Hooke Research Fellow, Mathematical Institute
PDRF, Christ Church
email: kaibo.hu [at] maths.ox.ac.uk
+44 1865 615307
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
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) advanced numerical methods (high order methods, preconditioning etc.) and applications (fluid and solid mechanics, magnetohydrodynamics etc.),
5) scientific computing, computation of spectrum, localization.
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 (one week or more):
Faculty of Mathematics, University of Vienna (Sep-Oct 2021)
Department of Mathematics, University of Oslo (Sep 2021, Feb-May 2017, Sep 2015-Nov 2016)
Isaac Newton Institute for Mathematical Sciences, Cambridge (Sep-Nov 2019)
Department of Mathematics, ETH Zürich (Jul-Aug 2019)
Department of Mathematics, Pennsylvania State University (Jan 2017, Mar 2016)
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.
Major / recent publications:
- Finite Element Systems for vector bundles : elasticity and curvature; Snorre H. Christiansen and Kaibo Hu, accepted, Foundations of Computational Mathematics (2021) arXiv:1906.09128
- 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)
- Spurious solutions for high order curl problems; Kaibo Hu, Qian Zhang, Jiayu Han, Lixiu Wang, Zhimin Zhang, submitted (2021)
- A discrete elasticity complex on three-dimensional Alfeld splits; Snorre H. Christiansen, Jay Gopalakrishnan, Johnny Guzmán, Kaibo Hu (2020) arXiv:2009.07744
- A family of finite element Stokes complexes in three dimensions; Kaibo Hu, Qian Zhang and Zhimin Zhang (2020) arXiv:2008.03793
- 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)