  This paper proposes to address the issue of complexity reduction for the
numerical simulation of multiscale media in a quasi-periodic setting. We
consider a stationary elliptic diffusion equation defined on a domain $D$ such
that $\overline{D}$ is the union of cells $\{\overline{D_i}\}_{i\in I}$ and we
introduce a two-scale representation by identifying any function $v(x)$ defined
on $D$ with a bi-variate function $v(i,y)$, where $i \in I$ relates to the
index of the cell containing the point $x$ and $y \in Y$ relates to a local
coordinate in a reference cell $Y$. We introduce a weak formulation of the
problem in a broken Sobolev space $V(D)$ using a discontinuous Galerkin
framework. The problem is then interpreted as a tensor-structured equation by
identifying $V(D)$ with a tensor product space $\mathbb{R}^I \otimes V(Y)$ of
functions defined over the product set $I\times Y$. Tensor numerical methods
are then used in order to exploit approximability properties of quasi-periodic
solutions by low-rank tensors.
