An Efficient Implementation of Multiscale Simulation Software PNP-cDFT
- PDF / 1,931,377 Bytes
- 5 Pages / 612 x 792 pts (letter) Page_size
- 64 Downloads / 221 Views
An Efficient Implementation of Multiscale Simulation Software PNP-cDFT Da Meng, Guang Lin* and Maria L. Sushko Pacific Northwest National Laboratory, Richland, WA 99352, U.S.A. ABSTRACT An efficient implementation of PNP-cDFT, a multiscale method for computing the chemical potentials of charged species is designed and evaluated. Spatial decomposition of the multi particle system is employed in the parallelization of classical density functional theory (cDFT) algorithm. Furthermore, a truncation strategy is used to reduce the computational complexity of cDFT algorithm. The simulation results show that the parallel implementation has close to linear scalability in parallel computing environments. It also shows that the truncated versions of cDFT improve the efficiency of the methods substantially. INTRODUCTION A novel hierarchical multiscale model has been proposed to study the mechanism of ion and electron transport in the material at the nano- to micrometer scales [1-4]. The method couples classical density functional theory (cDFT) with the Possion-Nernst-Plank (PNP) formalism, where cDFT is used for mesoscale study of the interactions of particles and the PNP is used for dynamic effects. The application of the method to complex system, however, is limited by its computing complexity. In this paper, an efficient implementation of cDFT is introduced. THEORETICAL MODEL Diffusion channel (Figure 1) [3] is represented as a uniform medium. Li+ migrates in the channel from one interstitial lattice site to another. In a 1D model, these equilibrium lattice sites are represented as a one-dimensional array of stationary points, i.e. only sites I0 are considered and Li+ migrates is through hopping between I0. In a 3D model, sites II0 and II* are also considered, the motion of Li+ may follow different paths. The flux of charged particles in stationary conditions is calculated within the PossionNernst-Plank (PNP) formalism [1-3]: !!! 1 !∅ !!!! !!!!" + !! ! !! ! + + −!! = !! ! !(!) !" !" !" !" !" !!! =0 !" 1 ! !∅ − !! ! !(!)!(!) =! !! !! ! ! ! !" !" !
In these equations, Ji are the fluxes for Li+ and electrons, Di(z) and ρi(z) are their diffusion ______________________ *Corresponding author. Email address: [email protected]
coefficients and densities along the channel (z axis) in a 1D case, respectively, A(z) is the cross section of the channel, ϕ is the electrostatic potential, µ0 and µex are the ideal and excess chemical potential of Li+ and electrons, respectively, kT is the thermal energy, and e is the electron charge. In this system of equations, the first describes the flux, the second is the stationary condition, and the third is Poisson’s equation for the calculation of the electrostatic potential.
Figure 1. Diffusion channel of Li+ in LiPON. Blue spheres are interstitial equilibriums (I0); Yellow spheres (II0) and gray spheres (II*) are metastable sites. a, 2b and 2c are the size along three crystallographic directions. The cDFT is used to evaluate the chemical potentials of charged species. In this model, the total
Data Loading...
