My CV can be found here.
- Structure-preserving/compatible discretization, finite element exterior calculus
- multilevel preconditioning
- applications in multiphysics problems (plasma, MHD), continuum mechanics and general relativity
My current research is focused on the structure-preserving discretization and multilevel preconditioning for partial differential equations, particularly on the finite element exterior calculus (construction of finite elements, high order methods etc.).
I work on problems in coupled multiphysics systems (plasma and magnetohydrodynamcis), continuum mechanics and relativity. Nonlinearity and complex differential structures are usually present in these problems.
I also have an interest in geometric mechanics, discrete physical and geometric/topological structures and the relation between discrete theories and discretizations of PDEs.
- Ph.D student, Sep. 2012 - Jul. 2017
Beijing International Center for Mathematical Research,
Peking University, Beijing, China.
Advisor: Prof. Jinchao Xu
Thesis: Finite Element Exterior Calculus for Multiphysics Problems
- B.S. in Computational Mathematics, 2008-2012
Nankai University, Tianjin, China.
Thesis: Implementation of Nine Discontinuous Galerkin Methods
for Convection-Dominated Convection-Diffusion Equations
- July, 2017. The State Key Laboratory of Scientific and Engineering Computing (LSEC), Chinese Academy of Sciences, China.
- February - May, 2017. Department of Mathematics, University of Oslo, Norway.
- January, 2017. Department of Mathematics, Pennsylvania State University, USA.
- March, 2016. Department of Mathematics, Pennsylvania State University, USA.
- September 2015 - November 2016. Department of Mathematics, University of Oslo, Norway.
- Stable finite element methods preserving ∇ · B = 0 exactly for MHD models; Kaibo Hu, Yicong Ma and Jinchao Xu; Numerische Mathematik, 2016, DOI 10.1007/s00211-016-0803-4. link
- Robust preconditioners for incompressible MHD models; Yicong Ma, Kaibo Hu, Xiaozhe Hu and Jinchao Xu; Journal of Computational Physics, 2016; Volume 316, 1 July 2016, Pages 721–746. link
- Stable magnetic field-current finite element schemes for magnetohydrodynamics systems; Kaibo Hu and Jinchao Xu; in Chinese; Science China Mathematics, 7 (2016): 006. link
- Nodal finite element de Rham complexes; Snorre H. Christiansen, Jun Hu and Kaibo Hu; Numerische Mathematik; Accepted, 2017. link
- Structure-preserving finite element methods for stationary MHD models; Kaibo Hu and Jinchao Xu; Mathematics of Computation; Accepted, 2017. link
- Generalized Finite Element Systems for smooth differential forms and Stokes problem; Snorre H. Christiansen and Kaibo Hu; Numerische Mathematik; Accepted, 2018. arXiv:1605.08657.
- Well-conditioned frames for finite element methods, Kaibo Hu and Ragnar Winther; arXiv: 1705.07113.
- Magnetic-electric formulations for stationary magnetohydrodynamics models; Kaibo Hu, Weifeng Qiu, Ke Shi and Jinchao Xu; arXiv:1711.11330.
- Poincaré path integrals for elasticity; Snorre H. Christiansen, Kaibo Hu and Espen Sande; arXiv:1801.07058.
- Sobolev inequalities and discrete compactness for discrete differential forms; Juncai He, Kaibo Hu and Jinchao Xu; arXiv:1804.03428.
- Nonstandard finite element de Rham complexes on cubical meshes; Andrew Gillette, Kaibo Hu and Shuo Zhang; arXiv:1804.04390.
- Christiansen, Snorre H; Hu, Jun & Hu, Kaibo (2017). Nodal finite element de Rham complexes. Numerische Mathematik. ISSN 0029-599X. Published ahead of print, s 1- 36 . doi: 10.1007/s00211-017-0939-x Full text in Research Archive.
- Hu, Kaibo & Winther, Ragnar (2017). Well-Conditioned Frames for Finite Element Methods.