{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:23:45Z","timestamp":1759191825471,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,10]],"date-time":"2012-04-10T00:00:00Z","timestamp":1334016000000},"content-version":"vor","delay-in-days":100,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"],"award-info":[{"award-number":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"],"award-info":[{"award-number":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Chinese Universities Specialized Research Fund for the Doctoral Program","award":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"],"award-info":[{"award-number":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"]}]},{"name":"Tianyuan Foundation","award":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"],"award-info":[{"award-number":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"]}]},{"name":"Sichuan Province Sci. and Tech. Research Project","award":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"],"award-info":[{"award-number":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"]}]},{"name":"Sichuan Province Sci. and Tech. Research Project","award":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"],"award-info":[{"award-number":["61170311","60973015","20110185110020","12ZC1802","2011JY0002"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>An algebraic multigrid (AMG) with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods. In the setup process of AMG, we employ the double pairwise aggregation (DPA) scheme firstly proposed by Y. Notay (2006) as the coarsening method. We compare it with the smoothed aggregation algebraic multigrid and meanwhile show shifted Laplacian preconditioners. According to numerical results, we find that DPA algorithm is a good choice in AMG for Helmholtz equations in reducing time and memory. Spectral estimation of system preconditioned by the three methods and the influence of second\u2010order and fourth\u2010order accurate discretizations on\nthe three techniques are also considered.<\/jats:p>","DOI":"10.1155\/2012\/367909","type":"journal-article","created":{"date-parts":[[2012,4,10]],"date-time":"2012-04-10T21:01:32Z","timestamp":1334091692000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Comparison of Algebraic Multigrid Preconditioners for Solving Helmholtz Equations"],"prefix":"10.1155","volume":"2012","author":[{"given":"Dandan","family":"Chen","sequence":"first","affiliation":[]},{"given":"Ting-Zhu","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Liang","family":"Li","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,10]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(83)90139-0"},{"volume-title":"Preconditioned Iterative solution of the 2D Helmholtz equation, report 02\/12","year":"2002","author":"Laird A. 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Introduction to algebraic multigrid Course Note of an Algebraic Multigrid Course at the university of Heidelberg in the Wintersemester 1998."}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/367909.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/367909.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/367909","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:56:58Z","timestamp":1718089018000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/367909"}},"subtitle":[],"editor":[{"given":"Edmond","family":"Chow","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/367909"],"URL":"https:\/\/doi.org\/10.1155\/2012\/367909","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-12-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-02-06","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"367909"}}