{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T10:03:34Z","timestamp":1766484214011,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:00:00Z","timestamp":1660608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62071102","12102087","61921002"],"award-info":[{"award-number":["62071102","12102087","61921002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>At present, electron optical simulator (EOS) takes a long time to solve linear FEM systems. The algebraic multigrid preconditioned conjugate gradient (AMGPCG) method can improve the efficiency of solving systems. This paper is focused on the implementation of the AMGPCG method in EOS. The aggregation-based scheme, which uses two passes of a pairwise matching algorithm and the K-cyle scheme, is adopted in the aggregation-based algebraic multigrid method. Numerical experiments show the advantages and disadvantages of the AMG algorithm in peak memory and solving efficiency. The AMGPCG is more efficient than the iterative methods used in the past and only needs one coarsening when EOS computes the particle motion trajectory.<\/jats:p>","DOI":"10.3390\/e24081133","type":"journal-article","created":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T23:44:25Z","timestamp":1660693465000},"page":"1133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Research of the Algebraic Multigrid Method for Electron Optical Simulator"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2086-9876","authenticated-orcid":false,"given":"Zhi","family":"Wang","sequence":"first","affiliation":[{"name":"Vacuum Electronics National Laboratory, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quan","family":"Hu","sequence":"additional","affiliation":[{"name":"Vacuum Electronics National Laboratory, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China"},{"name":"Shenzhen Institute for Advanced Study, University of Electronic Science and Technology of China, Shenzhen 518000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Fang","family":"Zhu","sequence":"additional","affiliation":[{"name":"Vacuum Electronics National Laboratory, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Li","sequence":"additional","affiliation":[{"name":"Vacuum Electronics National Laboratory, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu-Lu","family":"Hu","sequence":"additional","affiliation":[{"name":"Vacuum Electronics National Laboratory, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Huang","sequence":"additional","affiliation":[{"name":"Vacuum Electronics National Laboratory, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhong-Hai","family":"Yang","sequence":"additional","affiliation":[{"name":"Vacuum Electronics National Laboratory, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1696","DOI":"10.1109\/TED.2010.2049214","article-title":"Recent developments on EOS 2-D\/3-D electron gun and collector modeling code","volume":"57","author":"Hu","year":"2010","journal-title":"IEEE Trans. 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