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This paper addresses optimal design problems governed by multi-state stationary diffusion equations, aiming at the simultaneous optimization of the domain shape and the distribution of two isotropic materials in prescribed proportions.…

Optimization and Control · Mathematics 2026-02-19 Marko Erceg , Petar Kunštek , Marko Vrdoljak

This paper presents a method for simultaneous optimization of the outer shape and internal topology of aircraft wings, with the objective of minimizing drag subject to lift and compliance constraints for multiple load cases. The physics are…

Computational Engineering, Finance, and Science · Computer Science 2023-05-01 Lukas C. Høghøj , Cian Conlan-Smith , Ole Sigmund , Casper Schousboe Andreasen

In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem is formulated by introducing cost functional. We…

Optimization and Control · Mathematics 2022-11-17 Mame Gor Ngom , Ibrahima Faye , Diaraf Seck

We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is…

Optimization and Control · Mathematics 2026-04-01 Peter Gangl , Michael H. Gfrerer

This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…

Optimization and Control · Mathematics 2022-08-30 Bastien Chaudet-Dumas

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…

Optimization and Control · Mathematics 2014-12-16 Christian Leithäuser , René Pinnau , Robert Feßler

In this paper we analyze a shape optimization problem, with Stokes equations as the state problem, defined on a domain with a part of the boundary that is described as the graph of the control function. The state problem formulation is…

Numerical Analysis · Mathematics 2014-03-17 Ivan Fumagalli , Nicola Parolini , Marco Verani

An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…

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…

Numerical Analysis · Mathematics 2021-08-13 John Sebastian H. Simon , Hirofumi Notsu

This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…

Optimization and Control · Mathematics 2025-02-10 Livia Betz

We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…

Optimization and Control · Mathematics 2023-01-23 Harald Garcke , Paul Hüttl , Christian Kahle , Patrik Knopf , Tim Laux

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…

Optimization and Control · Mathematics 2015-06-11 Klaus Deckelnick , Michael Hinze , Tobias Jordan

In this work we study a general shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. Moreover, we also analyze…

Analysis of PDEs · Mathematics 2016-12-28 Julian Fernandez Bonder , Antonella Ritorto , Ariel Martin Salort

This paper continues earlier work and is concerned with the inverse problem of parameter identification in variational inequalities of the second kind that does not only treat the parameter linked to a bilinear form, but importantly also…

Optimization and Control · Mathematics 2021-01-01 Joachim Gwinner

A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal…

Computational Engineering, Finance, and Science · Computer Science 2020-10-23 Prabhat Kumar , Roger A. Sauer , Anupam Saxena

This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…

Optimization and Control · Mathematics 2018-04-30 Christian Clason , Armin Rund , Karl Kunisch

This work deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…

Optimization and Control · Mathematics 2022-08-30 Bastien Chaudet-Dumas

This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available…

Optimization and Control · Mathematics 2017-02-27 Christian Clason , Karl Kunisch

We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the…

Optimization and Control · Mathematics 2014-07-08 Juan-Carlos De Los Reyes , Christian Meyer