Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains
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Publication:2286499
DOI10.1016/j.matpur.2019.09.002zbMath1431.49050OpenAlexW2972854788WikidataQ122112559 ScholiaQ122112559MaRDI QIDQ2286499
Publication date: 22 January 2020
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.matpur.2019.09.002
Nonsmooth analysis (49J52) Optimization of shapes other than minimal surfaces (49Q10) Sensitivity analysis for optimization problems on manifolds (49Q12) Moving boundary problems for PDEs (35R37) PDEs in connection with control and optimization (35Q93)
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Cites Work
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- Distortion compensation as a shape optimisation problem for a sharp interface model
- Shape derivatives for minima of integral functionals
- Sobolev spaces on non-Lipschitz subsets of \(\mathbb {R}^n\) with application to boundary integral equations on fractal screens
- An optimal triangulation for second-order elliptic problems
- Boundary value problems for the Laplacian in convex and semiconvex domains
- Design sensitivity analysis of structural systems
- Structure of shape derivatives for nonsmooth domains
- Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
- Anatomy of the shape Hessian
- The elastic energy-momentum tensor
- Shape sensitivity for the Laplace--Beltrami operator with singularities.
- Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. II. Transl. from the German by Boris Plamenevskii
- Shape variation and optimization. A geometrical analysis
- Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT
- Anatomy of the shape Hessian via Lie brackets
- The inhomogeneous Dirichlet problem in Lipschitz domains
- Topological derivatives in shape optimization
- Singularities of electromagnetic fields in polyhedral domains
- Regularity and singularities of optimal convex shapes in the plane
- Structure of shape derivatives
- Comparison of approximate shape gradients
- Stability in shape optimization with second variation
- Variational approach to shape derivatives for a class of Bernoulli problems
- A Variational Method for Second Order Shape Derivatives
- Distributed shape derivativeviaaveraged adjoint method and applications
- ANALYTIC REGULARITY FOR LINEAR ELLIPTIC SYSTEMS IN POLYGONS AND POLYHEDRA
- Differentiability of the Dirichlet to Neumann Map Under Movements of Polygonal Inclusions with an Application to Shape Optimization
- Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. I : Résultats généraux pour le problème de Dirichlet
- Shapes and Geometries
- Efficient PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics
- Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. II : Quelques opérateurs particuliers
- Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics
- Variational approach to shape derivatives
- On the analysis of boundary value problems in nonsmooth domains
- Differentiation with Respect to the Domain in Boundary Value Problems
- Optimum Experimental Design by Shape Optimization of Specimens in Linear Elasticity
- Higher-Order Moving Mesh Methods for PDE-Constrained Shape Optimization
- Weak and Strong Form Shape Hessians and Their Automatic Generation
- Reproducing kernel Hilbert spaces and variable metric algorithms in PDE-constrained shape optimization
- A proof of the trace theorem of Sobolev spaces on Lipschitz domains
- A Unified Discrete–Continuous Sensitivity Analysis Method for Shape Optimization
- A transmission problem on a polygonal partition: regularity and shape differentiability
- Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model
- Certified Descent Algorithm for shape optimization driven by fully-computable a posteriori error estimators
- Estimates of first and second order shape derivatives in nonsmooth multidimensional domains and applications
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