Time and spacetime finite elements for coupled atomistic-continuum dynamics

Objective

Computer simulations are a major part of analysis, prediciton and design of structural, electronic, energy and bio-medical materials. Traditionally, simulations are based on either atomistic or continuum mathematical models. We are developing methods that leverage the strengths of each within a consistent mathematical framework.

Approach

For the continuum and coupled models, we use spacetime discontinuous Galerkin formulation with coupling derived from balance of momentum and energy. For atomistic models we use high-order time finite element methods. For the same cost (number of force evaluations), our method has energy error at machine precision and clearly outperforms the standard velocity-Verlet algorithm (see figure). The accuracy of atomic trajectories also improves significantly.

Impact

Our new time-stepping scheme significantly improves the efficiency and reliability of atomistic simulations of materials, and should be useful in astronomy and other fields. By leveraging the strengths of continuum and atomistic methods we may address larger complex systems, such as nano-scale and biological structures and energy devices.

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