HOMOGENIZATION OF THE SYSTEM OF HIGH‐CONTRAST MAXWELL EQUATIONS

DOI10.1112/S0025579314000424zbMath1337.35140MaRDI QIDQ5255891

Shane Cooper, Kirill D. Cherednichenko

Publication date: 22 June 2015

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

asymptotic behaviorhomogenizationMaxwell equationsperiodic composite medium

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) Degenerate elliptic equations (35J70) General theory of partial differential operators (47F05) Second-order elliptic equations (35J15) Composite media; random media in optics and electromagnetic theory (78A48) Homogenization in optics and electromagnetic theory (78M40)

Related Items (15)

ASYMPTOTIC BEHAVIOUR OF THE SPECTRA OF SYSTEMS OF MAXWELL EQUATIONS IN PERIODIC COMPOSITE MEDIA WITH HIGH CONTRAST ⋮ Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media ⋮ Homogenization near resonances and artificial magnetism in three dimensional dielectric metamaterials ⋮ Mathematical analysis of transmission properties of electromagnetic meta-materials ⋮ Multiscale topology optimization of electromagnetic metamaterials using a high-contrast homogenization method ⋮ The electromagnetic waves generated by a cluster of nanoparticles with high refractive indices ⋮ Homogenization of high-contrast composites under differential constraints ⋮ The effective permittivity and permeability generated by a cluster of moderately contrasting nanoparticles ⋮ Two-scale homogenization for a general class of high contrast PDE systems with periodic coefficients ⋮ Homogenization of High-contrast Mumford--Shah Energies ⋮ The geometric average of curl-free fields in periodic geometries ⋮ Bloch Waves in Bubbly Crystal Near the First Band Gap: A High-Frequency Homogenization Approach ⋮ Full Two-Scale Asymptotic Expansion and Higher-Order Constitutive Laws in the Homogenization of the System of Quasi-static Maxwell Equations ⋮ Heterogeneous Multiscale Method for the Maxwell equations with high contrast ⋮ Localized orthogonal decomposition for two-scale Helmholtz-type problems

Cites Work

• Bethe-Sommerfeld conjecture
• Periodic unfolding and homogenization
• Asymptotic analysis in elasticity problems on thin periodic structures
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Spectral Properties of Classical Waves in High-Contrast Periodic Media
• Spectral properties of periodic media in the large coupling limit
• On an extension of the method of two-scale convergence and its applications
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