Related papers: Shape and topology optimization for variational in…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi-static motions of…
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs.…
Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the…
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the…
Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their…
We formulate a novel numerical method suitable for the solution of topology optimization problems in solid mechanics. The most salient feature of the new approach is that the space and time discrete equations of the numerical method can be…
Most of today's state-of-the-art methods for perspective shape from shading are modelled in terms of partial differential equations (PDEs) of Hamilton-Jacobi type. To improve the robustness of such methods w.r.t. noise and missing data,…
Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters in large systems of interacting…
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…
A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during…
We introduce a novel formulation for curvature regularization by penalizing normal curvatures from multiple directions. This total normal curvature regularization is capable of producing solutions with sharp edges and precise isotropic…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…
In this paper, we present a novel framework for deriving the evolution equation of the level set function in topology optimization, departing from conventional Hamilton-Jacobi based formulations. The key idea is the introduction of an…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
This paper presents a density-based topology optimization approach considering additive manufacturing limitations. The presented method considers the minimum size of parts, the minimum size of cavities, the inability of printing overhanging…
This paper is devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization problem is to find an optimal superconductor shape which minimizes a certain cost…