## Abstract

Diffusive Molecular Dynamics (DMD) is a class of recently developed computational models for the simulation of long-term diffusive mass transport at atomistic length scales. Compared to previous atomistic models, e.g., transition state theory based accelerated molecular dynamics, DMD allows the use of larger time-step sizes, but has a higher computational complexity at each time-step due to the need to solve a nonlinear optimization problem at every time-step. This paper presents two numerical methods to accelerate DMD based simulations. First, we show that when a many-body potential function, e.g., embedded atom method (EAM), is employed, the cost of DMD is dominated by the computation of the mean of the potential function and its derivatives, which are high-dimensional random variables. To reduce the cost, we explore both first- and second-order mean field approximations. Specifically, we show that the first-order approximation, which uses a point estimate to calculate the mean, can reduce the cost by two to three orders of magnitude, but may introduce relatively large error in the solution. We show that adding an approximate second-order correction term can significantly reduce the error without much increase in computational cost. Second, we show that DMD can be significantly accelerated through subcycling time integration, as the cost of integrating the empirical diffusion equation is much lower than that of the optimization solver. To assess the DMD model and the numerical approximation methods, we present two groups of numerical experiments that simulate the diffusion of hydrogen in palladium nanoparticles. In particular, we show that the computational framework is capable of capturing the propagation of an atomically sharp phase boundary over a time window of more than 30 seconds. The effects of the proposed numerical methods on solution accuracy and computation time are also assessed quantitatively.

Original language | English |
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Pages (from-to) | 470-492 |

Number of pages | 23 |

Journal | Journal of Computational Physics |

Volume | 350 |

DOIs | |

State | Published - Dec 1 2017 |

### Bibliographical note

Funding Information:The authors gratefully acknowledge the support of the Institute for Critical Technologies and Applied Sciences (ICTAS) at Virginia Tech through a Junior Faculty Collaboration (JFC) project, the Ministerio de Economía y Competitividad of Spain under grant number DPI2015-66534-R , and the U.S. Army Research Laboratory (ARL) through the Materials in Extreme Dynamic Environments (MEDE) Collaborative Research Alliance (CRA) under Award Number W911NF-11-R-0001 .

Publisher Copyright:

© 2017 Elsevier Inc.

## Keywords

- Diffusive molecular dynamics
- Hydrogen diffusion
- Long-term processes
- Mean field approximation
- Phase transformation
- Subcycling time integration

## ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy (all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics