Related papers: Topology optimization in Bernoulli free boundary p…
Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
We expose here a novel application of the so-called coupled complex boundary method -- first put forward by Cheng et al. (2014) to deal with inverse source problems -- in the framework of shape optimization for solving the exterior…
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…
To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…
Bernoulli's free boundary problem is an overdetermined problem in which one seeks an annular domain such that the capacitary potential satisfies an extra boundary condition. There exist two different types of solutions called elliptic and…
We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion.…
This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin…
The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of…
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…
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…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the Bernoulli equation. The Newton-like scheme is developed by employing shape derivatives in the weak…
We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…
We propose conditioning field initialization for neural network based topology optimization. In this work, we focus on (1) improving upon existing neural network based topology optimization, (2) demonstrating that by using a prior initial…
We consider the exterior free boundary Bernoulli problem in the case of a rough given domain. An asymptotic analysis shows that the solution of the initial problem can be approximated by the solution of a non-rough Bernoulli problem at…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
A Bernoulli free boundary problem with geometrical constraints is studied. The domain $\Om$ is constrained to lie in the half space determined by $x_1\geq 0$ and its boundary to contain a segment of the hyperplane $\{x_1=0\}$ where…
We investigate a fixed domain approach in shape optimization, using a regularization of the Heaviside function both in the cost functional and in the state system. We consider the compliance minimization problem in linear elasticity, a well…