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Moreover, this method possesses the significant advantage of making the linear systems of the Peaceman\u2014Rachford iteration block diagonal and therefore perfectly appropriate for parallel processing. Not only is sparsity not affected but a reduction of the bandwidth occurs. In fact, for appropriate choices of nonconforming finite element spaces, this method makes directly possible elementwise processing. This option remains available in general for higher\u2010dimensional problems by applying the splitting algorithm recursively. Practical implementation requires nothing more than the standard finite element assembly procedure and some bookkeeping to relate a few different orderings of the nodes. In addition to all these attractive features, the method is rapidly convergent and remains highly competitive even when used on a serial machine.<\/jats:p>","DOI":"10.1002\/nla.1680020405","type":"journal-article","created":{"date-parts":[[2005,11,1]],"date-time":"2005-11-01T19:23:27Z","timestamp":1130873007000},"page":"363-393","source":"Crossref","is-referenced-by-count":9,"title":["Peaceman\u2014Rachford procedure and domain decomposition for finite element problems"],"prefix":"10.1002","volume":"2","author":[{"given":"William J.","family":"Layton","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick J.","family":"Rabier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2005,7,8]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396750"},{"key":"e_1_2_1_3_2","first-page":"358","volume-title":"SIAM","author":"Barragy E.","year":"1990"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4090-5"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385503"},{"key":"e_1_2_1_6_2","first-page":"33","article-title":"Conforming and nonconforming finite element methods for solving the stationary Stokes equations I","volume":"3","author":"Crouzeix M.","year":"1973","journal-title":"R.A.I.R.O."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385888"},{"key":"e_1_2_1_8_2","first-page":"320","article-title":"On a method of solving the Poisson equation","volume":"3","author":"Dyakonov E. 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