Distributed shape derivative via averaged adjoint method and applications [PDF]
, 2015 The structure theorem of Hadamard-Zol\'esio states that the derivative of a shape functional is a distribution on the boundary of the domain depending only on the normal perturbations of a smooth enough boundary.
A. Laurain, K. Sturm
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On the shape derivative of polygonal inclusions in the conductivity problem [PDF]
E S A I M: Control, Optimisation and Calculus of VariationsWe consider the conductivity problem for a homogeneous body with an inclusion of a different, but known, conductivity. Our interest concerns the associated shape derivative, i.e., the derivative of the corresponding electrostatic potential with respect ...
M. Hanke
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Designing gradient coils with the shape derivative and the closed B-spline curves. [PDF]
Magnetic Resonance ImagingThis study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging).
Toru Takahashi
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A shape derivative algorithm for reconstructing elastic dislocations in geophysics [PDF]
Research in the Mathematical SciencesWe consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth.
Andrea Aspri +3 more
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Coupling Shape Optimization and Topological Derivative for Maxwell Equations
Abstract and Applied Analysis, 2022 The paper deals with a coupling algorithm using shape and topological derivatives of a given cost functional and a problem governed by nonstationary Maxwell’s equations in 3D. To establish the shape and topological derivatives, an adjoint method is used.
SY Alassane
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Strong Shape Derivative for the Wave Equation with Neumann Boundary Condition
System Modelling and Optimization, 2011 The paper provides shape derivative analysis for the wave equation with mixed boundary conditions on a moving domain Ω s in the case of non smooth neumann boundary datum.
J. Zolésio, L. Bociu
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On Topological Derivative in Shape Optimization [PDF]
, 1997 In the paper the topological derivative for arbitrary shape functional is defined. Examples are provided for elliptic equations and the elasticity system in the plane. The topological derivative can be used for solving shape optimization problems in structural mechanics.
Sokolowski, Jan, Zochowski, Antoni
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A shape-derivative approach to some PDE model in image restoration [PDF]
Electronic Journal of Differential Equations, 2018 In this paper we analyze the shape derivative of a cost functional appearing in image restoration. The main feature of this cost functional is the appearance of a variable exponent.
Carla Baroncini, Julian Fernandez Bonder
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Shape Derivative for Penalty-Constrained Nonsmooth–Nonconvex Optimization: Cohesive Crack Problem [PDF]
Journal of Optimization Theory and Applications, 2022 A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities is studied with respect to its shape differentiability.
V. Kovtunenko, K. Kunisch
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Shape preserving piecewise rational interpolation [PDF]
, 1983 An explicit representation of a C1 piecewise rational cubic function is developed which can be used to solve the problem of shape preserving interpolation.
Gregory, JA, Delbourgo, R
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