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In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

Optimization and Control · Mathematics 2020-11-03 Caroline Geiersbach , Estefania Loayza-Romero , Kathrin Welker

Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…

Numerical Analysis · Mathematics 2023-05-29 Martin Berggren

We introduce a novel mesh-free and direct method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic representation of the shape derivative and is applicable for…

Optimization and Control · Mathematics 2026-01-27 Luka Schlegel , Volker Schulz , Frank T. Seifried , Maximilian Würschmidt

We introduce a novel method for the implementation of shape optimziation in fluid dynamics applications, where we propose to use the shape derivative to determine deformation fields with the help of the $p-$ Laplacian for $p > 2$. This…

Optimization and Control · Mathematics 2021-03-30 Peter Marvin Müller , Niklas Kühl , Martin Siebenborn , Klaus Deckelnick , Michael Hinze , Thomas Rung

We model a microchannel cooling system and consider the optimization of its shape by means of shape calculus. A three-dimensional model covering all relevant physical effects and three reduced models are introduced. The latter are derived…

Optimization and Control · Mathematics 2025-10-14 Sebastian Blauth , Christian Leithäuser , René Pinnau

Adjoint-based shape optimization most often relies on Eulerian flow field formulations. However, since Lagrangian particle methods are the natural choice for solving sedimentation problems in oceanography, extensions to the Lagrangian…

Fluid Dynamics · Physics 2022-09-07 Luka Schlegel , Volker Schulz

This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with nonhomogeneous boundary condition. The structure of shape gradient with respect to the shape of the variable domain…

Optimization and Control · Mathematics 2007-05-23 Z. M. Gao , Y. C. Ma , H. W. Zhuang

The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…

Optimization and Control · Mathematics 2016-09-16 Christian Heinemann , Kevin Sturm

While topological derivatives have proven useful in applications of topology optimisation and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial…

Optimization and Control · Mathematics 2022-07-20 Peter Gangl , Kevin Sturm

This article revolves around shape and topology optimization, in the applicative context where the objective and constraint functionals depend on the solution to a physical boundary value problem posed on the optimized domain. We introduce…

Optimization and Control · Mathematics 2024-09-13 Charles Dapogny , Bruno Levy , Edouard Oudet

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…

Optimization and Control · Mathematics 2007-05-23 Zhiming Gao , Yichen Ma , Hongwei Zhuang

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…

Optimization and Control · Mathematics 2022-05-09 Victor A. Kovtunenko , Karl Kunisch

This paper provides an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The orientation angle optimization is based on a topological derivative, which measures the…

Computational Engineering, Finance, and Science · Computer Science 2023-06-21 Masaki Noda , Kei Matsushima , Takayuki Yamada

Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…

Analysis of PDEs · Mathematics 2021-06-21 Stefano Almi , Ulisse Stefanelli

In this paper, we analyze the effects of contact models on contact-implicit trajectory optimization for manipulation. We consider three different approaches: (1) a contact model that is based on complementarity constraints, (2) a smooth…

Robotics · Computer Science 2019-01-31 Aykut Ozgun Onol , Philip Long , Taskin Padir

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…

Optimization and Control · Mathematics 2022-11-23 Cornel Marius Murea , Dan Tiba

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…

Computer Vision and Pattern Recognition · Computer Science 2017-09-18 Zorah Lähner , Matthias Vestner , Amit Boyarski , Or Litany , Ron Slossberg , Tal Remez , Emanuele Rodolà , Alex Bronstein , Michael Bronstein , Ron Kimmel , Daniel Cremers

In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this…

Analysis of PDEs · Mathematics 2020-12-29 E. Beretta , E. Francini , S. Vessella

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…

Optimization and Control · Mathematics 2025-12-30 Cornel Marius Murea , Dan Tiba

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…

Optimization and Control · Mathematics 2020-12-17 Daniel Luft , Volker H. Schulz , Kathrin Welker