A Newton method for Bernoulli's free boundary problem in three dimensions

DOI10.1007/s00607-008-0260-8zbMath1152.49044OpenAlexW2121745610MaRDI QIDQ956681

Helmut Harbrecht

Publication date: 25 November 2008

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-008-0260-8

zbMATH Keywords

waveletsfree boundary problemboundary integral equationsNewton methodshape calculus

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Numerical methods for wavelets (65T60) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (12)

Computing quantities of interest for random domains with second order shape sensitivity analysis ⋮ From computer aided design to wavelet BEM ⋮ Nonlinear integral equations for Bernoulli's free boundary value problem in three dimensions ⋮ On the new coupled complex boundary method in shape optimization framework for solving stationary free boundary problems ⋮ Shape Optimization for Free Boundary Problems – Analysis and Numerics ⋮ Robust optimal ship hulls based on Michell's wave resistance ⋮ Shape optimization and subdivision surface based approach to solving 3D Bernoulli problems ⋮ Solving a Bernoulli type free boundary problem with random diffusion ⋮ A scalar prototype problem of deep abrasive drilling with an infinite free boundary: an asymptotic modeling study ⋮ Preconditioning of wavelet BEM by the incomplete Cholesky factorization ⋮ A cut finite element method for the Bernoulli free boundary value problem ⋮ A physics-informed learning approach to Bernoulli-type free boundary problems

Cites Work

• Multilevel preconditioning
• Shape optimization and fictitious domain approach for solving free boundary problems of Bernoulli type
• Efficient treatment of stationary free boundary problems
• On the geometric form of Bernoulli configurations
• Differentiation with Respect to the Domain in Boundary Value Problems
• Shape optimization and trial methods for free boundary problems
• Boundary integral representations of second derivatives in shape optimization
• On Convergence in Elliptic Shape Optimization
• Wavelet Galerkin Schemes for Boundary Integral Equations---Implementation and Quadrature
• Compression Techniques for Boundary Integral Equations---Asymptotically Optimal Complexity Estimates
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