Status:
Hooke Research Fellow, Mathematical Institute
PDRF, Christ Church
email: kaibo.hu [at] maths.ox.ac.uk
+44 1865 615307
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
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) advanced numerical methods (high order methods, preconditioning etc.) and applications (fluid and solid mechanics, magnetohydrodynamics etc.),
5) scientific computing, computation of spectrum, localization.
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 (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)
Teaching:
I will give lectures on "Finite element exterior calculus" in Michaelmas Term 2021.
4 * 2 hours, Wednesday 10:00 – 12:00 from Week 3 (27th Oct), L3, Andrew Wiles Building
Prizes, awards, and scholarships:
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Hooke Research Fellowship, Mathematical Institute, University of Oxford, UK. 2020.
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Marie Skłodowska-Curie Individual Fellowship offer, EU, 2020.
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New World Mathematics Award, 2017.
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Outstanding Youth Paper Prize, Beijing Society of Computational Mathematics, September 2016.
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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)