Results 1 to 10 of about 6,713,628 (313)
Mathematics, 2014 A shape optimization method is used to study the exterior Bernoulli free boundaryproblem. We minimize the Kohn–Vogelius-type cost functional over a class of admissibledomains subject to two boundary value problems. The first-order shape derivative of the
Jerico B. Bacani, Gunther Peichl
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On the Topological Derivative in Shape Optimization [PDF]
SIAM Journal on Control and Optimization, 1999 In this paper the topological derivative for an 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.
J. Sokołowski, A. Zochowski
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Shape derivative of the Cheeger constant [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2015 This paper deals with the existence of the shape derivative of the Cheeger constant $h_1(\Omega)$ of a bounded domain $\Omega$. We prove that if $\Omega$ admits a unique Cheeger set, then the shape derivative of $h_1(\Omega)$ exists, and we provide an ...
E. Parini, N. Saintier
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On a Shape Derivative Formula in the Brunn-Minkowski Theory [PDF]
SIAM Journal on Control and Optimization, 2017 We extend a formula for the computation of the shape derivative of an integral cost functional with respect to a class of convex domains, using the so-called support functions and gauge functions to express it. This is a priori a formula in shape optimization theory.
Abdesslem Boulkhemair
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Shape Derivative of Drag Functional [PDF]
SIAM Journal on Control and Optimization, 2010 In this paper, compressible, stationary Navier–Stokes equations are considered. The model is well-posed, and there exist weak solutions in bounded domains, subject to inhomogeneous boundary conditions. The shape sensitivity analysis is performed for Navier–Stokes boundary value problems in the framework of small perturbations of the so-called ...
P. Plotnikov, J. Sokołowski
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The shape derivative of the Gauss curvature [PDF]
Revista de la Unión Matemática Argentina, 2017 We introduce new results about the shape derivatives of scalar- and vector-valued functions, extending the results from (Dogan-Nochetto 2012) to more general surface energies. They consider surface energies defined as integrals over surfaces of functions
Aníbal Chicco-Ruiz +2 more
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Shape Derivative of the Dirichlet Energy for a Transmission Problem [PDF]
Archive for Rational Mechanics and Analysis, 2019 For a transmission problem in a truncated two-dimensional cylinder located beneath the graph of a function u , the shape derivative of the Dirichlet energy (with respect to u ) is shown to be well-defined and is computed in terms of u .
P. Laurençot, Christoph Walker
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International Journal of Differential Equations, 2015 The exterior Bernoulli free boundary problem was studied via shape optimization technique. The problem was reformulated into the minimization of the so-called Kohn-Vogelius objective functional, where two state variables involved satisfy two boundary ...
Jerico B. Bacani, Julius Fergy T. Rabago
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The Shapes of Things: A Practical Guide to Differential Geometry and the Shape Derivative [PDF]
, 2015 Many things around us have properties that depend on their shape-for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a shape variable.
Shawn W. Walker
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On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem
Abstract and Applied Analysis, 2013 The exterior Bernoulli free boundary problem is being considered. The solution to the problem is studied via shape optimization techniques. The goal is to determine a domain having a specific regularity that gives a minimum value for the Kohn-Vogelius ...
Jerico B. Bacani, Gunther Peichl
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