Numerical studies of the Steklov eigenvalue problem via conformal mappings

DOI10.1016/j.amc.2018.11.048zbMath1428.35245arXiv1805.01959OpenAlexW2902280721MaRDI QIDQ2008563

Chiu-Yen Kao, Weaam Alhejaili

Publication date: 26 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.01959

zbMATH Keywords

conformal mappingshape optimizationspectral methodSteklov eigenvaluesextremal eigenvalue problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Variational methods for second-order elliptic equations (35J20)

Related Items (4)

Optimization of Steklov-Neumann eigenvalues ⋮ A DRBEM approximation of the Steklov eigenvalue problem ⋮ Maximal convex combinations of sequential Steklov eigenvalues ⋮ Analytical and numerical assessments of boundary variations in Steklov eigenvalue problems

Uses Software

• Schwarz-Christoffel

Cites Work

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• An extremal eigenvalue problem for the Wentzell-Laplace operator
• An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem
• The method of fundamental solutions applied to boundary eigenvalue problems
• A two-grid discretization scheme for the Steklov eigenvalue problem
• A two-grid method of the non-conforming Crouzeix-Raviart element for the Steklov eigenvalue problem
• A moving boundary model motivated by electric breakdown. II: Initial value problem
• Optimization of the first Steklov eigenvalue in domains with holes: a shape derivate approach
• Simulation of a nonlinear Steklov eigenvalue problem using finite-element approximation
• Spectral geometry of the Steklov problem (survey article)
• On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues
• Sums of reciprocal Stekloff eigenvalues
• The Legacy of Vladimir Andreevich Steklov
• The Accuracy of Numerical Conformal Mapping Methods: A Survey of Examples and Results
• The stability of a two-dimensional rising bubble
• Isoparametric finite-element approximation of a Steklov eigenvalue problem
• Convex shape optimization for the least biharmonic Steklov eigenvalue
• Shape optimization for low Neumann and Steklov eigenvalues
• A virtual element method for the Steklov eigenvalue problem
• Liquid Sloshing Dynamics
• Computational Methods for Extremal Steklov Problems
• A type of multilevel method for the Steklov eigenvalue problem
• Optimal Shapes Maximizing the Steklov Eigenvalues

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