94 citations · 361 across the 25 of their papers we have counts for
25 papers
Discrete Poincare and Bogovskii operators on cochains and Whitney forms
Johnny Guzmán, Anil N. Hirani, Bingyan Liu +1
Smooth Poincare operators are a tool used to show the vanishing of smooth de Rham cohomology on contractible manifolds and have found use in the analysis of finite element methods…
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…
Averaging Property of Wedge Product and Naturality in Discrete Exterior Calculus
Mark D. Schubel, Daniel Berwick-Evans, Anil N. Hirani
In exterior calculus on smooth manifolds, the exterior derivative and wedge product are natural with respect to smooth maps between manifolds, that is, these operations commute wit…
Discrete exterior calculus discretization of two-phase incompressible Navier-Stokes equations with a conservative phase field method
Minmiao Wang, Pankaj Jagad, Anil N. Hirani +1
We present a discrete exterior calculus (DEC) based discretization scheme for incompressible two-phase flows. Our physically-compatible exterior calculus discretization of single p…
Conservative Integrators for Piecewise Smooth Systems with Transversal Dynamics
Anil N. Hirani, Andy T. S. Wan, Nikolas Wojtalewicz
We introduce conservative integrators for long term integration of piecewise smooth systems with transversal dynamics and piecewise smooth conserved quantities. In essence, for a p…
GraphSAT -- a decision problem connecting satisfiability and graph theory
Vaibhav Karve, Anil N. Hirani
Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure…