Generalized Matching Boundary Conditions Based on Fourier Transform Technique

Abstract

This paper presents a class of generalized matching boundary conditions (GMBCs) for the coupled atomistic/continuum simulation of lattice dynamics. This work is an extension of the MBCs originally proposed by Tang et al. Using the combination of a Fourier transform technique and the generalization of MBCs for arbitrary wavenumbers, a more efficient MBC implementation is developed. After describing the basic methodology, the focus turns to several specific parameterized forms of GMBC. Finally, the proposed approach is validated through several numerical examples, and its robustness is exhibited based upon the capability of wave energy absorption illustrated by the energy history and wave reflection. It is shown that the combination of GMBC expressions and the Fourier transform technique for wavenumber selection enhances both the efficiency and accuracy of the MBCs.