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On numerical study of constrained coupled shape optimization problems based on a new shape derivative method

Numerical Methods for Partial Differential Equations, 2022
In this article, we deal with a numerical method for the approximation of a class of coupled shape optimization problems, which consist in minimizing an appropriate general volume cost functional subjected to coupled boundary value problems by means of a
A. Boulkhemair, A. Chakib, Azeddine Sadik   +2 more
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Structure of shape derivatives

Journal of Evolution Equations, 2002
In this paper, we describe the precise structure of second "shape derivatives", that is derivatives of functions whose argument is a variable subset of \( \mathbb{R}^N \). This is done for Frechet derivatives in adequate Banach spaces. Besides the structure itself, interest lies in the way it is derived: the starting point is a "functional analytic ...
Arian Novruzi, Michel Pierre
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Shape derivatives without taking the shape derivative

PAMM, 2007
AbstractA general framework for calculating shape derivatives for optimization problems with partial differential equations as constraints is presented. Exploiting the structure of the cost functional the proposed technique allows to obtain the shape derivative of the cost without the necessity to involve the shape derivative of the state variable ...
Kazufumi Ito, K. Kunisch, G. Peichl
semanticscholar   +2 more sources

Shape derivative of discretized problems

Computer Methods in Applied Mechanics and Engineering, 1993
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M. Souli, J. Zolésio
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Topological Derivatives in Shape Optimization

Interaction of Mechanics and Mathematics, 2013
The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks.
Novotny, A.A., Sokolowski, Jan
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The strip method for shape derivatives

International Journal for Numerical Methods in Engineering, 2021
AbstractA major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive.
Sean Hardesty, Harbir Antil, Drew P. Kouri, Denis Ridzal   +3 more
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On the shape of n-derivations

Commentationes Mathematicae, 2020
Summary: We present some classification results for \(n\)-derivations over certain commutative rings.
Maciejewski, Maciej, Prószyński, Andrzej   +1 more
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Material and Shape Derivative Method for Quasi-Linear Elliptic Systems with Applications in Inverse Electromagnetic Interface Problems

SIAM Journal on Numerical Analysis, 2012
I. Cimrák
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Shapes of derivative neopolarograms

Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 1977
Abstract A derivative neopolarogram is the peaked curve that is generated by semidifferentiation of the current that flows in response to an imposed ramp signal on a stationary electrode. Theory is presented that describes the shapes of such curves for both reversible and irreversible electrode processes at planar and spherical electrodes.
Penny Dalrymple-Alford, Masashi Goto, Keith B. Oldham   +2 more
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