Bloch wave approach to almost periodic homogenization and approximations of effective coefficients
Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable form for almost periodic operators. In particular, the notion...
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| description | Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable form for almost periodic operators. In particular, the notion of Bloch eigenvalues and eigenvectors does not exist for almost periodic operators. However, we are able to recover the homogenization result in this case, by employing a sequence of periodic approximations to almost periodic operators. We also establish a rate of convergence for approximations of homogenized tensors for a class of almost periodic media. The results are supported by a numerical study. |
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This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable form for almost periodic operators. In particular, the notion of Bloch eigenvalues and eigenvectors does not exist for almost periodic operators. However, we are able to recover the homogenization result in this case, by employing a sequence of periodic approximations to almost periodic operators. We also establish a rate of convergence for approximations of homogenized tensors for a class of almost periodic media. The results are supported by a numerical study.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Bloch waves ; Dirichlet problem ; Eigenvalues ; Eigenvectors ; Homogenization ; Operators (mathematics) ; Spectral methods ; Tensors</subject><ispartof>arXiv.org, 2020-03</ispartof><rights>2020. 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| subjects | Bloch waves Dirichlet problem Eigenvalues Eigenvectors Homogenization Operators (mathematics) Spectral methods Tensors |
| title | Bloch wave approach to almost periodic homogenization and approximations of effective coefficients |
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