{"paper":{"title":"A Fast Tree Algorithm for Electric Field Calculation in Electrical Discharge Simulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CE","authors_text":"Chijie Zhuang, Jinliang He, Lei Liu, Rong Zeng, Xin Zhou, Yong Zhang","submitted_at":"2017-10-16T15:24:12Z","abstract_excerpt":"The simulation of electrical discharges has been attracting a great deal of attention. In such simulations, the electric field computation dominates the computational time. In this paper, we propose a fast tree algorithm that helps to reduce the time complexity from $O(N^2)$ (from using direct summation) to $O(N\\log N)$. The implementation details are discussed and the time complexity is analyzed. A rigorous error estimation shows the error of the tree algorithm decays exponentially with the number of truncation terms and can be controlled adaptively. Numerical examples are presented to valida"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05781","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}