Multiscale coupling in function space—weak coupling between molecular dynamics and continuum mechanics

We present a function space‐oriented coupling approach for the multiscale simulation of non‐linear processes in mechanics using finite elements and molecular dynamics concurrently. The key idea is to construct a transfer operator between the different scales on the basis of weighted local averaging instead of using point wise taken values. The local weight functions are constructed by assigning a partition of unity to the molecular degrees of freedom (Shepard's approach). This allows for decomposing the micro scale displacements into a low‐frequency and a high‐frequency part by means of a weighted L 2 ‐projection. Numerical experiments illustrating the stabilizing effect of our coupling approach are given. Copyright © 2009 John Wiley & Sons, Ltd.