The time‐harmonic electromagnetic wave scattering by a biperiodic elastic body

This paper concentrates on an interaction scattering problem between the time‐harmonic electromagnetic waves and an unbounded periodic elastic medium. The uniqueness results of the interaction problem are established for small frequencies or all frequencies except a discrete set in both the absorbin...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-05, Vol.47 (7), p.6354-6381
Main Authors: Zhu, Tielei, Wei, Changkun, Yang, Jiaqing
Format: Article
Language:English
Subjects:
Boundary conditions
Elastic bodies
Elastic media
elastic waves
electromagnetic field
Electromagnetic radiation
exponential convergence
Perfectly matched layers
periodic structure
PML
Wave scattering
well‐posedness
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Summary:This paper concentrates on an interaction scattering problem between the time‐harmonic electromagnetic waves and an unbounded periodic elastic medium. The uniqueness results of the interaction problem are established for small frequencies or all frequencies except a discrete set in both the absorbing and nonabsorbing medium, and then the existence of solutions is derived by the classical Fredholm alternative. The perfectly matched layer (PML) method is proposed to truncate the unbounded scattering domain to a bounded computational domain. We prove the well‐posedness of the solution for the truncated PML problem, where a homogeneous boundary condition is imposed on the outer boundary of the PML. The exponential convergence of the PML method is established in terms of the thickness and parameters of the PML. The proof is based on the PML extension and the exponential decay properties of the modified fundamental solution.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9923