Algorithms for bridging scale method parameters

Multiple scale simulation methods have been the focus of much attention in recent years. The Bridging Scale method (BSM) of Liu and co-workers was developed as a framework for the dynamic concurrent coupling of atomistics and continua. A key feature of the BSM is a non-reflecting atomistic interfacial condition which relies on a time history integral. In this work, we present a practical review of the relevant theory as well as a new algorithm used in the determination of the kernel function of the time history integral. We also provide a detailed description of the random displacement terms from the interfacial condition, which are required for finite temperature BSM simulations.