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A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…

Numerical Analysis · Mathematics 2024-05-09 Gustav Eriksson , Vidar Stiernström

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

Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discontinuity interface is the unknown. Using Gr\"oger's…

Optimization and Control · Mathematics 2022-01-28 Yuri Flores Albuquerque , Antoine Laurain , Kevin Sturm

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to…

Analysis of PDEs · Mathematics 2018-03-20 Elena Beretta , Stefano Micheletti , Simona Perotto , Matteo Santacesaria

This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier--Stokes equations with mixed boundary conditions containing the pressure. The minimization problem…

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

This paper develops a framework connecting discrete adjoint gradient-error analysis with an optimization method that uses directional error tolerances, and applies it to airfoil shape optimization governed by a conservative full-potential…

Optimization and Control · Mathematics 2026-05-19 Humberto Gimenes Macedo , Luís Felipe Bueno

Particle based optimization algorithms have recently been developed as sampling methods that iteratively update a set of particles to approximate a target distribution. In particular Stein variational gradient descent has gained attention…

Machine Learning · Computer Science 2021-03-19 Francesco D'Angelo , Vincent Fortuin

In the last decade, parameter-free approaches to shape optimization problems have matured to a state where they provide a versatile tool for complex engineering applications. However, sensitivity distributions obtained from shape…

Computational Engineering, Finance, and Science · Computer Science 2023-10-04 Lars Radtke , Georgios Bletsos , Niklas Kühl , Tim Suchan , Thomas Rung , Alexander Düster , Kathrin Welker

We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…

Optimization and Control · Mathematics 2024-06-21 Johannes Haubner , Michael Ulbrich

In this paper, we propose a level set-based shape optimization method for acoustic wave propagation problems with a deformable structure. First, we propose a mathematical model for acoustic wave propagation with a deformed structure based…

Computational Engineering, Finance, and Science · Computer Science 2023-04-04 Yuki Noguchi , Takayuki Yamada

This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…

Numerical Analysis · Mathematics 2013-07-05 Xiaohui Peng , Katsiaryna Niakhai , Bartosz Protas

In this paper, we propose a novel shape optimization approach for the source identification of elliptic equations. This identification problem arises from two application backgrounds: actuator placement in PDE-constrained optimal controls…

Optimization and Control · Mathematics 2024-07-04 Wei Gong , Ziyi Zhang

It is common to manufacture an object by decomposing it into parts that can be assembled. This decomposition is often required by size limits of the machine, the complex structure of the shape, etc. To make it possible to easily assemble…

Computational Engineering, Finance, and Science · Computer Science 2023-10-31 Xingyuan Sun , Chenyue Cai , Ryan P. Adams , Szymon Rusinkiewicz

We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…

Numerical Analysis · Mathematics 2024-04-18 Junqing Chen , Bangti Jin , Haibo Liu

The complex physics and numerous failure modes of structural impact creates challenges when designing for impact resistance. While simple geometries of layered material are conventional, advances in 3D printing and additive manufacturing…

Optimization and Control · Mathematics 2023-01-04 Andrew Akerson

Shape optimization based on surface gradients and the Hadarmard-form is considered for a compressible viscous fluid. Special attention is given to the difference between the 'function composition' approach involving local shape derivatives…

Optimization and Control · Mathematics 2013-12-23 Matthias Sonntag , Stephan Schmidt , Nicolas R. Gauger

The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. The shape optimization problem is formulated by introducing a tracking-type cost functional…

Optimization and Control · Mathematics 2017-12-15 Markus Muhr , Vanja Nikolić , Barbara Wohlmuth , Linus Wunderlich

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…

Optimization and Control · Mathematics 2024-03-12 Tim Suchan , Volker Schulz , Kathrin Welker

The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility based on Griffith's criterion. This method requires a…

Optimization and Control · Mathematics 2025-04-01 Tim Suchan , Chaitanya Kandekar , Wolfgang E. Weber , Kathrin Welker

An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…

Computational Physics · Physics 2025-01-03 Ruifeng Yuan , Lei Wu