Efficient evaluation of Coulomb interactions in kinetic Monte Carlo simulations of charge transport.

The application of predictive and reliable modeling techniques for the simulation of charge transport in functional materials is an essential step for the development of advanced platforms for electronics, optoelectronics, and photovoltaics. In this context, kinetic Monte Carlo (KMC) methods have emerged as a valuable tool, especially for the simulation of systems where charge transport can be described by the hopping of charge carriers across localized quantum states, as, for example, in organic semiconductor materials. The accuracy, computational efficiency, and reliability of KMC simulations of charge transport, however, crucially depend on the methods and approximations used to evaluate electrostatic interactions arising from the distribution of charges in the system. The long-range nature of Coulomb interactions and the need to simulate large model systems to capture the details of charge transport phenomena in complex devices lead, typically, to a computational bottleneck, which hampers the application of KMC methods. Here, we propose and assess computational schemes for the evaluation of electrostatic interactions in KMC simulations of charge transport based on the locality of the charge redistribution in the hopping regime. The methods outlined in this work provide an overall accuracy that outperforms typical approaches for the evaluation of electrostatic interactions in KMC simulations at a fraction of the computational cost. In addition, the computational schemes proposed allow a spatial decomposition of the evaluation of Coulomb interactions, leading to an essentially linear scaling of the computational load with the size of the system.

A survey of the parallel performance and accuracy of Poisson solvers for electronic structure calculations.

We present an analysis of different methods to calculate the classical electrostatic Hartree potential created by charge distributions. Our goal is to provide the reader with an estimation on the performance-in terms of both numerical complexity and accuracy-of popular Poisson solvers, and to give an intuitive idea on the way these solvers operate. Highly parallelizable routines have been implemented in a first-principle simulation code (Octopus) to be used in our tests, so that reliable conclusions about the capability of methods to tackle large systems in cluster computing can be obtained from our work.

Comparison of scalable fast methods for long-range interactions.

Based on a parallel scalable library for Coulomb interactions in particle systems, a comparison between the fast multipole method (FMM), multigrid-based methods, fast Fourier transform (FFT)-based methods, and a Maxwell solver is provided for the case of three-dimensional periodic boundary conditions. These methods are directly compared with respect to complexity, scalability, performance, and accuracy. To ensure comparable conditions for all methods and to cover typical applications, we tested all methods on the same set of computers using identical benchmark systems. Our findings suggest that, depending on system size and desired accuracy, the FMM- and FFT-based methods are most efficient in performance and stability.