Algorithmic Aspects of Multigrid Methods for Optimization in Shape Spaces

DOI10.1137/16M1104561zbMath1380.49062arXiv1611.05272OpenAlexW2767229563WikidataQ125827488 ScholiaQ125827488MaRDI QIDQ4597612

Kathrin Welker, Martin Siebenborn

Publication date: 13 December 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.05272

zbMATH Keywords

shape optimizationmultigrid methodshigh performance computingshape spaces

Mathematics Subject Classification ID

Newton-type methods (49M15) Parallel numerical computation (65Y05) Optimization of shapes other than minimal surfaces (49Q10) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Discrete approximations in optimal control (49M25) Shapes (aspects of topological manifolds) (57N25) PDEs in connection with control and optimization (35Q93)

Related Items

Shape Optimization for Variational Inequalities of Obstacle Type: Regularized and Unregularized Computational Approaches, Shape optimization for interface identification with obstacle problems, Fluid dynamic shape optimization using self-adapting nonlinear extension operators with multigrid preconditioners, Efficient Techniques for Shape Optimization with Variational Inequalities Using Adjoints, Stochastic Approximation for Optimization in Shape Spaces, Suitable spaces for shape optimization, An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations, Mesh quality preserving shape optimization using nonlinear extension operators, A Continuous Perspective on Shape Optimization via Domain Transformations, A novel W^1,∞ approach to shape optimisation with Lipschitz domains

Uses Software

• Gmsh

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computational comparison of surface metrics for PDE constrained shape optimization
• Topological derivatives in shape optimization
• 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
• Large-Scale Three-Dimensional Acoustic Horn Optimization
• Numerical Methods for Two-phase Incompressible Flows
• Efficient PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics
• Directional derivative of a minimax function
• Structured Inverse Modeling in Parabolic Diffusion Problems
• Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics
• Shape Differentiability Under Non-linear PDE Constraints
• Lagrange Multiplier Approach to Variational Problems and Applications
• Variational approach to shape derivatives
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût
• Introduction to Shape Optimization
• A Unified Discrete–Continuous Sensitivity Analysis Method for Shape Optimization
• Shape optimization by the homogenization method
• An introduction to the adjoint approach to design