On a numerical shape optimization approach for a class of free boundary problems

DOI10.1007/s10589-020-00212-zzbMath1469.49040OpenAlexW2960077788MaRDI QIDQ2023664

Abdelkrim Chakib, Abdesslam Boulkhemair, Amin Z. Sadik, Abdeljalil Nachaoui, Agaddin A. Niftiyev

Publication date: 3 May 2021

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10589-020-00212-z

zbMATH Keywords

free boundary problemcost functionalshape optimizationconvex domainoptimal solutionsupport functionshape derivativeBernoulli problem

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Optimality conditions for problems involving partial differential equations (49K20) Optimization of shapes other than minimal surfaces (49Q10) Discrete approximations in optimal control (49M25) Sensitivity analysis for optimization problems on manifolds (49Q12)

Related Items (4)

A new numerical approach for solving shape optimization fourth-order spectral problems among convex domains ⋮ On numerical study of constrained coupled shape optimization problems based on a new shape derivative method ⋮ On an effective approach in shape optimization problem for Stokes equation ⋮ On a numerical approach for solving some geometrical shape optimization problems in fluid mechanics

Cites Work

• A shape optimization approach for a class of free boundary problems of Bernoulli type.
• Optimal treatment of structures
• Tracking Dirichlet data in \(L^2\) is an ill-posed problem
• Shape optimization of systems governed by Bernoulli free boundary problems
• Shape optimization and fictitious domain approach for solving free boundary problems of Bernoulli type
• An embedding domain approach for a class of 2-d shape optimization problems: Mathematical analysis.
• Shape optimization approach for solving the Bernoulli problem by tracking the Neumann data: a Lagrangian formulation
• Approximation variationnelle des problèmes aux limites
• Numerical solution of the free-boundary Bernoulli problem using a level set formulation
• Variational approach to shape derivatives for a class of Bernoulli problems
• On a Shape Derivative Formula in the Brunn--Minkowski Theory
• Shapes and Geometries
• Tracking Neumann Data for Stationary Free Boundary Problems
• Convex Bodies The Brunn-MinkowskiTheory
• Fast Numerical Methods for Bernoulli Free Boundary Problems
• Notions of convexity
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