{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T21:25:53Z","timestamp":1772832353751,"version":"3.50.1"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv. Adapt. Data Anal."],"published-print":{"date-parts":[[2011,4]]},"abstract":"<jats:p>We give an overview of a number of algebraic multigrid methods targeting finite element discretization problems. The focus is on the properties of the constructed hierarchy of coarse spaces that guarantee (two-grid) convergence. In particular, a necessary condition known as \"weak approximation property,\" and a sufficient one, referred to as \"strong approximation property,\" are discussed. Their role in proving convergence of the TG method (as iterative method) and also on the approximation properties of the algebraic mottigrid (AMG) coarse spaces if used as discretization tool is pointed out. Some preliminary numerical results illustrating the latter aspect are also reported.<\/jats:p>","DOI":"10.1142\/s1793536911000830","type":"journal-article","created":{"date-parts":[[2011,9,8]],"date-time":"2011-09-08T09:53:56Z","timestamp":1315475636000},"page":"229-249","source":"Crossref","is-referenced-by-count":20,"title":["COARSE SPACES BY ALGEBRAIC MULTIGRID: MULTIGRID CONVERGENCE AND UPSCALING ERROR ESTIMATES"],"prefix":"10.1142","volume":"03","author":[{"given":"PANAYOT S.","family":"VASSILEVSKI","sequence":"first","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-561, Livermore, CA 94551, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/0720066"},{"key":"rf3","unstructured":"A.\u00a0Brandt, S.\u00a0McCormick and J. W.\u00a0Ruge, Sparsity and its Applications, ed. D. J.\u00a0Evans (Cambridge University Press, 1984)\u00a0pp. 257\u2013284."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598344303"},{"key":"rf5","first-page":"1","volume":"25","author":"Chartier T.","journal-title":"Spectral AMGe (\u03c1AMGe) SIAM J. Sci. Comput."},{"key":"rf6","unstructured":"T.\u00a0Chartier, Spectral Element Agglomerate AMGe, Domain Decomposition Methods in Science and Engineering XVI, Lecture Notes in Computational Science and Engineering\u00a055 (Springer-Verlag, Berlin-Heidelberg, 2007)\u00a0pp. 515\u2013524."},{"key":"rf7","unstructured":"N. H.\u00a0Decker, J.\u00a0Mandel and S. V.\u00a0Parter, On the role of regularity in multigrid methods, Multigrid Methods: Theory, Applications, and Supercomputing, ed. S. F.\u00a0McCormick (Marcel Decker, New York, 1988)\u00a0pp. 143\u2013156."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1002\/nla.437"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599361047"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1002\/nla.494"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1002\/nla.585"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1002\/nla.641"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596297112"},{"key":"rf16","volume-title":"Multilevel Block-Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving Finite Element Equations","author":"Vassilevski P. S.","year":"2008"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1137\/080726252"},{"key":"rf18","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/PL00021413","volume":"65","author":"Wagner C.","journal-title":"Computing"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598334277"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-004-0147-y"}],"container-title":["Advances in Adaptive Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793536911000830","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T08:58:39Z","timestamp":1686301119000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793536911000830"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4]]},"references-count":17,"journal-issue":{"issue":"01n02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2011,4]]}},"alternative-id":["10.1142\/S1793536911000830"],"URL":"https:\/\/doi.org\/10.1142\/s1793536911000830","relation":{},"ISSN":["1793-5369","1793-7175"],"issn-type":[{"value":"1793-5369","type":"print"},{"value":"1793-7175","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,4]]}}}