33 citations · 68 across the 8 of their papers we have counts for
8 papers
Two Frameworks and their Fourth Order Implicit Schemes for Time Discretization of Maxwell's Equations
Archana Arya, Kaushik Kalyanaraman
Our work is about energy conserving fourth-order time discretizations of a three-field formulation of Maxwell's equations in conjunction with a spatial discretization using higher-…
An Arbitrarily Higher-Order Time Implicit Scheme for Maxwell's Equations
Archana Arya, Kaushik Kalyanaraman
We propose an arbitrarily higher (even) order implicit leapfrog scheme for time discretization of a three-field formulation of Maxwell's equations. We use this in conjunction with…
Quantifying macrostructures in viscoelastic sub-diffusive flows
Tanisha Chauhan, Kaushik Kalyanaraman, Sarthok Sircar
We present a theory to quantify the formation of spatiotemporal macrostructures (or the non-homogeneous regions of high viscosity at moderate to high fluid inertia) for viscoelasti…
Energy Conserving Higher Order Mixed Finite Element Discretizations of Maxwell's Equations
Archana Arya, Kaushik Kalyanaraman
We study a system of Maxwell's equations that describes the time evolution of electromagnetic fields with an additional electric scalar variable to make the system amenable to a mi…
Delaunay Hodge Star
Anil N. Hirani, Kaushik Kalyanaraman, Evan B. VanderZee
We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual vo…
Numerical Experiments for Darcy Flow on a Surface Using Mixed Exterior Calculus Methods
Anil N. Hirani, Kaushik Kalyanaraman
There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes fra…
Cohomologous Harmonic Cochains
Anil N. Hirani, Kaushik Kalyanaraman, Han Wang +1
We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also u…
Least Squares Ranking on Graphs
Anil N. Hirani, Kaushik Kalyanaraman, Seth Watts
Given a set of alternatives to be ranked, and some pairwise comparison data, ranking is a least squares computation on a graph. The vertices are the alternatives, and the edge valu…