Optimization of spectral functions of Dirichlet-Laplacian eigenvalues
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Publication:602959
DOI10.1016/j.jcp.2010.07.040zbMath1201.65203OpenAlexW2021974250MaRDI QIDQ602959
Publication date: 5 November 2010
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2010.07.040
numerical examplesspectral functionshape optimizationLaplacian eigenvaluesquasi-Newton methodPayne-Pólya-Weinberger inequality
Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Estimates of eigenvalues in context of PDEs (35P15) Optimization of shapes other than minimal surfaces (49Q10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)
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Cites Work
- Optimization of scattering resonances
- Nonsmooth optimization via quasi-Newton methods
- Maximally resonant potentials subject to p-norm constraints
- Maximization of the quality factor of an optical resonator
- Shape recognition using eigenvalues of the Dirichlet Laplacian
- Bounds on eigenvalues of Dirichlet Laplacian
- Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues
- Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains
- Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods
- A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions
- Convex analysis and nonlinear optimization. Theory and examples
- Extremal eigenvalue problems for starlike planar domains
- Shape determination for deformed electromagnetic cavities
- Computations of Eigenvalue Avoidance in Planar Domains
- On the Ratio of Consecutive Eigenvalues
- Perturbative Analysis of the Method of Particular Solutions for Improved Inclusion of High-Lying Dirichlet Eigenvalues
- Eigenvalues of the Laplacian in Two Dimensions
- Potentials Producing Maximally Sharp Resonances
- The Eigenvalues of an Equilateral Triangle
- Isoperimetric bounds for higher eigenvalue ratios for the n-dimensional fixed membrane problem
- Eigenstructure of the Equilateral Triangle, Part I: The Dirichlet Problem
- ‘Can one hear the shape of a drum?’: revisited
- Extremum problems for Laplacian eigenvalues with free boundary
- Range of the first two eigenvalues of the laplacian
- Range of the First Three Eigenvalues of the Planar Dirichlet Laplacian
- Optimal Localization of Eigenfunctions in an Inhomogeneous Medium
- Reviving the Method of Particular Solutions
- Numerical minimization of eigenmodes of a membrane with respect to the domain
- Can One Hear the Shape of a Drum?
- Approximations and Bounds for Eigenvalues of Elliptic Operators
- Bounds for Eigenvalues and Eigenvectors of Symmetric Operators
- Level set methods for optimization problems involving geometry and constraints. I: Frequencies of a two-density inhomogeneous drum
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