{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:47:12Z","timestamp":1777675632404,"version":"3.51.4"},"reference-count":42,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T00:00:00Z","timestamp":1599177600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["230898523, 230723766"],"award-info":[{"award-number":["230898523, 230723766"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of High Performance Computing Applications"],"published-print":{"date-parts":[[2021,5]]},"abstract":"<jats:p>A nonlinear domain decomposition (DD) solver is considered with respect to improved energy efficiency. In this method, nonlinear problems are solved using Newton\u2019s method on the subdomains in parallel and in asynchronous iterations. The method is compared to the more standard Newton-Krylov approach, where a linear domain decomposition solver is applied to the overall nonlinear problem after linearization using Newton\u2019s method. It is found that in the nonlinear domain decomposition method, making use of the asynchronicity, some processor cores can be set to sleep to save energy and to allow better use of the power and thermal budget. Energy savings on average for each socket up to 77% (due to the RAPL hardware counters) are observed compared to the more traditional Newton-Krylov approach, which is synchronous by design, using up to 5120 Intel Broadwell (Xeon E5-2630v4) cores. The total time to solution is not affected. On the contrary, remaining cores of the same processor may be able to go to turbo mode, thus reducing the total time to solution slightly. Last, we consider the same strategy for the ASPIN (Additive Schwarz Preconditioned Inexact Newton) nonlinear domain decomposition method and observe a similar potential to save energy.<\/jats:p>","DOI":"10.1177\/1094342020953891","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T07:44:31Z","timestamp":1599205471000},"page":"237-253","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Energy efficiency of nonlinear domain decomposition methods"],"prefix":"10.1177","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4765-7387","authenticated-orcid":false,"given":"Axel","family":"Klawonn","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Cologne, K\u00f6ln, Germany"},{"name":"Center for Data and Simulation Science, University of Cologne, K\u00f6ln, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Lanser","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Cologne, K\u00f6ln, Germany"},{"name":"Center for Data and Simulation Science, University of Cologne, K\u00f6ln, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oliver","family":"Rheinbach","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Numerische Mathematik und Optimierung, Fakult\u00e4t f\u00fcr Mathematik und Informatik, Technische Universit\u00e4t Bergakademie Freiberg, Freiberg, Germany"},{"name":"Universit\u00e4tsrechenzentrum (URZ), Technische Universit\u00e4t Bergakademie Freiberg, Freiberg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gerhard","family":"Wellein","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Friedrich-Alexander University Erlangen-N\u00fcrnberg, Erlangen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Markus","family":"Wittmann","sequence":"additional","affiliation":[{"name":"Erlangen Regional Computing Center, Friedrich-Alexander University Erlangen-N\u00fcrnberg, Erlangen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2020,9,4]]},"reference":[{"key":"bibr1-1094342020953891","unstructured":"Balay S, Abhyankar S, Adams MF, et al. (2016a) PETSc Web page. Available at: http:\/\/www.mcs.anl.gov\/petsc (acceessed May 2018)."},{"key":"bibr2-1094342020953891","unstructured":"Balay S, Abhyankar S, Adams MF, et al. (2016b) PETSc users manual. Technical Report ANL-95\/11, Revision 3.7, Argonne National Laboratory. Available at: http:\/\/www.mcs.anl.gov\/petsc (acceessed May 2018)."},{"key":"bibr3-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/130936725"},{"key":"bibr4-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/S106482750037620X"},{"key":"bibr5-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1002\/fld.404"},{"key":"bibr6-1094342020953891","first-page":"345","volume-title":"Domain Decomposition Methods in Science and Engineering (Lyon, 2000), Theory and Engineering Applications of Computational Methods","author":"Cai XC","year":"2002"},{"key":"bibr7-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1007\/s11771-012-1348-z"},{"key":"bibr8-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/15M102887X"},{"key":"bibr9-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1002\/nme.76"},{"key":"bibr10-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1002\/1099-1506(200010\/12)7:7\/8<687::AID-NLA219>3.0.CO;2-S"},{"key":"bibr11-1094342020953891","unstructured":"Gro\u00df C (2009) A unifying theory for nonlinear additively and multiplicatively preconditioned globalization strategies: convergence results and examples from the field of nonlinear elastostatics and elastodynamics. PhD Thesis, Rheinische Friedrich-Wilhelms-Universit\u00e4t Bonn, Germany."},{"key":"bibr12-1094342020953891","unstructured":"Gro\u00df C, Krause R (2011) On the globalization of ASPIN employing trust-region control strategies\u2014convergence analysis and numerical examples. Technical Report 2011-03, Institute Computer Centre, Universita della Svizzera Italiana."},{"key":"bibr13-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1109\/IPDPSW.2015.70"},{"key":"bibr14-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1002\/cpe.3180"},{"key":"bibr15-1094342020953891","volume-title":"Proceedings of the 2005 ACM\/IEEE conference on supercomputing, SC \u201905","author":"Hsu CH","year":"2005"},{"key":"bibr16-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/15M1026122"},{"key":"bibr17-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1145\/2807591.2807638"},{"key":"bibr18-1094342020953891","unstructured":"Intel Corp (2016) Intel Xeon processor E5-2600 v4 product family specification update. Version: December 2016."},{"key":"bibr19-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1109\/SC.2005.39"},{"key":"bibr20-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1109\/CLUSTER.2011.33"},{"key":"bibr21-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/130920563"},{"key":"bibr22-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/140997907"},{"key":"bibr23-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-39929-4_25"},{"key":"bibr24-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1553\/etna_vol49s244"},{"key":"bibr25-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/16M1102495"},{"key":"bibr26-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.03.023"},{"key":"bibr27-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.200900329"},{"key":"bibr28-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20156"},{"key":"bibr29-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901388081"},{"key":"bibr30-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1145\/2901318.2901329"},{"key":"bibr31-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1109\/IPDPS.2010.5470463"},{"key":"bibr32-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1016\/j.parco.2011.07.001"},{"key":"bibr33-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/140970379"},{"key":"bibr34-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1137\/17M1128502"},{"key":"bibr35-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-26825-1_68"},{"key":"bibr36-1094342020953891","unstructured":"Microway (2018) Detailed specifications of the Intel Xeon E5-2600v4 \u201cBroadwell-EP\u201d processors. Available at: https:\/\/www.microway.com\/knowledge-center-articles\/detailed-specifications-of-the-intel-xeon-e5-2600v4-broadwell-ep-processors\/ (accessed 6 May 2018)."},{"key":"bibr37-1094342020953891","unstructured":"Negrello C, Gosselet P, Rey C (2018) Nonlinearly preconditioned FETI solver for substructured formulations of nonlinear problems. Available at: https:\/\/hal.archives-ouvertes.fr\/hal-01774589. Working paper or preprint (accessed May 2018)."},{"key":"bibr38-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1109\/IPDPSW.2012.116"},{"key":"bibr39-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1145\/1542275.1542340"},{"key":"bibr40-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1109\/ICPPW.2010.38"},{"key":"bibr41-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1007\/s11227-011-0699-9"},{"key":"bibr42-1094342020953891","doi-asserted-by":"publisher","DOI":"10.1109\/AMS.2008.80"}],"container-title":["The International Journal of High Performance Computing Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1094342020953891","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/1094342020953891","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1094342020953891","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T08:16:04Z","timestamp":1777450564000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1094342020953891"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,4]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["10.1177\/1094342020953891"],"URL":"https:\/\/doi.org\/10.1177\/1094342020953891","relation":{},"ISSN":["1094-3420","1741-2846"],"issn-type":[{"value":"1094-3420","type":"print"},{"value":"1741-2846","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,4]]}}}