2.6k citations · 3.2k across the 50 of their papers we have counts for
53 papers
A Scaling Approach to Elliptic Theory for Geometrically-Natural Differential Operators with Sobolev-Type Coefficients
Michael Holst, David Maxwell, Gantumur Tsogtgerel
We develop local elliptic regularity for operators having coefficients in a range of Sobolev-type function spaces (Bessel potential, Sobolev-Slobodeckij, Triebel-Lizorkin, Besov) w…
Finite Element Methods for Linear Maxwell's Equations in Bianisotropic Media Permitting Polarization Fields and Magnetic Currents
Tharindu Fernando, Martin Licht, Michael Holst
We review Maxwell's equations and constitutive relations for 3D bianisotropic media in a generalized form: we consider all four variables and allow for nonzero polarization or magn…
A Note On Determining Projections for Non-Homogeneous Incompressible Fluids
Benjamin Faktor, Michael Holst
In this note, we consider a viscous incompressible fluid in a finite domain in both two and three dimensions, and examine the question of determining degrees of freedom (projection…
Local Finite Element Approximation of Sobolev Differential Forms
Evan S. Gawlik, Michael J. Holst, Martin W. Licht
We address fundamental aspects in the approximation theory of vector-valued finite element methods, using finite element exterior calculus as a unifying framework. We generalize th…
Local sensitivity analysis of the `Membrane shape equation' derived from the Helfrich energy
P. Rangamani, A. Behzadan, M. Holst
The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric charact…
Applications and Challenges of Machine Learning to Enable Realistic Cellular Simulations
Ritvik Vasan, Meagan P. Rowan, Christopher T. Lee +3
In this perspective, we examine three key aspects of an end-to-end pipeline for realistic cellular simulations: reconstruction and segmentation of cellular structures; generation o…