“…Relevant examples of practical interest include: structural analysis of composite (Belsky et al, 1995;Xia and Curtin, 2001), biological (Travkin and Catton, 1995) and turbulent flows (Filippova et al, 2001), fine-scale laminates (Raghavan et al, 2001) and crystalline microstructures (Lee et al, 2004), air quality assessment (Russell and Kumar, 1996), flows through porous media (Bryant and Thompson, 2001), large-scale molecular dynamic simulations (Krsti et al, 2003), chemistry (Raimondeau and Vlachos, 2002), and a multitude of others. In stark contrast with the multiscale behaviour exhibited by such problems, classical computational methods for the numerical simulation of multiscale physical phenomena have been designed to operate at a certain preselected scale fixed by the choice of a discretisation parameter.…”