A multilevel, level-set method for optimizing eigenvalues in shape design problems
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Publication:1879612
DOI10.1016/j.jcp.2004.01.031zbMath1051.65073OpenAlexW2040489448MaRDI QIDQ1879612
Publication date: 23 September 2004
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2004.01.031
numerical exampleslevel set methodshape optimizationoptimal designinverse iterationmultilevel continuation techniques
Numerical optimization and variational techniques (65K10) Optimization of shapes other than minimal surfaces (49Q10) Decomposition methods (49M27) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Compliance or weight optimization in solid mechanics (74P05)
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Cites Work
- Unnamed Item
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- The mathematics of eigenvalue optimization
- Band structure optimization of two-dimensional photonic crystals in \(H\)-polarization
- Grid refinement and scaling for distributed parameter estimation problems
- Preconditioned all-at-once methods for large, sparse parameter estimation problems
- On Minimizing the Maximum Eigenvalue of a Symmetric Matrix
- Large-Scale Optimization of Eigenvalues
- Numerical Optimization
- Levenberg–Marquardt level set methods for inverse obstacle problems
- A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets
- On optimization techniques for solving nonlinear inverse problems
- On the relation between constraint regularization, level sets, and shape optimization
- On Eigenvalue Optimization
- Eigenfrequency optimization in optimal design
- Level set methods for optimization problems involving geometry and constraints. I: Frequencies of a two-density inhomogeneous drum