Atomstic-continuum coupling within Spacetime Discontinuous Galerkin Framework
Brent Kraczek, Duane D. Johnson and Robert B. Haber (UIUC)

We extend the continuum spacetime discontinuous Galerkin (SDG) method to address atomistic and coupled, atomistic-continuum problems. This balance-law formulation addresses distinct continuum and discrete physical models (e.g., velocity-Verlet molecular dynamics and continuum elastodynamics) within a common mathematical framework. It enforces kinematic compatibility, momentum balance and energy balance. We contrast the continuum and atomistic SDG methods, focusing on the differences due to continuous vs. discrete spatial models, discuss our atomistic-continuum coupling strategy, and describe connections between the atomistic SDG and velocity-Verlet algorithms. We compare numerical results obtained with the individual and coupled models to analytic solutions.

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