homological algebra, geometry, and mathematical and numerical analysis; geometric foundations of continuum mechanics,

2) discretizations of PDEs and discrete theories (discrete geometry, discrete mechanics etc.),

3) structure-preserving approaches for solving the Einstein equations in general relativity, with potential applications in computational astronomy and gravitational-wave sciences,

4) finite element methods (high order methods, preconditioning etc.) and applications (fluid and solid mechanics, magnetohydrodynamics etc.),

5) scientific computing, computation of spectrum, localization.

Major / recent publications

BGG sequences with weak regularity and applications; Andreas Čap, Kaibo Hu (2022) arXiv:2203.01300
Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations; Fabian Laakmann, Kaibo Hu, Patrick E. Farrell (2022) arXiv:2202.11586
Finite Element Systems for vector bundles : elasticity and curvature; Snorre H. Christiansen and Kaibo Hu, Foundations of Computational Mathematics (2022)
A family of finite element Stokes complexes in three dimensions; Kaibo Hu, Qian Zhang and Zhimin Zhang, SIAM Journal on Numerical Analysis (2022) arXiv:2008.03793
Spurious solutions for high order curl problems; Kaibo Hu, Qian Zhang, Jiayu Han, Lixiu Wang, Zhimin Zhang, IMA Journal of Numerical Analysis (2022)
Partially discontinuous nodal finite elements for H(curl) and H(div), Jun Hu, Kaibo Hu and Qian Zhang, Computational Methods in Applied Mathematics (2022) arXiv:2203.02103
Complexes from complexes; Douglas N. Arnold and Kaibo Hu, Foundations of Computational Mathematics (2021)
Helicity-conservative finite element discretization for incompressible MHD systems; Kaibo Hu, Young-Ju Lee and Jinchao Xu, Journal of Computational Physics (2021)
A discrete elasticity complex on three-dimensional Alfeld splits; Snorre H. Christiansen, Jay Gopalakrishnan, Johnny Guzmán, Kaibo Hu (2020) arXiv:2009.07744
Simple curl-curl-conforming finite elements in two dimensions; Kaibo Hu, Qian Zhang and Zhimin Zhang, SIAM Journal of Scientific Computing (2020)
A characterization of supersmoothness of multivariate splines; Michael S. Floater and Kaibo Hu, Advances in Computational Mathematics (2020)
Well-conditioned frames for high order finite element methods; Kaibo Hu and Ragnar Winther, Journal of Computational Mathematics (2020)
Poincaré path integrals for elasticity; Snorre H. Christiansen, Kaibo Hu and Espen Sande; Journal de Mathématiques Pures et Appliquées (2019)
Generalized Gaffney inequality and discrete compactness for discrete differential forms; Juncai He, Kaibo Hu and Jinchao Xu; Numerische Mathematik (2019)
Generalized Finite Element Systems for smooth differential forms and Stokes problem; Snorre H. Christiansen and Kaibo Hu; Numerische Mathematik (2018)
Structure-preserving finite element methods for stationary MHD models; Kaibo Hu and Jinchao Xu; Mathematics of Computation (2018)
Nodal finite element de Rham complexes; Snorre H. Christiansen, Jun Hu and Kaibo Hu; Numerische Mathematik (2018)
Robust Preconditioners for Incompressible MHD Models; Yicong Ma, Kaibo Hu, Xiaozhe Hu and Jinchao Xu; Journal of Computational Physics, (2016)
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.

Here are some slides/posters from my talks, on

Structure-preserving discretization and preconditioning for MHD (Princeton 2020)
Complexes from complexes (Cambridge 2019), and slides on the same topic for a broader audience (Zürich 2020)
Well-conditioned frames for high order finite elements (Oxford 2021)
Poincaré (homotopy) operators for elasticity (Valencia, ICIAM 2019)
Algebraic construction of finite elements (Beijing 2019)
Some Hilbert complexes in general relativity (ICERM, Brown 2020)
Nodal finite element de Rham complexes (Baltimore, JMM 2019)
Conformal Korn inequalities in 2D (Oxford, PDE working seminar, 2022)
Discretization of Hilbert complexes (survey talk) (MFO, Oberwolfach, 2022)

** The slides for my talk at Friday@4, Hiliary Term are here.

Prizes, awards, and scholarships

Hooke Research Fellowship, Mathematical Institute, University of Oxford, UK. 2020.
Marie Skłodowska-Curie Individual Fellowship offer, EU, 2020.
New World Mathematics Award, 2017.
Outstanding Youth Paper Prize, Beijing Society of Computational Mathematics, September 2016.
EASIAM (East Asia section of SIAM) Student Paper Prize, June, 2016.

Further details

Education and Employment

Postdoc, 2018 - 2021; School of Mathematics, University of Minnesota, USA.
Researcher, 2017 - 2018; Department of Mathematics, University of Oslo, Oslo, Norway.
Ph.D, 2012 - 2017; Beijing International Center for Mathematical Research; Peking University, Beijing, China.
B.S. in Computational Mathematics, 2008 - 2012; School of Mathematical Sciences, Nankai University, Tianjin, China.

Visits

Heidelberg University (2022), University of Vienna (2021), University of Oslo (2021, 2017, 2015-2016), Isaac Newton Institute for Mathematical Sciences (2019), ETH Zürich (2019), University of Illinois at Urbana-Champaign (2019), The Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences (2019, 2017), Pennsylvania State University (2017, 2016).

Forthcoming/recent events:

September 2022, INdAM Meeting "Approximation Theory and Numerical Analysis meet Algebra, Geometry, Topology", Palazzone di Cortona, Italy.
September 2022, 56th Meeting of the Society for Natural Philosophy: Mechanics and Analysis, Pisa, Italy. (round-table talk)
October 2022, seminar at University of Hong Kong, China.

July 2022, SciCADE International Conference on Scientific Computation and Differential Equations in Reykjavik, Iceland.
July 2022, Christ Church Scientific Afternoon, Oxford, UK.
June 2022, 30 years of Acta Numerica conference at the Banach Centre in Będlewo, Poland.
June 2022, MFO workshop "Hilbert Complexes: Analysis, Applications, and Discretizations", Oberwolfach, Germany.
June 2022, Canadian Applied and Industrial Mathematics Society annual meeting, UBC Okanagan Canada. (online)
June 2022, European Finite Element Fair, Aalto University, Finland.
April 2022, Culham Centre for Fusion Energy, UK.
March 2022, Heidelberg University, Germany.
December 2021, Los Alamos National Lab, USA (online seminar talk).
December 2021, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, China (online seminar talk).
September 2021, European finite element fair, Paris, France. (online talk)