A finite difference approach with velocity interfacial conditions for multiscale computations of crystalline solids

We propose a class of velocity interfacial conditions and formulate a finite difference approach for multiscale computations of crystalline solids with relatively strong nonlinearity and large deformation. Full atomistic computations are performed in a selected small subdomain only. With a coarse grid cast over the whole domain and the coarse scale dynamics computed by finite difference schemes, we perform a fast average of the fine scale solution in the atomistic subdomain to force agreement between scales. During each coarse scale time step, we adopt a linear wave approximation around the interface, with the wave speed updated using the coarse grid information. We then develop a class of velocity interfacial conditions with different order of accuracy. The interfacial conditions are straightforward to formulate, easy to implement, and effective for reflection reduction in crystalline solids with strong nonlinearity. The nice features are demonstrated through numerical tests.