Dynamic particle data structures for Wigner Monte Carlo simulations

Abstract

The over many decades lasting and still continuing miniaturization of semiconductor devices, combined with the subsequent increase of the integration density in microprocessors, led to minuscule device sizes in the range of a few nanometers. Quantum transport models are the only way to describe the plethora of quantum effects that are taking place in these systems. Among the models is the signed-particle Wigner model, which utilizes an ensemble Monte Carlo concept to solve the Wigner transport equation and thus offers an intuitive interpretation of quantum electron transport dynamics and provides a clear analogy to classical notions. The stochastic nature of the signed-particle model demands an extremely large number of numerical particles to reduce the variance of the resulting values. Additionally, the necessary particle generation and annihilation events, which are essential for practical utilization, modify the number of the simulated particles in every time step, further contributing to the computational challenge. Due to these challenges, the main objective of this thesis is an extensive quantitative performance analysis of dynamic particle data structures suitable for signed-particle Wigner models, that store all particles of the ensemble and their assigned attributes. The reference simulation tool ViennaWD, which utilizes a signed-particle Wigner model, is consulted to derive the necessary particle properties. Related open source projects, especially Monte Carlo particle simulators, are examined to obtain further possibilities for different implementations. The emphasis lies on the utilization of modern supercomputer clusters that employ multiple layers of parallelization techniques, such as the Vienna Scientific Cluster (VSC). A number of promising data structure implementations and corresponding test functions, which are inspired by the operations of the signed-particle model and necessary particle algorithms, are combined into a categorically and rigorously designed benchmark framework. This framework is written in the C++ programming language. It is used to perform numerical experiments on the VSC and yields execution times which are then analyzed. The goal is to develop a software benchmark tool that is able to determine particle data structure implementations which offer the best performance for the considered task. Even though the runtime results at the end of this thesis feature a variety of data structure designs from which a hierarchy of best suited implementations can be derived, the general objective lies in the usability, reusability, maintainability, flexibility and expandability of the benchmark framework. New data structures can be defined and easily incorporated into the framework to obtain execution runtimes for all available test functions. These concepts support the possibility to use the application to yield further insights beyond the implementations featured in this thesis and reinforces the principles of modern software engineering for computational science and engineering.