Related papers: Shape optimization for variational inequalities: t…
This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…
Motivated by a long-standing conjecture of Polya and Szeg\"o about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
We study the Stokes problem in a bounded planar domain $\Omega$ with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [6], in the present paper the threshold value may depend on the…
This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier--Stokes equations with mixed boundary conditions containing the pressure. The minimization problem…
We consider the inverse fault friction problem of determining the friction coefficient in the Tresca friction model, which can be formulated as an inverse problem for differential inequalities. We show that the measurements of elastic waves…
A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities (VI) is studied with respect to its shape differentiability. The specific problem stemming from quasi-brittle fracture…
We consider dynamic motion of a linearized elastic body with a crack subject to a modified contact law, which we call the Signorini contact condition of dynamic type, and to the Tresca friction condition. Whereas the modified contact law…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent…
This paper sets up an approach for shape optimization problems constrained by variational inequalities (VI) in an appropriate shape space. In contrast to classical VI, where no explicit dependence on the domain is given, VI constrained…
This paper is concerned with the optimal shape design of the newtonian viscous incompressible fluids driven by the stationary nonhomogeneous Navier-Stokes equations. We use three approaches to derive the structures of shape gradients for…
In this paper, a spectral method based on conformal mappings is proposed to solve Steklov eigenvalue problems and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
In this article, we consider the problem of optimal design of a compliant structure under a volume constraint, within the framework of linear elasticity. We introduce the pure displacement and the dual mixed formulations of the linear…
This work focuses on numerically solving a shape identification problem related to advection-diffusion processes with space-dependent coefficients using shape optimization techniques. Two boundary-type cost functionals are considered, and…
In this paper, we propose a novel shape optimization approach for the source identification of elliptic equations. This identification problem arises from two application backgrounds: actuator placement in PDE-constrained optimal controls…
We consider the solution of a stochastic convex optimization problem $\mathbb{E}[f(x;\theta^*,\xi)]$ over a closed and convex set $X$ in a regime where $\theta^*$ is unavailable and $\xi$ is a suitably defined random variable. Instead,…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
In this paper we analyze the relaxed form of a shape optimization problem with state equation $\{{array}{ll} -div \big(a(x)Du\big)=f\qquad\hbox{in}D \hbox{boundary conditions on}\partial D. {array}.$ The new fact is that the term $f$ is…