Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût

DOI10.1051/m2an/1986200303711zbMath0604.49003OpenAlexW2491155384MaRDI QIDQ3742221

Jean Cea

Publication date: 1986

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/193482

zbMATH Keywords

distributed systemsbibliographyoptimum design problemsdirectional derivation of the cost function

Mathematics Subject Classification ID

Newton-type methods (49M15) Control/observation systems governed by partial differential equations (93C20) Inverse problems for PDEs (35R30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Optimization problems in solid mechanics (74P99) Existence theories for optimal control problems involving partial differential equations (49J20) Continuity and differentiation questions (26B05)

Related Items

Concurrent Shape Optimization of the Part and Scanning Path for Powder Bed Fusion Additive Manufacturing, Shape identification of scatterers using a time-dependent adjoint method, Shape optimization for interface identification with obstacle problems, Topology optimization of structures undergoing brittle fracture, An optimization method for elastic shape matching, Level-set, penalization and Cartesian meshes: A paradigm for inverse problems and optimal design, Part and supports optimization in metal powder bed additive manufacturing using simplified process simulation, Augmented Lagrangian approach for a bilateral free boundary problem, Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics, Shape optimization of a linearly elastic rolling structure under unilateral contact using Nitsche's method and cut finite elements, Approximate Shape Gradients for Interface Problems, Towards a Lagrange–Newton Approach for PDE Constrained Shape Optimization, Shape Differentiability Under Non-linear PDE Constraints, A linearized approach to worst-case design in parametric and geometric shape optimization, Optimal control in ink-jet printing via instantaneous control, Shape optimization approach for solving the Bernoulli problem by tracking the Neumann data: a Lagrangian formulation, Generalized implicit function theorems and problems with a free boundary, A consistent relaxation of optimal design problems for coupling shape and topological derivatives, Shape sensitivity analysis via a penalization method, Shape optimization with a level set based mesh evolution method, Fracture resistance via topology optimization, Optimum Experimental Design by Shape Optimization of Specimens in Linear Elasticity, Shape optimization of an imperfect interface: steady-state heat diffusion, Hyperbolic equations with mixed boundary conditions: shape differentiability analysis, Design of thin micro-architectured panels with extension-bending coupling effects using topology optimization, Improved Discrete Boundary Type Shape Gradients for PDE-constrained Shape Optimization, Detection of holes in an elastic body based on eigenvalues and traces of eigenmodes, Robust shape optimization of continuous structures via the level set method, Multiscale topology optimization of electromagnetic metamaterials using a high-contrast homogenization method, A shape optimization algorithm based on directional derivatives for three‐dimensional contact problems, Shape optimization for Stokes flows using sensitivity analysis and finite element method, Functional level-set derivative for a polymer self consistent field theory Hamiltonian, Level set‐based shape optimization approach for the inverse optical tomography problem, Fréchet differentiability of the elasto-acoustic scattered field with respect to Lipschitz domains, Algorithmic Aspects of Multigrid Methods for Optimization in Shape Spaces, TOPOLOGICAL OPTIMIZATION FOR A QUASI-LINEAR PROBLEM WITH APPLICATION TO NON-NEWTONIAN FLUIDS, Level set-based shape optimization of deformable structures for achieving desired sound transmission and reflective responses, Robust Level-Set-Based Topology Optimization Under Uncertainties Using Anchored ANOVA Petrov–Galerkin Method, Optimal location of the support of the control for the 1-D wave equation: numerical investigations, Optimization of the shape of regions supporting boundary conditions, Elasto-plastic Shape Optimization Using the Level Set Method, Analyse des problèmes de forme par la dérivation des minimax. (Analysis of shape problems by minimax differentiation), Variation de forme pour une équation instationnaire du 4ème ordre dans un modèle de dislocations, Minimum stress optimal design with the level set method, Optimal shape design in three-dimensional Brinkman flow using asymptotic analysis techniques, On the active control of crack growth in elastic media, Structural optimization using sensitivity analysis and a level-set method., Shape optimization by free-form deformation: existence results and numerical solution for Stokes flows, Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing, Propagation for KPP bulk-surface systems in a general cylindrical domain, Shape and topology optimization, Suitable spaces for shape optimization, Anatomy of the shape Hessian, Shape and topology optimization considering anisotropic features induced by additive manufacturing processes, Structural optimization under internal porosity constraints using topological derivatives, Design of multi-layer materials using inverse homogenization and a level set method, An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations, Topology optimization of acoustic metasurfaces by using a two-scale homogenization method, Topology optimization of modulated and oriented periodic microstructures by the homogenization method, A new method for inverse electromagnetic casting problems based on the topological derivative, Damage and fracture evolution in brittle materials by shape optimization methods, A level-set method for vibration and multiple loads structural optimization, Optimal design of the support of the control for the 2D wave equation, Removing holes in topological shape optimization, Shape and parameter reconstruction for the Robin transmission inverse problem, Thermodynamic forces in single crystals with dislocations, The topological asymptotic expansion for the Quasi-Stokes problem, A deterministic approximation method in shape optimization under random uncertainties, Shape optimisation with the level set method for contact problems in linearised elasticity, Constrained shape optimization problem in elastic mechanics. Dedicated to Professor Dinh Nho Hao on the occasion of his 60th birthday, Distributed shape derivativeviaaveraged adjoint method and applications, Risk-averse structural topology optimization under random fields using stochastic expansion methods, Topology optimization for hyperbolic acoustic metamaterials using a high-frequency homogenization method, Shape optimization of a coupled thermal fluid-structure problem in a level set mesh evolution framework, Shape Optimization for Superconductors Governed by H(curl)-Elliptic Variational Inequalities, Sensitivity of the heat equation to jumps of conductivity, Topological sensitivity analysis for a three-dimensional parabolic type problem, High-order shape design sensitivity: A unified approach, The shape and topological optimizations' connection, Minimax Lagrangian Approach to the Differentiability of Nonlinear PDE Constrained Shape Functions Without Saddle Point Assumption, Coupling Between Shape Gradient and Topological Derivative in 2D Incompressible Navier-Stokes Flows, Reconstruction of contact regions in semiconductor transistors using Dirichlet-Neumann cost functional approach, Sensitivity analysis of a shape control problem for the Navier--Stokes equations, Comparison of approximate shape gradients, Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems, An abstract Lagrangian framework for computing shape derivatives

