  Modern `smart' materials have complex microscale structure, often with
unknown macroscale closure. The Equation-Free Patch Scheme empowers us to
non-intrusively, efficiently, and accurately simulate over large scales through
computations on only small well-separated patches of the microscale system.
Here the microscale system is a solid beam of random heterogeneous elasticity.
The continuing challenge is to compute the given physics on just the microscale
patches, and couple the patches across un-simulated macroscale space, in order
to establish efficiency, accuracy, consistency, and stability on the
macroscale. Dynamical systems theory supports the scheme. This research program
is to develop a systematic non-intrusive approach, both computationally and
analytically proven, to model and compute accurately macroscale system levels
of general complex physical and engineering systems.
