12 papers
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…
A 2-complex containing Sobolev spaces of matrix fields
Jay Gopalakrishnan, Kaibo Hu, Joachim Schöberl
Using a generalization of complexes, called 2-complexes, this paper defines and analyzes new Sobolev spaces of matrix fields and their interrelationships within a commuting diagram…
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…
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…
Finite element form-valued forms: Construction
Kaibo Hu, Ting Lin
We provide a finite element discretization of -form-valued -forms on triangulation in for general , and and any polynomial degree. The const…