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Bloch wave homogenization is a spectral method for obtaining effectivecoefficients for periodically heterogeneous media. This method hinges on thedirect integral decomposition of periodic operators, which is not available ina suitable form for almost periodic operators. In particular, the notion ofBloch eigenvalues and eigenvectors does not exist for almost periodicoperators. However, we are able to recover the homogenization result in thiscase, by employing a sequence of periodic approximations to almost periodicoperators. We also establish a rate of convergence for approximations ofhomogenized tensors for a class of almost periodic media. The results aresupported by a numerical study.

Bloch wave approach to almost periodic homogenization and approximations of effective coefficients