Journal
COMPTES RENDUS MECANIQUE
Volume 350, Issue 1, Pages 297-307Publisher
ACAD SCIENCES
DOI: 10.5802/crmeca.119
Keywords
Homogenization; Dirichlet-to-Neumann; Cell problems; Band problems; FFT-based solvers
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This paper establishes a formulation of band problems into fully periodic cell problems on bounded domains by introducing a Dirichlet-to-Neumann operator and a boundary corrector in a Fourier framework, and proposes a fixed-point algorithm and an example choice of corrector. Comparisons with other computational methods support this proposition.
The homogenization of microstructured interfaces requires solving specific problems posed on semi-infinite bands. To tackle these problems with existing FFT-based algorithms, a reformulation of these band problems into fully periodic cell problems, posed on bounded domains, is established. This is performed thanks to a Dirichlet-to-Neumann operator and a decomposition of the solution involving a boundary corrector, in a Fourier framework. A fixed-point algorithm and an example choice of corrector are proposed. Comparisons with other computational methods support this proposition.
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