Related papers: A curvature-regularized variational problem with a…
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…
When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using an independent background discretisation, not aligned with…
We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition…
This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and…
In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven…
We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with…
We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a fully Eulerian interfacial energy. In order to penalize large…
In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…
The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
In this article, a compliance minimisation scheme for designing spatially varying orthotropic porous structures is proposed. With the utilisation of conformal mapping, the porous structures here can be generated by two controlling field…
In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
A variational model for describing the morphology of two-phase continua by allowing for the interplay between coherent and incoherent interfaces is introduced. Coherent interfaces are characterized by the microscopical arrangement of atoms…
Linear convergence of first-order methods is typically characterized by global optimization conditions whose constants reflect worst-case geometry of the ambient space. In high-dimensional or structured problems, these global constants can…
A model for kinetic roughening of one-dimensional interfaces is presented within an intrinsic geometry framework that is free from the standard small-slope and no-overhang approximations. The model is meant to probe the consequences of the…
We propose a boundary-corrected weak Galerkin mixed finite element method for solving elliptic interface problems in 2D domains with curved interfaces. The method is formulated on body-fitted polygonal meshes, where interface edges are…
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area…