Open AccessBloch wave approach to almost periodic homogenization and approximations of effective coefficients
Author(s) -
Sivaji Ganesh Sista,
Vivek Tewary
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021119
Subject(s) - homogenization (climate) , eigenvalues and eigenvectors , mathematics , bloch wave , periodic function , mathematical analysis , quasi periodic , approximations of π , physics , quantum mechanics , biodiversity , ecology , astrophysics , biology
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 almost periodic homogenization result 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.