Abstract
Noise is a major concern for Particle-In-Cell (PIC) simulations. We propose a new theoretical and algorithmic framework to evaluate and reduce the noise level for PIC simulations based on the Kernel Density Estimation (KDE) theory, which has been widely adopted in machine learning and big data science. According to this framework, the error on particle density estimation for PIC simulations can be characterized by the Mean Integrated Square Error (MISE), which consists of two parts, systematic error and noise. A careful analysis shows that in the standard PIC methods, noise is the dominant error, and the noise level can be reduced if we select different shape functions that are capable of balancing the systematic error and the noise. To improve, we use the von Mises distribution as the shape function and seek an optimal particle width that minimizes the MISE, represented by a cross-validation function. It is shown that this procedure significantly reduces the noise and the MISE for PIC simulations. A particle-wise width adjustment algorithm and a width update algorithm are also developed to further reduce the MISE. Simulations using the examples of Langmuir wave and Landau damping demonstrate that relative to the standard PIC methods, the KDE algorithm developed in the present study reduces the noise level on density estimation by 98% and gives a much more accurate result on the linear damping rate. To achieve the same accuracy, the KDE algorithm is 40% faster.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.