Shape derivatives in differential forms. I: An intrinsic perspective

DOI10.1007/s10231-012-0259-9zbMath1278.35056OpenAlexW2014231836MaRDI QIDQ383824

Ralf Hiptmair, Jingzhi Li

Publication date: 6 December 2013

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-012-0259-9

zbMATH Keywords

Lie derivativedual formulationHadamard structure theoremshigher-order shape derivativesshape HessiansZolésio's velocity method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Differential forms in global analysis (58A10) Existence theories for optimal control problems involving partial differential equations (49J20) Boundary value problems for linear higher-order PDEs (35G15) PDEs in connection with control and optimization (35Q93)

Related Items (12)

Shape Optimization of Peristaltic Pumps Transporting Rigid Particles in Stokes Flow ⋮ A robust numerical method for the random interface grating problem via shape calculus, weak Galerkin method, and low-rank approximation ⋮ Electrostatic force computation with boundary element methods ⋮ Variational approach to shape derivatives for elasto-acoustic coupled scattering fields and an application with random interfaces ⋮ Locally optimal configurations for the two-phase torsion problem in the ball ⋮ First order $k$-th moment finite element analysis of nonlinear operator equations with stochastic data ⋮ Shape derivatives for scattering problems ⋮ Second Moment Analysis for Robin Boundary Value Problems on Random Domains ⋮ A Riemannian view on shape optimization ⋮ Computation of moments for Maxwell's equations with random interfaces via pivoted low-rank approximation ⋮ Second order directional shape derivatives of integrals on submanifolds ⋮ Stability analysis of the two-phase torsional rigidity near a radial configuration

Cites Work

• Anatomy of the shape Hessian
• Anatomy of the shape Hessian via Lie brackets
• Differential forms. With applications to the physical sciences
• Finite elements in computational electromagnetism
• Finite element exterior calculus, homological techniques, and applications
• Frechet derivatives in inverse obstacle scattering
• Acoustic and electromagnetic equations. Integral representations for harmonic problems
• Discrete Hodge operators
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