Interface Problem In Multi-Scale Modelling

The purpose of this article is to introduce two types of interface problems involved in multiscale simulations:artificial interface problems in wave propagation and natural interface problems in dislocation simulations.In wave propagation problems,we discuss both boundary problems and interface problems.In the boundary problem,we propose a new absorbing boundary condition to eliminate non-physical reflected waves generated by artificial boundaries,and reduce the impact of computational domain size limitation on the results.We call it the Learning Boundary Condition(LBC).The theoretical derivation of traditional methods is complex and only applicable to some simple boundaries.In contrast,our method combines data fitting with numerical format analysis.It can establish absorbing boundary conditions on various types of regions in a format-stable situation,and can be easily extended to equations of various types and different dimensional spaces.We conduct numerical simulations of various boundaries to verify the effectiveness of the method.Regarding interface problems,we propose the Hierarchical Interface Condition to address the issue of wave propagation in regions with different physical models and different discretization methods.By adding an auxiliary variable on the interface,which has the same dynamic process as the fictitious force,we eliminate reflection.Using the Pade via Lanczos(PVL)method,we can simulate the dynamics of the auxiliary variable with fewer degrees of freedom,thereby successfully eliminating non-physical waves generated by spatial inhomogeneity at a lower computational cost.Under certain conditions,we prove the convergence of this method and provide a convergence order.We apply the hierarchical interface condition to wave propagation between discretized regions of different scales,and conduct numerical simulations,which demonstrate the effectiveness of the method.In dislocation problems,we focus on the interaction between dislocations and free boundaries,which is an important factor affecting material plastic deformation.Through molecular simulations,we found that the inclination angle is an important variable in the interaction between dislocations and free boundaries,which not only determines the configuration between two structures but also remains stable with variables such as system size and system temperature.We conduct large-scale molecular simulation experiments and collect experimental data.Meanwhile,we propose the static and dynamic equations of the inclination angle using the dislocation model in continuum mechanics and the Onsager principle of dissipative processes.By comparing the molecular simulation results with the results of the continuous model,we prove the correctness of the continuous model.This indicates that our results can serve as the boundary condition for the discrete dynamics of dislocations,replacing the previous non-physical vertical boundary condition.