2 citations · 2 across the 1 of their papers we have counts for
9 papers
Finite elements for symmetric and traceless tensors in three dimensions
Kaibo Hu, Ting Lin, Bowen Shi
We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes and show their exactness on contractible domains. This complex includes vector…
Convergence and Stability of Discrete Exterior Calculus for the Hodge Laplace Problem in Two Dimensions
Chengbin Zhu, Snorre H. Christiansen, Kaibo Hu +1
We prove convergence and stability of the discrete exterior calculus (DEC) solutions for the Hodge-Laplace problems in two dimensions for families of meshes that are non-degenerate…
Finite element methods for isometric embedding of Riemannian manifolds
Guangwei Gao, Kaibo Hu, Buyang Li +1
The isometric embedding problem for Riemannian manifolds, which connects intrinsic and extrinsic geometry, is a central question in differential geometry with deep theoretical sign…
Hodge-Dirac wave systems and structure-preserving discretizations of the linearized Einstein equations
Marien-Lorenzo Hanot, Kaibo Hu
We derive a reformulation of the linearized Arnowitt-Deser-Misner (ADM) equations as a Hodge-Dirac wave system with the divdiv complex, addressing challenges in numerical relativit…
Helicity-preserving finite element discretization for magnetic relaxation
Mingdong He, Patrick E. Farrell, Kaibo Hu +1
The Parker conjecture, which explores whether magnetic fields in perfectly conducting plasmas can develop tangential discontinuities during magnetic relaxation, remains an open que…
Many facets of cohomology: Differential complexes and structure-aware formulations
Kaibo Hu
Complexes and cohomology, traditionally central to topology, have emerged as fundamental tools across applied mathematics and the sciences. This survey explores their roles in dive…