A multiscale approach and a hybrid FE-BE algorithm for heterogeneous scattering of Maxwell’s equations. (English) Zbl 1362.78009
Summary: In this paper we discuss the multiscale approach for the scattering problem of Maxwell’s equations in a heterogeneous material with a periodic microstructure. The new contributions in this paper are the determination of the multiscale correctors and the strong convergence in the norm of the space \(\mathbf{H}(\mathbf{curl}; \Omega)\) with an explicit rate for the approximate solutions (see Theorem 2.4). Consequently, we present a multiscale hybrid finite element method-boundary element method (FE-BE). The numerical examples are carried out to validate the theoretical results of this paper.
MSC:
| 78M10 | Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory |
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 65F10 | Iterative numerical methods for linear systems |
| 78A25 | Electromagnetic theory (general) |
| 78A40 | Waves and radiation in optics and electromagnetic theory |
| 78A45 | Diffraction, scattering |
| 78A48 | Composite media; random media in optics and electromagnetic theory |
| 78M40 | Homogenization in optics and electromagnetic theory |
| 78M15 | Boundary element methods applied to problems in optics and electromagnetic theory |
Keywords:
electromagnetic scattering problem; Maxwell’s equations; homogenization; multiscale asymptotic expansion; heterogeneous materialReferences:
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