Level set method with topological derivatives in shape optimization

DOI10.1080/00207160802033350zbMath1155.65055OpenAlexW2065544645MaRDI QIDQ3535716

Piotr Fulmanski, Jean-François Scheid, Antoine Laurain, Jan Sokolowski

Publication date: 14 November 2008

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160802033350

zbMATH Keywords

numerical exampleslevel set methodasymptotic analysisshape optimizationoptimal designtopological derivative

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (14)

A variational binary level-set method for elliptic shape optimization problems ⋮ Topological imaging methods for the iterative detection of multiple impedance obstacles ⋮ Two algorithms for a class of elliptic problems in shape optimization ⋮ Topological derivative for steady-state orthotropic heat diffusion problem ⋮ Stability Analysis of the Reconstruction Step of the Voronoi Implicit Interface Method ⋮ Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum ⋮ Variational piecewise constant level set methods for shape optimization of a two-density drum ⋮ Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method ⋮ Shape and parameter reconstruction for the Robin transmission inverse problem ⋮ Distributed shape derivativeviaaveraged adjoint method and applications ⋮ Optimal Internal Dissipation of a Damped Wave Equation Using a Topological Approach ⋮ Analysis of a level set method for topology optimization ⋮ An iterative method for shape optimal design of Stokes-Brinkman equations with heat transfer model ⋮ Shape optimization for an obstacle located in incompressible Boussinesq flow

Cites Work

• Solutions with exponential character to a linear functional equation and roots of its characteristic equation
• Self-adjoint extensions of differential operators in application to shape optimization
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Asymptotic analysis of shape functionals
• A PDE-based fast local level set method
• On numerical solution of shape inverse problems
• Level set methods and dynamic implicit surfaces
• Variation and optimization of formes. A geometric analysis
• Modelling of topological derivatives for contact problems
• A Level Set Method in Shape and Topology Optimization for Variational Inequalities
• On the Topological Derivative in Shape Optimization
• Optimality Conditions for Simultaneous Topology and Shape Optimization
• A Duality Approach for the Boundary Variation of Neumann Problems
• Selfadjoint Extensions for the Elasticity System in Shape Optimization
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