A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures
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Publication:333520
DOI10.1007/s40324-016-0067-zzbMath1364.35029OpenAlexW2300498841MaRDI QIDQ333520
Grégoire Allaire, Muthusamy Vanninathan, Marc Briane
Publication date: 31 October 2016
Published in: S\(\vec{\text{e}}\)MA Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s40324-016-0067-z
Optimality conditions for problems involving partial differential equations (49K20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
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Cites Work
- Unnamed Item
- Unnamed Item
- Diffractive geometric optics for Bloch wave packets
- The general theory of homogenization. A personalized introduction
- Non-homogeneous media and vibration theory
- Theory of Bloch waves
- Correctors for the homogenization of the wave and heat equations
- On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media
- Bloch Approximation in Homogenization and Applications
- A Priori Error Analysis of the Finite Element Heterogeneous Multiscale Method for the Wave Equation over Long Time
- Burnett coefficients and laminates
- Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization
- DISPERSIVE EFFECTIVE MODELS FOR WAVES IN HETEROGENEOUS MEDIA
- Bloch wave homogenization of linear elasticity system
- On Burnett coefficients in periodic media
- Elastic wave dispersion in microstructured membranes
- OPTIMAL BOUNDS ON DISPERSION COEFFICIENT IN ONE-DIMENSIONAL PERIODIC MEDIA
- A Dispersive Effective Medium for Wave Propagation in Periodic Composites
- First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof
- Homogenization of Periodic Structures via Bloch Decomposition
- Non-local dispersive model for wave propagation in heterogeneous media: multi-dimensional case
- Bloch-Wave Homogenization on Large Time Scales and Dispersive Effective Wave Equations
- Finite Element Heterogeneous Multiscale Method for the Wave Equation: Long-Time Effects
- On Burnett coefficients in periodic media in low contrast regime
- Shape optimization by the homogenization method
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