16 citations · 25 across the 14 of their papers we have counts for
16 papers
A Function-Space Framework for BDDC Preconditioning in Control- and State-Constrained Sparse Optimal Control
Harbir Antil, Keegan L. A. Kirk, Umarkhon Rakhimov
We develop a Balancing Domain Decomposition by Constraints (BDDC) preconditioner for the interface systems arising from active-set semi-smooth Newton linearizations of elliptic opt…
Duality-Based Error Identities for Subgradient Flows Based on the Brézis-Ekeland-Nayroles Principle
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
We derive duality-based error identities for a broad class of subgradient flows induced by time-dependent convex integral functionals. Starting from the Bré…
Duality Framework for Flux Constrained Flow in Porous Media: Analysis and Numerics
Harbir Antil, Keegan L. A. Kirk, Felipe Pérez
We introduce and analyze Darcy flow through a saturated porous medium subject to bilateral constraints on the normal flux across a portion of the boundary. The problem is posed as…
A Finite Element Approximation of an Optimal Insulation Problem with Convective Heat Transfer
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
A finite element discretization of an optimal insulation problem with convective heat transfer is considered. The model is formulated as a non-smooth, two-variable convex minimizat…
Convection Effects and Optimal Insulation: Modelling and Analysis
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
In this paper, we study an insulation problem that seeks to determine the optimal distribution of a given amount of insulating material coating an insulated boundary part $Γ_…
A Hybridizable Discontinuous Galerkin Method for the Miscible Displacement Problem Under Minimal Regularity
Keegan L. A. Kirk, Beatrice Riviere
A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement prob…
Duality-Based Algorithm and Numerical Analysis for Optimal Insulation Problems on Non-Smooth Domains
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
This article develops a numerical approximation of a convex non-local and non-smooth minimization problem. The physical problem involves determining the optimal distribution, given…
Modeling and Analysis of an Optimal Insulation Problem on Non-Smooth Domains
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
In this paper, we study an insulation problem that seeks the optimal distribution of a fixed amount of insulating material coating an insulated boundary $Γ_I\subseteq \partia…
A Discontinuous Galerkin Method for the Extracellular Membrane Intracellular Model
Rami Masri, Keegan L. A. Kirk, Eirill Hauge +1
We formulate and analyze interior penalty discontinuous Galerkin methods for coupled elliptic PDEs modeling excitable tissue, represented by intracellular and extracellular domains…
Solutions to Elliptic and Parabolic Problems via Finite Difference Based Unsupervised Small Linear Convolutional Neural Networks
Adrian Celaya, Keegan Kirk, David Fuentes +1
In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equa…
Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn-Hilliard problem
Keegan L. A. Kirk, Rami Masi, Beatrice Riviere
The mixed form of the Cahn-Hilliard equations is discretized by the hybridizable discontinuous Galerkin method. For any chemical energy density, existence and uniqueness of the num…
Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier--Stokes equations
Keegan L. A. Kirk, Ayçıl Çeşmelioǧlu, Sander Rhebergen
We prove that a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations converges to a weak solution as the time step and mesh size tend t…
Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier--Stokes equations
Keegan L. A. Kirk, Tamás L. Horváth, Sander Rhebergen
We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations. Key features of the numerical scheme include point-wis…
On Polynomial Solutions of Linear Differential Equations with Applications
Kyle R. Bryenton1, Andrew R. Cameron, Keegan L. A. Kirk +3
The analysis of many physical phenomena can be reduced to the study of solutions of differential equations with polynomial coefficients. In the present work, we establish the neces…
Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains
Keegan L. A. Kirk, Tamas L. Horvath, Aycil Cesmelioglu +1
This paper presents the first analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. The analysis is b…
A Note on the Generalized and Universal Associated Legendre Equations
Keegan L. A. Kirk, Kyle R. Bryenton, Nasser Saad
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relat…