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In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…

Optimization and Control · Mathematics 2021-06-09 José A. Iglesias , Kevin Sturm , Florian Wechsung

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

In this paper we present an abstract nonsmooth optimization problem for which we recall existence and uniqueness results. We show a numerical scheme to approximate its solution. The theory is later applied to a sample static contact problem…

Optimization and Control · Mathematics 2023-09-19 Anna Ochal , Michal Jureczka , Piotr Bartman

Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view…

Optimization and Control · Mathematics 2022-03-15 Stephan Schmidt , Volker H. Schulz

We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity…

Numerical Analysis · Mathematics 2019-02-05 Erik Burman , Daniel Elfverson , Peter Hansbo , Mats G. Larson , Karl Larsson

In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…

Optimization and Control · Mathematics 2015-06-01 M. Dambrine , C. Dapogny , H. Harbrecht

The application of modern topology optimization techniques to single physics systems has seen great advances in the last three decades. However, the application of these tools to sophisticated multiphysics systems such as fluid-structure…

Numerical Analysis · Mathematics 2023-08-11 Mohamed Abdelhamid , Aleksander Czekanski

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…

Optimization and Control · Mathematics 2020-04-07 Cornel Marius Murea , Dan Tiba

We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable…

Graphics · Computer Science 2022-07-26 Sebastian Weiss , Robert Maier , Rüdiger Westermann , Daniel Cremers , Nils Thuerey

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

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

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…

Optimization and Control · Mathematics 2025-08-26 Xiaowei Pang

Design optimization problems, e.g., shape optimization, that involve deformable bodies in unilateral contact are challenging as they require robust contact solvers, complex optimization methods that are typically gradient-based, and…

Numerical Analysis · Mathematics 2024-05-07 Jingyi Wang , Jerome Solberg , Mike A. Puso , Eric B. Chin , Cosmin G. Petra

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 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

This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…

Numerical Analysis · Mathematics 2024-01-08 Manaswinee Bezbaruah , Matthias Maier , Winnifried Wollner

The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact…

Computational Engineering, Finance, and Science · Computer Science 2021-03-15 Gore Lukas Bluhm , Ole Sigmund , Konstantinos Poulios

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 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

In this work, the problem of shape optimization, subject to PDE constraints, is reformulated as an $L^p$ best approximation problem under divergence constraints to the shape tensor introduced in Laurain and Sturm: ESAIM Math. Model. Numer.…

Numerical Analysis · Mathematics 2024-04-02 Gerhard Starke