  This paper applies topology optimisation to the design of structures with
periodic microstructural details without length scale separation, i.e.
considering the complete macroscopic structure and its response, while
resolving all microstructural details, as compared to the often used
homogenisation approach. The approach takes boundary conditions into account
and ensures connected and macroscopically optimised microstructures regardless
of the difference in micro- and macroscopic length scales. This results in
microstructures tailored for specific applications rather than specific
properties.
  Dealing with the complete macroscopic structure and its response is
computationally challenging as very fine discretisations are needed in order to
resolve all microstructural details. Therefore, this article shows the benefits
of applying a contrast-independent spectral preconditioner based on the
multiscale finite element method (MsFEM) to large structures with
fully-resolved microstructural details.
  The density-based topology optimisation approach combined with a Heaviside
projection filter and a stochastic robust formulation is used on various
problems, with both periodic and layered microstructures. The presented
approach is shown to allow for the topology optimisation of very large problems
in \textsc{Matlab}, specifically a problem with 26 million displacement degrees
of freedom in 26 hours using a single computational thread.
