Towards a Lagrange–Newton Approach for PDE Constrained Shape Optimization

DOI10.1007/978-3-319-17563-8_10zbMath1329.49092arXiv1405.3266OpenAlexW307546875MaRDI QIDQ3466795

Martin Siebenborn, Kathrin Welker, Volker H. Schulz

Publication date: 25 January 2016

Published in: New Trends in Shape Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.3266

zbMATH Keywords

Riemannian manifoldshape optimizationNewton method

Mathematics Subject Classification ID

Newton-type methods (49M15) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (4)

Computational comparison of surface metrics for PDE constrained shape optimization ⋮ Shape optimization for interface identification with obstacle problems ⋮ Efficient PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics ⋮ An SQP Method for Equality Constrained Optimization on Hilbert Manifolds

Cites Work

• Unnamed Item
• A Riemannian view on shape optimization
• Sobolev metrics on shape space of surfaces
• Efficient shape optimization for certain and uncertain aerodynamic design
• Preconditioning the pressure tracking in fluid dynamics by shape Hessian information
• Design sensitivity analysis of structural systems
• Structure of shape derivatives
• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Riemannian geometries on spaces of plane curves
• Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
• Level set methods for geometric inverse problems in linear elasticity
• Directional derivative of a minimax function
• Impulse Response Approximations of Discrete Shape Hessians with Application in CFD
• Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût

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