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Shape design sensitivity of a membrane
• Quelques résultats sur l'identification de domaines
• On isoperimetric problems for domains with partly known boundaries
• On the existence of a solution in a domain identification problem
• Optimization of elastic bars in torsion
• Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Méthodes de résolution des problèmes approches
• A dual algorithm for the solution of nonlinear variational problems via finite element approximation
• Numerical solution of two-dimensional magnetostatic problems by augmented lagrangian methods
• Optimality conditions in the problem of seeking the hole shapes in elastic bodies
• Lectures on optimization - theory and algorithms. Notes by M. K. V. Murthy
• Analyse numérique du champ magnetique d'un alternateur par éléments finis et sur-relaxation ponctuelle non linéaire
• A practical method for determining Green's functions using Hadamard's variational formula
• An elementary solution of a variational problem of aerodynamics
• Parameter and domain dependence of eigenvalues of elliptic partial differential equations
• On calculating with B-splines
• Su un problema di frontiera libera connesso a questioni di idraulica
• Convexity of domain functionals
• Eigenfrequencies of an Elliptic Membrane
• Variation d'un point de retournement par rapport au domaine
• The Stefan Problem: Comments on its Present State
• Hadamard's variational formula for a mixed problem and an application to a problem related to a signorini-like variational inequality
• Brève communication. Utilisation en analyse numérique de la formule de variation d'Hadamard
• Efficient optimal design of structures by generalized steepest descent programming
• On the optimum shape of fillets in plates subjected to multiple in‐plane loading cases
• Two‐dimensional shape optimal design
• On optimum design in fluid mechanics
• Can One Hear the Shape of a Drum?
• Problems of Optimal Structural Design
• Sufficiency Proofs for the Problem of the Optimum Transversal Contour
• The Stefan Problem in Several Space Variables
• An Example of a Max-Min Problem in Partial Differential Equations
• The Numerical Evaluation of B-Splines