Related papers: Shape optimisation with nearly conformal transform…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
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…
This paper describes a node relocation algorithm based on nonlinear optimization which delivers excellent results for both unstructured and structured plane triangle meshes over convex as well as non-convex domains with high curvature. The…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
A novel methodology to efficiently approximate the Hessian for numerical shape optimization is considered. The method enhances operator symbol approximations by including body fitted coordinates and spatially changing symbols in a semi…
Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase…
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…
Generative models have attracted considerable attention for their ability to produce novel shapes. However, their application in mechanical design remains constrained due to the limited size and variability of available datasets. This study…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
Riemannian structures on infinite-dimensional manifolds arise naturally in shape analysis and shape optimization. These applications lead to optimization problems on manifolds which are not modeled on Banach spaces. The present article…
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…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
We study an optimization problem that aims to determine the shape of an obstacle that is submerged in a fluid governed by the Stokes equations. The mentioned flow takes place in a channel, which motivated the imposition of a Poiseuille-like…
The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper…
We compare surface metrics for shape optimization problems with constraints, consisting mainly of partial differential equations (PDE), from a computational point of view. In particular, classical Laplace-Beltrami type based metrics are…
The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
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…
In this work, we develop a framework based on piecewize B\'ezier curves to plane shapes deformation and we apply it to shape optimization problems. We describe a general setting and some general result to reduce the study of a shape…