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Two‐scale cut‐and‐projection convergence; homogenization of quasiperiodic structures
Author(s) -
Wellander Niklas,
Guenneau Sebastién,
Cherkaev Elena
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4345
Subject(s) - quasiperiodic function , homogenization (climate) , mathematics , mathematical analysis , convergence (economics) , projection (relational algebra) , projection method , mathematical optimization , algorithm , dykstra's projection algorithm , biodiversity , ecology , economics , biology , economic growth
We demonstrate how the problem of finding the effective property of quasiperiodic constitutive relations can be simplified to the periodic homogenization setting by transforming the original quasiperiodic material structure to a periodic heterogeneous material in a higher dimensional space. The characterization of two‐scale cut‐and‐projection convergence limits of partial differential operators is presented. Copyright © 2017 John Wiley & Sons, Ltd.