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The construction of periodic unfolding operators on some compact Riemannian manifolds

  • Sören Dobberschütz EMAIL logo and Michael Böhm
Published/Copyright: January 29, 2014

Abstract.

The notion of periodic unfolding has become a standard tool in the theory of periodic homogenization. However, all the results obtained so far are only applicable to the “flat” Euclidean space n. In this paper, we present a generalization of the method of periodic unfolding applicable to structures defined on certain compact Riemannian manifolds. While many results known from unfolding in domains of n can be recovered, for the unfolding of gradients a transport operator has to be defined. This operator connects vector fields on the manifold and in the reference cell, which allows for the formulation of general two-scale problems. We illustrate the use of the new unfolding technique with a simple elliptic model-problem.

Received: 2013-04-23
Revised: 2014-01-22
Accepted: 2014-01-22
Published Online: 2014-01-29
Published in Print: 2014-03-01

© 2014 by Walter de Gruyter Berlin/Boston

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