Linear scaling relaxation of the atomic positions in nanostructures

We present a method to determine the equilibrium geometry of large atomistic systems with linear scaling. It is based on a separate treatment of long and short wavelength components of the forces. While the rapidly varying part is handled by conventional methods, the treatment of the slowly varying part is based on elasticity theory. As illustrated by numerical examples containing up to a million atoms this method allows an efficient relaxation of large nanostructures.