{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T03:36:28Z","timestamp":1787542588221,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>We introduce AMGe, an algebraic multigrid method for solving the discrete equations that arise in Ritz-type finite element methods for partial differential equations. Assuming access to the element stiffness matrices, we have that AMGe is based on the use of two local measures, which are derived from global measures that appear in existing multigrid theory. These new measures are used to determine local representations of algebraically \"smooth\" error components that provide the basis for constructing effective interpolation and, hence, the coarsening process for AMG. Here, we focus on the interpolation process; choice of the coarse \"grids\" based on these measures is the subject of current research. We develop a theoretical foundation for AMGe and present numerical results that demonstrate the efficacy of the method.<\/jats:p>","DOI":"10.1137\/s1064827598344303","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1570-1592","source":"Crossref","is-referenced-by-count":167,"title":["Algebraic Multigrid Based on Element Interpolation (AMGe)"],"prefix":"10.1137","volume":"22","author":[{"given":"M.","family":"Brezina","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. J.","family":"Cleary","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R. D.","family":"Falgout","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V. E.","family":"Henson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. E.","family":"Jones","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T. A.","family":"Manteuffel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S. F.","family":"McCormick","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. W.","family":"Ruge","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0902035"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6290"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1991-1079008-4"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(86)90095-0"},{"key":"R5","unstructured":"A. Brandt, S. F. McCormick, and J. W. Ruge,\n                      Algebraic Multigrid (AMG) for Automatic Multigrid Solutions with Application to Geodetic Computations\n                      , Tech. report, Institute for Computational Studies, Fort Collins, CO, 1982."},{"key":"R6","unstructured":"A. Brandt, S. McCormick, J. Ruge, Algebraic multigrid (AMG) for sparse matrix equations, Cambridge Univ. 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St\u00fcben, Efficient solution of finite difference and finite element equations, Inst. Math. Appl. Conf. Ser. New Ser., Vol. 3, Oxford Univ. Press, New York, 1985, 169\u201321287i:65047"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"J. Ruge, K. St\u00fcben, Algebraic multigrid, Frontiers Appl. Math., Vol. 3, SIAM, Philadelphia, PA, 1987, 73\u2013130972756","DOI":"10.1137\/1.9781611971057.ch4"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(83)90023-1"},{"key":"R19","unstructured":"Klaus St\u00fcben, Ulrich Trottenberg, Kristian Witsch, Software development based on multigrid techniques, North\u2010Holland, Amsterdam, 1984, 241\u2013267823814"},{"key":"R20","unstructured":"P. Van\u011bk, M. Brezina, and J. Mandel,\n                      Convergence analysis of algebraic multigrid based on smoothed aggregation\n                      , Numer. Math., to appear."},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596297112"},{"key":"R22","unstructured":"W. L. Wan,\n                      An Energy\u2010Minimizing Interpolation for Multigrid Methods\n                      , UCLA CAM Report 97\u201018, Department of Mathematics, UCLA, Los Angeles, CA, 1997."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598334277"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827598344303","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:51:43Z","timestamp":1787334703000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827598344303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":23,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1137\/S1064827598344303"],"URL":"https:\/\/doi.org\/10.1137\/s1064827598344303","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}