63 citations · 185 across the 25 of their papers we have counts for
28 papers
Optimal block preconditioners for a mass-conserving mixed stress formulation of Stokes flow
Kaibo Hu, Jongho Park, Jindong Wang
We present optimal block diagonal and triangular preconditioners for a mass-conserving mixed stress formulation of Stokes flow. The algebraic formulation leads to a double saddle p…
ReLU Neural de Rham Complexes
Kaibo Hu, Jindong Wang, Jinchao Xu
We construct finite-dimensional de Rham subcomplexes generated by fixed-neuron shallow ReLU neural networks, a class of spaces known to provide optimal approximation rates. For…
Bounded Poincaré operators for twisted and BGG complexes
Andreas Čap, Kaibo Hu
We construct bounded Poincaré operators for twisted complexes and BGG complexes with a wide class of function classes (e.g., Sobolev spaces) on bounded Lipschitz domains. These ope…
An exterior calculus framework for polytopal methods
Francesco Bonaldi, Daniele A. Di Pietro, Jerome Droniou +1
We develop in this work the first polytopal complexes of differential forms. These complexes, inspired by the Discrete De Rham and the Virtual Element approaches, are discrete vers…
Nonlinear elasticity complex and a finite element diagram chase
Kaibo Hu
In this paper, we present a nonlinear version of the linear elasticity (Calabi, Kröner, Riemannian deformation) complex which encodes isometric embedding, metric, curvature and the…
Discrete tensor product BGG sequences: splines and finite elements
Francesca Bonizzoni, Kaibo Hu, Guido Kanschat +1
In this paper, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand (BGG) diagrams and complexes over cubical meshes of arbitrary dimension via the use of tensor…
Oberwolfach report : Discretization of Hilbert complexes
Kaibo Hu
The report is based on an extended abstract for the MFO workshop "Hilbert Complexes: Analysis, Applications, and Discretizations", held at Oberwolfach during 19-25 June 2022. The a…
Partially discontinuous nodal finite elements for and
Jun Hu, Kaibo Hu, Qian Zhang
We investigate discretization of and in two and three space dimensions by partially discontinuous nodal finite elements, i.e., vector-valued La…
BGG sequences with weak regularity and applications
Andreas Čap, Kaibo Hu
We investigate some Bernstein-Gelfand-Gelfand (BGG) complexes on bounded Lipschitz domains in consisting of Sobolev spaces. In particular, we compute the cohomology…
Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations
Fabian Laakmann, Patrick E. Farrell, Kaibo Hu
We develop structure-preserving finite element methods for the incompressible, resistive Hall magnetohydrodynamics (MHD) equations. These equations incorporate the Hall current ter…
Spurious solutions for high order curl problems
Kaibo Hu, Qian Zhang, Jiayu Han +2
We investigate numerical solutions of high order curl problems with various formulations and finite elements. We show that several classical conforming finite elements lead to spur…
A discrete elasticity complex on three-dimensional Alfeld splits
Snorre H. Christiansen, Jay Gopalakrishnan, Johnny Guzmán +1
We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via t…
A family of finite element Stokes complexes in three dimensions
Kaibo Hu, Qian Zhang, Zhimin Zhang
We construct finite element Stokes complexes on tetrahedral meshes in three-dimensional space. In the lowest order case, the finite elements in the complex have 4, 18, 16, and 1 de…
Helicity-conservative finite element discretization for incompressible MHD systems
Kaibo Hu, Young-Ju Lee, Jinchao Xu
We construct finite element methods for the incompressible magnetohydrodynamics (MHD) system that precisely preserve magnetic and cross helicity, the energy law and the magnetic Ga…
Complexes from complexes
Douglas N. Arnold, Kaibo Hu
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum me…
Simple curl-curl-conforming finite elements in two dimensions
Kaibo Hu, Qian Zhang, Zhimin Zhang
We construct smooth finite element de Rham complexes in two space dimensions. This leads to three families of curl-curl conforming finite elements, two of which contain two existin…
Finite Element Systems for vector bundles : elasticity and curvature
Snorre H. Christiansen, Kaibo Hu
We develop a theory of Finite Element Systems, for the purpose of discretizing sections of vector bundles, in particular those arizing in the theory of elasticity. In the presence…
A characterization of supersmoothness of multivariate splines
Michael S. Floater, Kaibo Hu
We consider spline functions over simplicial meshes in $\RR^n$. We assume that the spline pieces join together with some finite order of smoothness but the pieces themselves are in…
Nonstandard finite element de Rham complexes on cubical meshes
Andrew Gillette, Kaibo Hu, Shuo Zhang
We propose two general operations on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods…
Generalized Gaffney inequality and discrete compactness for discrete differential forms
Juncai He, Kaibo Hu, Jinchao Xu
We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on -regular domains, including general Lipschitz domains. In computa…
Poincaré path integrals for elasticity
Snorre H. Christiansen, Kaibo Hu, Espen Sande
We propose a general strategy to derive null-homotopy operators for differential complexes based on the Bernstein-Gelfand-Gelfand (BGG) construction and properties of the de Rham c…
Convergence of a - based finite element method for MHD models on Lipschitz domains
Kaibo Hu, Weifeng Qiu, Ke Shi
We discuss a class of magnetic-electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a…
Well-conditioned frames for high order finite element methods
Kaibo Hu, Ragnar Winther
The purpose of this paper is to discuss representations of high order finite element spaces on simplicial meshes in any dimension. When computing with high order piecewise po…
Nodal Finite Element de Rham Complexes
Snorre H. Christiansen, Jun Hu, Kaibo Hu
We construct 2D and 3D finite element de Rham sequences of arbitrary polynomial degrees with extra smoothness. Some of these elements have nodal degrees of freedom (DoFs) and can b…