A boundary piecewise constant level set method for boundary control of eigenvalue optimization problems
type: Item
instance of: scholarly article
title: A boundary piecewise constant level set method for boundary control of eigenvalue optimization problems
zbMATH Open document ID: 1221.65298
author: Zheng-Fang Zhang
author: XiaoLiang Cheng
published in: Journal of Computational Physics
publication date: 2011-01-31T00:00:00Z
review text: This paper investigates optimization of the least eigenvalue of \(-\Delta\) with the constraint of one dimension Hausdorff measure of Dirichlet boundary. We propose the boundary piecewise constant level set (BPCLS) method based on the regularity technique to combine two types of boundary conditions into a single Robin boundary condition. We derive the first variation of the least eigenvalue w.r.t. the BPCLS function and propose a penalty BPCLS algorithm and an augmented Lagrangian BPCLS algorithm. Numerical results are reported for experiments on ellipse and \(L\)-shape domains.
Mathematics Subject Classification ID: 65N25
zbMATH DE Number: 5842964
zbMATH Keywords: level set method
zbMATH Keywords: eigenvalue optimization problem
zbMATH Keywords: finite element method
reviewed by: Raytcho D. Lazarov
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: j.jcp.2010.10.005
OpenAlex ID: W2054513939
cites work: An Augmented Lagrangian‐Based Approach to the Oseen Problem
cites work: A Locally Divergence-Free Interior Penalty Method for Two-Dimensional Curl-Curl Problems
cites work: Reinforcement problems for elliptic equations and variational inequalities
cites work: Incorporating topological derivatives into level set methods.
cites work: Reinforcement problems in elasto-plasticity
cites work: Exact Controllability of an Aeroacoustic Model with a Neumann and a Dirichlet Boundary Control
cites work: Extremal eigenvalue problems for composite membranes. I
cites work: Where Best to Hold a Drum Fast
cites work: Bounds for the heat diffusion through windows of given area
cites work: Windows of given area with minimal heat diffusion
cites work: Threshold dynamics for the piecewise constant Mumford-Shah functional
cites work: Global and Finite Termination of a Two-Phase Augmented Lagrangian Filter Method for General Quadratic Programs
cites work: Total variation diminishing Runge-Kutta schemes
cites work: Strong stability-preserving high-order time discretization methods
cites work: A multilevel, level-set method for optimizing eigenvalues in shape design problems
cites work: Pseudo-gradient and Lagrangian boundary control system formulation of electromagnetic fields
cites work: Weighted ENO Schemes for Hamilton--Jacobi Equations
cites work: Constrained Dirichlet Boundary Control in $L^2$ for a Class of Evolution Equations
cites work: The mathematics of eigenvalue optimization
cites work: Q3436985
cites work: A binary level set model and some applications to Mumford-Shah image segmentation
cites work: A variant of the level set method and applications to image segmentation
cites work: Scale Space and PDE Methods in Computer Vision
cites work: A parallel splitting up method and its application to Navier-Stokes equations
cites work: A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
cites work: Motion of multiple junctions: A level set approach
cites work: Numerical Optimization
cites work: Level set methods for optimization problems involving geometry and constraints. I: Frequencies of a two-density inhomogeneous drum
cites work: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
cites work: High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations
cites work: Large-Scale Optimization of Eigenvalues
cites work: Nonlinear total variation based noise removal algorithms
cites work: Q3655836
cites work: Solvability of boundary value problems in a theory of plane-strain elasticity with boundary reinforcement
cites work: On Eigenvalue Optimization
cites work: A piecewise constant level set method for elliptic inverse problems
cites work: A variational level set approach to multiphase motion
cites work: A Monotonic Algorithm for Eigenvalue Optimization in Shape Design Problems of Multi-density Inhomogeneous Materials
cites work: Greedy algorithms for eigenvalue optimization problems in shape design of two-density inhomogeneous materials
DOI: 10.1016/J.JCP.2010.10.005
description: scientific article; zbMATH DE number 5842964