{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:49:41Z","timestamp":1759837781690,"version":"3.41.2"},"reference-count":22,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,29]],"date-time":"2012-04-29T00:00:00Z","timestamp":1335657600000},"content-version":"vor","delay-in-days":119,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"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>The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation\u2010Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized\u2010sparse\u2010approximate\u2010inverse\u2010 (FSAI\u2010) type preconditioners. We present an enhanced parallel implementation of the FSAI preconditioner and make use of the recently developed Block FSAI\u2010IC preconditioner, which combines the FSAI and the Block Jacobi\u2010IC preconditioners. Results onto matrices of large size arising from finite element discretization of geomechanical models reveal that DACG accelerated by these type of preconditioners is competitive with respect to the available public parallel <jats:italic>hypre<\/jats:italic> package, especially in the computation of a few of the leftmost eigenpairs. The parallel DACG code accelerated by FSAI is written in MPI\u2010Fortran 90 language and exhibits good scalability up to one thousand processors.<\/jats:p>","DOI":"10.1155\/2012\/872901","type":"journal-article","created":{"date-parts":[[2012,4,29]],"date-time":"2012-04-29T21:01:37Z","timestamp":1335733297000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Parallel Rayleigh Quotient Optimization with FSAI\u2010Based Preconditioning"],"prefix":"10.1155","volume":"2012","author":[{"given":"Luca","family":"Bergamaschi","sequence":"first","affiliation":[]},{"given":"Angeles","family":"Mart\u00ednez","sequence":"additional","affiliation":[]},{"given":"Giorgio","family":"Pini","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,29]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1365"},{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895281484"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479894270427"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(199703\/04)4:2&lt;69::AID-NLA98&gt;3.3.CO;2-6"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/0731064"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(200004\/05)7:3&lt;99::AID-NLA188&gt;3.3.CO;2-X"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(02)00457-7"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/0614004"},{"key":"e_1_2_8_9_2","series-title":"Lecture Notes in Computer Sciences","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1007\/11403937_47","volume-title":"VECPAR 2004","author":"Bergamaschi L.","year":"2005"},{"key":"e_1_2_8_10_2","first-page":"191","article-title":"An efficient parallel MLPG method for poroelastic models","volume":"49","author":"Bergamaschi L.","year":"2009","journal-title":"Computer Modeling in Engineering & Sciences"},{"key":"e_1_2_8_11_2","doi-asserted-by":"crossref","unstructured":"BergamaschiL.andMart\u00ednezA. 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