Topological Derivative for PDEs on Surfaces

DOI10.1137/20M1339040zbMath1481.49043arXiv2005.09011OpenAlexW4205426634WikidataQ114074198 ScholiaQ114074198MaRDI QIDQ5020742

Peter Gangl, Kevin Sturm

Publication date: 7 January 2022

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.09011

zbMATH Keywords

level set methodtopological derivativeóptimization

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Optimization of shapes other than minimal surfaces (49Q10) PDE constrained optimization (numerical aspects) (49M41)

Related Items (3)

Automated computation of topological derivatives with application to nonlinear elasticity and reaction-diffusion problems ⋮ The topological state derivative: an optimal control perspective on topology optimisation ⋮ An abstract Lagrangian framework for computing shape derivatives

Uses Software

• NGSolve

Cites Work

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• The Topological Asymptotic for PDE Systems: The Elasticity Case
• A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem
• Topological asymptotic analysis of the Kirchhoff plate bending problem
• On the Topological Derivative in Shape Optimization
• A simplified derivation technique of topological derivatives for quasi-linear transmission problems
• Topological sensitivities via a Lagrangian approach for semilinear problems

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