Multiscale Modeling of Wavepropagation: FDTD/MD Hybrid Method
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Multiscale Modeling of Wave Propagation: FDTD/MD Hybrid Method Krishna Muralidharan, Pierre A. Deymier and Joseph H. Simmons Dept of Materials Science and Engineering, University of Arizona, Tucson, AZ 85712, U.S.A ABSTRACT Atomic level processes often play an important role in the way a material responds to an external field. Thus in order to model the behavior of materials accurately, it is necessary to develop simulation techniques which can effectively couple atomistic effects to the macroscopic properties of the model system and vice-versa. In other words, a multiscale methodology needs to be developed to bridge the different length and time scales. In this work we study the propagation of an elastic wave through a coupled continuum-atomistic medium. The equations of motion for the wave propagation through the continuum are solved using the Finite Difference Time Domain Method (FDTD). Simultaneously we use Molecular Dynamics (MD) to examine the effect of the wave packet on the atomic dynamics and the effect of atomic dynamics on the propagation of the wave. The handshaking between the FDTD region and the MD region is concurrent. INTRODUCTION Multiscale simulations have recently received much attention in several branches of physical sciences. Multiscaling involves a seamless coupling of length and time scales and is often necessary to model many materials processes efficiently as well as accurately. Multiscale simulations can either be serial or concurrent. Recently, some algorithms that allow the coupling between atomistic and continuum regions have been proposed. These include the concurrent coupling of length scales as proposed by Broughton et al. [1], Abraham et al. [2], and the coarsegrained procedure developed by Rudd et al. [3]. In linear elasticity the fundamental properties such as stress, strain and the various moduli are thermo-mechanical quantities. These quantities are defined such that they satisfy both the thermodynamic and the long time limit. Calculating some of these quantities from pure atomistic models does not present significant difficulties as long as systems are large enough and times long enough are used. An elastic continuum does not obey the same physics over all possible wavelengths as that of an atomic system. This could give rise to potential problems when a coupling between atomistic and continuum simulations is attempted. Further, problems in bridging continuum and atomistic regions may arise when the system is pushed outside the thermodynamic and long time limit. A result of these issues is that one can expect some amount of elastic impedance mismatch between a coupled continuum-atomic system when the thermodynamics and long time limits are not satisfied. In this work, we attempt to examine and quantify the impedance mismatch between continuum and atomistic regions as the continuum spatial and temporal scales are forced toward atomic scales. We have coupled dynamically an elastic continuum modeled with the finite difference time domain (FDTD) method and an atomistic system model
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