Efficient rearrangement algorithms for shape optimization on elliptic eigenvalue problems

DOI10.1007/s10915-012-9629-0zbMath1263.65107OpenAlexW1986044496MaRDI QIDQ1945360

Chiu-Yen Kao, Shu Su

Publication date: 8 April 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-012-9629-0

zbMATH Keywords

numerical examplesRayleigh quotientshape optimizationmaximal eigenvalueelliptic operatorelliptic eigenvalue problemsrearrangement algorithmminimal eigenvaluevibrating membranesmaximal ratio of eigenvalues

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Vibrations in dynamical problems in solid mechanics (74H45) Estimates of eigenvalues in context of PDEs (35P15) Membranes (74K15) Optimization of shapes other than minimal surfaces (49Q10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (16)

A minimization problem for an elliptic eigenvalue problem with nonlinear dependence on the eigenparameter ⋮ Extremal energies of Laplacian operator: different configurations for steady vortices ⋮ A rearrangement minimization problem corresponding top-Laplacian equation ⋮ Minimizing eigenvalues for inhomogeneous rods and plates ⋮ Tuning the total displacement of membranes ⋮ Optimal shape design for the \(p\)-Laplacian eigenvalue problem ⋮ Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization ⋮ Extremal spectral gaps for periodic Schrödinger operators ⋮ Study of a Mixed Dispersal Population Dynamics Model ⋮ Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives ⋮ Linear convergence of a rearrangement method for the one-dimensional Poisson equation ⋮ Minimization of the First Nonzero Eigenvalue Problem for Two-Phase Conductors with Neumann Boundary Conditions ⋮ Extremal rearrangement problems involving Poisson's equation with Robin boundary conditions ⋮ Extremal principal eigenvalue of the bi-Laplacian operator ⋮ Minimization of inhomogeneous biharmonic eigenvalue problems ⋮ Finite element approximation to the extremal eigenvalue problem for inhomogenous materials

Uses Software

• WinGULF

Cites Work

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