84 citations · 117 across the 17 of their papers we have counts for
18 papers
An A Posteriori Error Estimator for Electrically Coupled Liquid Crystal Equilibrium Configurations
J. H. Adler, D. B. Emerson
This paper derives an a posteriori error estimator for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen mo…
Parameter-free preconditioning for nearly-incompressible linear elasticity
James H Adler, Xiaozhe Hu, Yuwen Li +1
It is well known that via the augmented Lagrangian method, one can solve Stokes' system by solving the nearly incompressible linear elasticity equation. In this paper, we show that…
Morpho -- A programmable environment for shape optimization and shapeshifting problems
Chaitanya Joshi, Daniel Goldstein, Cole Wennerholm +6
An emerging theme across many domains of science and engineering is materials that change shape, often dramatically. Determining their structure involves solving a shape optimizati…
A Stable Mimetic Finite-Difference Method for Convection-Dominated Diffusion Equations
James H. Adler, Casey Cavanaugh, Xiaozhe Hu +2
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated reg…
Monolithic multigrid for a reduced-quadrature discretization of poroelasticity
James H. Adler, Yunhui He, Xiaozhe Hu +2
Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer…
A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations
James H. Adler, Casey Cavanaugh, Xiaozhe Hu +1
Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of t…
Monolithic Multigrid for Magnetohydrodynamics
J. H. Adler, T. Benson, E. C. Cyr +3
The magnetohydrodynamics (MHD) equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strong…
First-order system least squares finite-elements for singularly perturbed reaction-diffusion equations
James H. Adler, Scott MacLachlan, Niall Madden
We propose a new first-order-system least squares (FOSLS) finite-element discretization for singularly perturbed reaction-diffusion equations. Solutions to such problems feature la…
Discrete Energy Laws for the First-Order System Least-Squares Finite-Element Approach
J. H. Adler, I. Lashuk, S. P. MacLachlan +1
This paper analyzes the discrete energy laws associated with first-order system least-squares (FOSLS) discretizations of time-dependent partial differential equations. Using the he…
New stabilized discretizations for poroelasticity and the Stokes' equations
Carmen Rodrigo, Xiaozhe Hu, Peter Ohm +3
In this work, we consider the popular P1-RT0-P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation does not satisf…
Computing equilibrium states of cholesteric liquid crystals in elliptical channels with deflation algorithms
David B. Emerson, Patrick E. Farrell, James H. Adler +2
We study the problem of a cholesteric liquid crystal confined to an elliptical channel. The system is geometrically frustrated because the cholesteric prefers to adopt a uniform ra…
Robust Block Preconditioners for Biot's Model
James H. Adler, Francisco J. Gaspar, Xiaozhe Hu +2
In this paper, we design robust and efficient block preconditioners for the two-field formulation of Biot's consolidation model, where stabilized finite-element discretizations are…
A Deflation Technique for Detecting Multiple Liquid Crystal Equilibrium States
J. H. Adler, D. B. Emerson, P. E. Farrell +1
Multiple equilibrium states arise in many physical systems, including various types of liquid crystal structures. Having the ability to reliably compute such states enables more ac…
Competition of Lattice and Basis for Alignment of Nematic Liquid Crystals
Andrew DeBenedictis, Candy Anquetil-Deck, Douglas J. Cleaver +4
Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here, we consider how such alignment c…
Constrained Optimization for Liquid Crystal Equilibria: Extended Results
J. H. Adler, D. B. Emerson, S. P. MacLachlan +1
This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these…
Energy Minimization for Liquid Crystal Equilibrium with Electric and Flexoelectric Effects
J. H. Adler, T. J. Atherton, T. R. Benson +2
This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and externa…
An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis
J. H. Adler, T. J. Atherton, D. B. Emerson +1
This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effect…
First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow
J. H. Adler, J. Brannick, C. Liu +2
This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical…