Particle Control in Phase Space by Global K-Means Clustering

2015/04/15 by J. Frederiksen, J. Trier Frederiksen, Giovanni Lapenta +6 · 1 citation
Physics and Astronomy · #Computational Physics (physics.comp-ph) #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #High Energy Astrophysical Phenomena (astro-ph.HE) #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Particle Detector Development and Performance #Particle physics theoretical and experimental studies #Plasma Physics (physics.plasm-ph) #astro-ph.HE #astro-ph.IM #physics.comp-ph #physics.plasm-ph

paper · pdf · doi:10.48550/arxiv.1504.03849

Revision 1. Major revisions. Added discussion. 18 pages, 22 figures, submitted to Journal of Computational Physics

openalex publication_date 2015/04/15 · arxiv created 2015/11/30 · arxiv updated 2015/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We devise and explore an iterative optimization procedure for controlling particle populations in particle-in-cell (PIC) codes via merging and splitting of computational macro-particles. Our approach, is to compute an optimal representation of the global particle phase space structure while decreasing or increasing the entire particle population, based on k-means clustering of the data. In essence the procedure amounts to merging or splitting particles by statistical means, throughout the entire simulation volume in question, while minimizing a 6-dimensional total distance measure to preserve the physics. Particle merging is by far the most demanding procedure when considering conservation laws of physics; it amounts to lossy compression of particle phase space data. We demonstrate that our k-means approach conserves energy and momentum to high accuracy, even for high compression ratios, R ≈ 3 --- i.e., N_f \lesssim 0.33N_i. Interestingly, we find that an accurate particle splitting step can be performed using k-means as well; this from an argument of symmetry. The split solution, using k-means, places splitted particles optimally, to obtain maximal spanning on the phase space manifold. Implementation and testing is done using an electromagnetic PIC code, the \ppcode. Nonetheless, the k-means framework is general; it is not limited to Vlasov-Maxwell type PIC codes. We discuss advantages and drawbacks of this optimal phase space reconstruction.

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