Computing Arlequin coupling coefficient for concurrent FE-MD approaches

Arlequin coupling coefficient is essential for concurrent FE-MD models with overlapping domains, but the calculation of its value is quite difficult when the geometry of the coupling region is complicated. In this work, we introduce a general procedure for the preprocessing of a concurrent FE-MD model, given that the mesh and atoms have already been created. The procedure is independent of the geometry of the coupling region and can be used for both 2D and 3D problems. The procedure includes steps of determining the relative positions of atoms inside the FE elements in the coupling region, as well as computing the Arlequin coupling coefficient for an arbitrary point inside the coupling region or on its boundary. Two approaches are provided for determining the coefficient: the direct approach and the temperature approach.