A concurrent multiscale method based on the alternating Schwarz scheme for coupling atomic and continuum scales with first-order compatibility

Abstract

As well known, one of the major challenges in developing a multiscale model is how to ensure a seamless interface between the constituent length/time scales. In order to overcome this challenge, a novel concurrent multiscale numerical method is proposed in this paper, which is based on the alternating Schwarz method, to provide the seamless coupling between the atomic and continuum scales. The novelty in this method is the use of the strong-form meshless Hermite---cloud method in the continuum domain for approximation of both the field variable and corresponding first-order derivative simultaneously. As a result, the coupling between the domains is achieved by ensuring the compatibility of both the field variable and the first-order derivative simultaneously across the overlapping transition region. The proposed scheme is validated numerically through both the static and transient benchmark case studies in 1- and 2-D domains. The numerical results show that the proposed method is simple, efficient, and accurate, and also provides a seamless coupling between the two domains.