Computational Methods for Extremal Steklov Problems

DOI10.1137/16M1067263zbMath1432.65164arXiv1601.00605MaRDI QIDQ5346492

Braxton Osting, Chiu-Yen Kao, Eldar Akhmetgaliyev

Publication date: 24 May 2017

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.00605

zbMATH Keywords

isoperimetric inequalityshape optimizationSteklov eigenvaluesextremal eigenvalue problemsfluid sloshing

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Optimization of shapes other than minimal surfaces (49Q10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (15)

Numerical calculation of extremal Steklov eigenvalues in 3D and 4D ⋮ Steklov Eigenvalues of Nearly Spherical Domains ⋮ A combined finite element and Bayesian optimization framework for shape optimization in spectral geometry ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Applications of possibly hidden symmetry to Steklov and mixed Steklov problems on surfaces ⋮ Optimization of Steklov-Neumann eigenvalues ⋮ A DRBEM approximation of the Steklov eigenvalue problem ⋮ Optimal Shapes Maximizing the Steklov Eigenvalues ⋮ Numerical studies of the Steklov eigenvalue problem via conformal mappings ⋮ Analyticity of Steklov eigenvalues of nearly circular and nearly spherical domains ⋮ Maximal convex combinations of sequential Steklov eigenvalues ⋮ Steklov eigenvalues of reflection-symmetric nearly circular planar domains ⋮ Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems ⋮ On accuracy of approximate boundary and distributed \(H^1\) shape gradient flows for eigenvalue optimization ⋮ Analytical and numerical assessments of boundary variations in Steklov eigenvalue problems

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