Related papers: Sharp interface limit for a phase field model in s…
In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…
We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…
We discuss a topology optimization problem for an elastoplastic medium. The distribution of material in a region is optimized with respect to a given target functional taking into account compliance. The incremental elastoplastic problem…
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
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 consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…
We investigate the systematic design of compliant morphing structures composed of materials reacting to an external stimulus. We add a perimeter penalty term to ensure existence of solutions. We propose a phase-field approximation of this…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
We consider general shape optimization problems governed by Dirichlet boundary value problems. The proposed approach may be extended to other boundary conditions as well. It is based on a recent representation result for implicitly defined…
This article is concerned with the problem of minimising the Willmore energy in the class of \emph{connected} surfaces with prescribed area which are confined to a small container. We propose a phase field approximation based on De Giorgi's…
We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadrature for the phase field function and hence is very easy to…
In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter $\epsilon$, representing the interface thickness between the tumorous and non tumorous cells,…
We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a functional of two order parameters. The first one reflects the orientational order while the…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact line problem are studied by asymptotic analysis and numerical simulations. The effects of the {mobility} number as well…
In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…
We discuss the sharp interface limit of a diffuse interface model for a two-phase flow of two partly miscible viscous Newtonian fluids of different densities, when a certain parameter \epsilon>0 related to the interface thickness tends to…
We construct gradient structures for free boundary problems with nonlinear elasticity and study the impact of moving contact lines. In this context, we numerically analyze how phase-field models converge to certain sharp-interface limits…
Diffuse interface descriptions offer many advantages for the modeling of microstructure evolution. However, the numerical representation of moving diffuse interfaces on discrete numerical grids involves spurious grid friction, which limits…