Numerical calculation of extremal Steklov eigenvalues in 3D and 4D

DOI10.1016/j.camwa.2021.11.008OpenAlexW3215533033MaRDI QIDQ825487

Pedro R. S. Antunes

Publication date: 17 December 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.01884

zbMATH Keywords

shape optimizationmethod of fundamental solutionsSteklov eigenvalues

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) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (2)

Steklov Eigenvalues of Nearly Spherical Domains ⋮ Analytical and numerical assessments of boundary variations in Steklov eigenvalue problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An extremal eigenvalue problem for the Wentzell-Laplace operator
• The method of fundamental solutions applied to boundary eigenvalue problems
• The Steklov spectrum on moving domains
• The first Steklov eigenvalue, conformal geometry, and minimal surfaces
• Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains
• Finite point-sets on S 2 with minimum distance as large as possible
• Some inequalities for Stekloff eigenvalues
• The method of fundamental solutions for elliptic boundary value problems
• Numerical optimization of low eigenvalues of the Dirichlet and Neumann laplacians
• A numerical algorithm to reduce ill-conditioning in meshless methods for the Helmholtz equation
• On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions
• On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues
• Über eine Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems
• The Method of Fundamental Solutions Applied to Some Inverse Eigenproblems
• Numerical calculation of eigensolutions of 3D shapes using the method of fundamental solutions
• The Tammes Problem for N = 14
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems
• Steklov eigenvalues of reflection-symmetric nearly circular planar domains
• Numerical Minimization of Dirichlet Laplacian Eigenvalues of Four-Dimensional Geometries
• Computational Methods for Extremal Steklov Problems
• Numerical minimization of eigenmodes of a membrane with respect to the domain
• The method of functional equations for the approximate solution of certain boundary value problems
• Optimal Shapes Maximizing the Steklov Eigenvalues
• Linear integral equations

This page was built for publication: Numerical calculation of extremal Steklov eigenvalues in 3D and 4D