Related papers: Sharp-interface limit of a multi-phase spectral sh…
Inspired by continuum mechanical contact problems with geological fault networks, we consider elliptic second order differential equations with jump conditions on a sequence of multiscale networks of interfaces with a finite number of…
This paper concerns the sharp interface limit of solutions to the inhomogeneous incompressible Navier-Stokes/Allen-Cahn coupled system in a bounded domain $\Omega \subset \mathbb{R}^n,\ n =2,3$. Based on a relative energy method, we prove…
In traditional phase-field modeling of multiphase materials, a significant challenge arises from the non-local nature of fracture energy regularization, where interfacial toughness is inherently coupled with the properties of the…
We investigate a phase-field version of the Faber--Krahn theorem based on a phase-field optimization problem introduced in Garcke et al. [ESAIM Control Optim. Calc. Var. 29 (2023), Paper No. 10] formulated for the principal eigenvalue of…
We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic…
We introduce a new technique to optimize a linear cost function subject to a one-dimensional affine homogeneous quadratic integral inequality, i.e., the requirement that a homogeneous quadratic integral functional, affine in the…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…
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…
The problem of simulating solid-state dewetting of thin films in three dimensions (3D) by using a sharp-interface approach is considered in this paper. Based on the thermodynamic variation, a speed method is used for calculating the first…
We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…
In this paper, we propose and analyze a diffuse interface model for inductionless magnetohydrodynamic fluids. The model couples a convective Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes system for fluid flow…
We consider the sharp interface limit of a coupled Stokes/Allen-Cahn system, when a parameter $\varepsilon>0$ that is proportional to the thickness of the diffuse interface tends to zero, in a two dimensional bounded domain. For…
We provide a novel sharp-interface analysis via Gamma-convergence for a non-local and non-homogeneous diffuse-interface model for phase transitions, featuring an interplay between a non-local interaction kernel and a spatially dependent…
In this paper, we present an efficient algorithm for solving a linear optimization problem with entropic constraints, a class of problems that arises in game theory and information theory. Our analysis distinguishes between the cases of…
We present two sharp, closed-form empirical Bernstein inequalities for symmetric random matrices with bounded eigenvalues. By sharp, we mean that both inequalities adapt to the unknown variance in a tight manner: the deviation captured by…
We present a general framework for accurately evaluating finite difference operators in the presence of known discontinuities across an interface. Using these techniques, we develop simple-to-implement, second-order accurate methods for…
We consider the shape optimization of an object in Navier--Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we…