Shape optimization by free-form deformation: existence results and numerical solution for Stokes flows

DOI10.1007/s10915-013-9807-8zbMath1303.49017OpenAlexW2104178725MaRDI QIDQ474956

Sandro Salsa, Francesco Ballarin, Andrea Manzoni, Gianluigi Rozza

Publication date: 25 November 2014

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-013-9807-8

zbMATH Keywords

shape optimizationcomputational fluid dynamicsStokes equationsfinite elements methodfree-form deformationsperturbation of identity

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20) Flow control and optimization for incompressible viscous fluids (76D55)

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Cites Work

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• Parametric free-form shape design with PDE models and reduced basis method
• Optimal treatment of structures
• What is the optimal shape of a pipe?
• Aerodynamic design via control theory
• Variation and optimization of formes. A geometric analysis
• A numerical approach for shape optimization of fluid flow domains
• Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence
• On a shape control problem for the stationary Navier-Stokes equations
• Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût
• Boundary Velocity Control of Incompressible Flow with an Application to Viscous Drag Reduction
• On the Goldstein-Levitin-Polyak gradient projection method
• Numerical Optimization
• The Differentiability of the Drag with Respect to the Variations of a Lipschitz Domain in a Navier--Stokes Flow
• Shape Optimization of Body Located in Incompressible Viscous Flow Based on Optimal Control Theory
• On the numerical computation of the optimum profile in Stokes flow
• Perspectives in Flow Control and Optimization
• Introduction to Shape Optimization
• Optimum profiles in two-dimensional Stokes flow
• On optimum profiles in Stokes flow
• Shape optimization for viscous flows by reduced basis methods and free‐form deformation
• S<scp>HAPE</scp> O<scp>PTIMIZATION IN</scp> F<scp>LUID</scp> M<scp>ECHANICS</scp>