Related papers: Sharp interface limit for a phase field model in s…
Topology optimization is used for the design of high-performance structures but remains fundamentally limited by its iterative nature, requiring repeated finite element analyses that prevent real-time deployment and large-scale design…
Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…
We study the two and three dimensional stochastic Cahn-Hilliard equation in the sharp interface limit, where the positive parameter $\epsilon$ tends to zero, which measures the width of transition layers generated during phase separation.…
We consider the problem of minimizing Euler's elastica energy for simple closed curves confined to the unit disk. We approximate a simple closed curve by the zero level set of a function with values +1 on the inside and -1 on the outside of…
In this work, we study shape optimization problems in the Stokes flows. By phase-field approaches, the resulted total objective function consists of the dissipation energy of the fluids and the Ginzburg--Landau energy functional as a…
The numerical resolution efficiency of phase-field models is limited by grid friction, grid anisotropy and pinning. The 1D sharp phase-field model eliminates grid friction and pinning by a global restoration of Translational Invariance (TI)…
We study a recent formulation for fluid-structure interaction problems based on the use of a distributed Lagrange multiplier in the spirit of the fictitious domain approach. In this paper, we focus our attention on a crucial computational…
Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…
In this work we investigate a combination of classical PDE constrained optimization methods and a rounding strategy based on shape optimization for the identification of interfaces. The goal is to identify radioactive regions in a…
This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design…
We discuss the sharp interface limit, leading to a mean curvature flow energy, for the rate function of the large deviation principle of a Glauber+Kawasaki process with speed change. We provide an explicit formula of the limiting functional…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Topology design optimization offers tremendous opportunity in design and manufacturing freedoms by designing and producing a part from the ground-up without a meaningful initial design as required by conventional shape design optimization…
An efficient topology optimization method applicable to both continuum and rarefied gas flows is proposed in the framework of gas-kinetic theory. The areas of gas and solid are marked by the material density, based on which a fictitious…
We present first a brief review of the existing literature on shape optimization, stressing the recent use of Hamiltonian systems in topology optimization. In the second section, we collect some preliminaries on the implicit parametrization…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…
The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular…
Contact-aware topology optimization faces challenges in robustness, accuracy, and applicability to internal structural surfaces under self-contact. This work builds on the recently proposed barrier-based Incremental Potential Contact (IPC)…
We propose a variational principle combining a phase-field functional for structural topology optimization with a mixed (three-field) Hu-Washizu functional, then including directly in the formulation equilibrium, constitutive, and…