Dr Kaibo Hu
Royal Society University Research Fellow
Mathematical Institute, Christ Church
email: kaibo.hu [at] maths.ox.ac.uk
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
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
2022 Michaelmas Term - 2023 Hilary Term: BSP project (orthogonal polynomials)
2023 Trinity Term:
Christ Church - calculus of variations (tutorials + revision)
Mathematical Institute - MMSC dissertation project
I work on numerical analysis and PDEs, 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.
- Bounded Poincaré operators for twisted and BGG complexes; Andreas Čap, Kaibo Hu; (2023) arXiv:2304.07185.
- Supersmoothness of the Alfeld split; Michael S. Floater, Kaibo Hu (2023)
- An exterior calculus framework for polytopal methods; Francesco Bonaldi, Deniele A. Di Pietro, Jerome Droniou, Kaibo Hu (2023) arXiv:2303.11093.
- Nonlinear elasticity complex and a finite element diagram chase; Kaibo Hu, (2023) arXiv:2302.02442.
- Discrete tensor product BGG sequences: splines and finite elements; Francesca Bonizzoni, Kaibo Hu, Guido Kanschat, Duygu Sap, (2023) arXiv:2302.02434.
- BGG sequences with weak regularity and applications; Andreas Čap, Kaibo Hu; accepted, Foundations of Computational Mathematics (2023) 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)
- 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)
- 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) report (MFO, Oberwolfach, 2022)
- Bounded Poincaré operators for BGG complexes (Chinese Academy of Sciences, 2022)
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SIAM Computational Science and Engineering Early Career Prize, 2023.
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Royal Society University Research Fellowship, 2022-2027.
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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 Paper Prize for Young Researchers, Beijing Society of Computational Mathematics, September 2016.
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EASIAM (East Asia section of SIAM) Student Paper Prize, June, 2016.
Education and Employment
- Royal Society University Research Fellow, 2022-present; Mathematical Institute, University of Oxford, UK.
- Hooke Research Fellow, 2021-2022; Mathematical Institute, University of Oxford, UK.
- 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
Peking University (2023, upcoming), Queen Mary University of London (2023), TU Delft (2022), TU Wien (2022), 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:
- June 2023, the 29th Biennial Numerical Analysis Conference, University of Strathclyde, Glasgow, UK. Co-organiser of MS "Structure-preserving discretization of Hilbert complexes" with Deepesh Toshniwal.
- July 2023, Structure preserving numerical methods for partial differential equations, Bernoulli Center, EPFL, Switzerland.
- July 2023, PKU Mathematics Forum (北大数学校友论坛), Beijing, China.
- August 2023, The 2023 International Workshop on Scientific Computing, Feng Kang Youth Forum on Scientific Computing (FKYF), The Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences, Beijing, China.
- August 2023, ICIAM, Tokyo, Japan. Co-organiser of MS "Finite element complexes and multivariate splines" with Nelly Villamizar.
- May 2024, Banff International Research Station (BIRS) “Homological Perspective on Splines and Finite Elements” workshop, University of British Columbia Okanagan (UBCO), Canada.
- April 27, 2023. With Davide Spriano, I was co-organising a Maths Afternoon at Christ Church.
- February 2023, SIAM Conference on Computational Science and Engineering (CSE23), Amsterdam, Netherlands.
- February 2023, Computational Mathematics and Applications Seminar, Oxford, UK.
- February 2023, Imperial–UCL Numerics Seminar, London, UK.
- February 2023, Topological Data Analysis group meeting, Oxford, UK.
- January 2023, visit Queen Mary University London, UK.
- December 2022, visit and seminar talk at TU Delft, Netherlands.
- December 2022, Gravity Seminar Series of STAG (gravity/string theory/mathematical physics group) of Mathematical Sciences, University of Southampton, UK.
- December 2022, The 8th Workshop for Young Researchers in Scientific Computing, Chinese Academy of Sciences, China (online).
- November 2022, online seminar at Chinese Academy of Sciences, China.
- October-November 2022, visit TU Wien, Austria.
- October 2022, seminar at University of Hong Kong, China.
- September 2022, 56th Meeting of the Society for Natural Philosophy: Mechanics and Analysis, Pisa, Italy. (round-table talk)
- September 2022, INdAM Meeting "Approximation Theory and Numerical Analysis meet Algebra, Geometry, Topology", Palazzone di Cortona, Italy.
- 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)