{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T05:40:15Z","timestamp":1743572415755,"version":"3.40.3"},"publisher-location":"Cham","reference-count":35,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031856969","type":"print"},{"value":"9783031856976","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-85697-6_2","type":"book-chapter","created":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T05:06:45Z","timestamp":1743570405000},"page":"17-33","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Trade-Off Between Energy Consumption and\u00a0Solution Accuracy for\u00a0a\u00a0Multithreaded Spectral Method Implementation"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3102-6858","authenticated-orcid":false,"given":"Thomas","family":"Rauber","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5364-2088","authenticated-orcid":false,"given":"Gudula","family":"R\u00fcnger","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,1]]},"reference":[{"issue":"4","key":"2_CR1","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1002\/cpe.3341","volume":"27","author":"J Aliaga","year":"2015","unstructured":"Aliaga, J., Anzt, H., Castillo, M., Fern\u00e1ndez, J.C., Le\u00f3n, G., P\u00e9rez, J., Quintana-Ort\u00ed, E.S.: Unveiling the performance-energy trade-off in iterative linear system solvers for multithreaded processors. Concurr. Comput.\u202f: Pract. Exper. 27(4), 885\u2013904 (2015). https:\/\/doi.org\/10.1002\/cpe.3341","journal-title":"Concurr. Comput. : Pract. Exper."},{"key":"2_CR2","unstructured":"Balay, S., et al.: PETSc users manual. Technical report. ANL-95\/11 - Revision 3.8, Argonne National Laboratory (2017)"},{"issue":"4","key":"2_CR3","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1109\/TCAD.2016.2597215","volume":"36","author":"E Bezati","year":"2017","unstructured":"Bezati, E., Casale-Brunet, S., Mattavelli, M., Janneck, J.W.: Clock-gating of streaming applications for energy efficient implementations on FPGAs. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 36(4), 699\u2013703 (2017). https:\/\/doi.org\/10.1109\/TCAD.2016.2597215","journal-title":"IEEE Trans. Comput. Aided Des. Integr. Circuits Syst."},{"key":"2_CR4","doi-asserted-by":"crossref","unstructured":"Brankin, R., Gladwell, I., Shampine, L.: RKSUITE release 1.0 (1991)","DOI":"10.1016\/0898-1221(90)90188-P"},{"key":"2_CR5","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/0168-9274(93)90037-R","volume":"11","author":"K Burrage","year":"1993","unstructured":"Burrage, K.: Parallel methods for initial value problems. Appl. Numer. Math. 11, 5\u201325 (1993)","journal-title":"Appl. Numer. Math."},{"key":"2_CR6","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198534327.001.0001","author":"K Burrage","year":"1995","unstructured":"Burrage, K.: Parallel and sequential methods for ordinary differential equations. Oxford Sci. Publ. (1995). https:\/\/doi.org\/10.1093\/oso\/9780198534327.001.0001","journal-title":"Oxford Sci. Publ."},{"key":"2_CR7","doi-asserted-by":"publisher","unstructured":"Carretero, J., et al.: Energy-efficient algorithms for ultrascale systems. Supercomput. Front. Innov. 2(2), 77\u2013104 (2015). https:\/\/doi.org\/10.14529\/jsfi150205","DOI":"10.14529\/jsfi150205"},{"issue":"1","key":"2_CR8","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s11227-016-1654-6","volume":"73","author":"S Catal\u00e1n","year":"2016","unstructured":"Catal\u00e1n, S., Igual, F.D., Mayo, R., Rodr\u00edguez-S\u00e1nchez, R., Quintana-Ort\u00ed, E.S.: Time and energy modeling of a high-performance multi-threaded Cholesky factorization. J. Supercomput. 73(1), 139\u2013151 (2016). https:\/\/doi.org\/10.1007\/s11227-016-1654-6","journal-title":"J. Supercomput."},{"key":"2_CR9","doi-asserted-by":"publisher","unstructured":"Dong, T., Dobrev, V., Kolev, T.V., Rieben, R.N., Tomov, S., Dongarra, J.: A step towards energy efficient computing: redesigning a hydrodynamic application on CPU-GPU. In: 2014 IEEE 28th International Parallel and Distributed Processing Symposium, Phoenix, AZ, USA, May 19-23, 2014, pp. 972\u2013981 (2014). https:\/\/doi.org\/10.1109\/IPDPS.2014.103","DOI":"10.1109\/IPDPS.2014.103"},{"issue":"1","key":"2_CR10","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0771-050X(80)90013-3","volume":"6","author":"J Dormand","year":"1980","unstructured":"Dormand, J., Prince, P.: A family of embedded Runge-Kutta formulae. J. Comput. Appl. Math. 6(1), 19\u201326 (1980). https:\/\/doi.org\/10.1016\/0771-050X(80)90013-3","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"2_CR11","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1109\/MM.2017.38","volume":"37","author":"J Doweck","year":"2017","unstructured":"Doweck, J., et al.: Inside 6th-generation intel core: new microarchitecture code-named Skylake. IEEE Micro 37(2), 52\u201362 (2017). https:\/\/doi.org\/10.1109\/MM.2017.38","journal-title":"IEEE Micro"},{"issue":"1","key":"2_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cam.2005.03.026","volume":"187","author":"M Ehrhardt","year":"2006","unstructured":"Ehrhardt, M., Zisowsky, A.: Fast calculation of energy and mass preserving solutions of Schr\u00f6dinger-Poisson systems on unbounded domains. J. Comput. Appl. Math. 187(1), 1\u201328 (2006). https:\/\/doi.org\/10.1016\/j.cam.2005.03.026","journal-title":"J. Comput. Appl. Math."},{"key":"2_CR13","unstructured":"Enright, W.H., Higham, D.J., Owren, B., Sharp, P.W.: A Survey of the Explicit Runge-Kutta Method. Technical report, 94-291, University of Toronto, Department of Computer Science (1995)"},{"issue":"2","key":"2_CR14","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1145\/2408776.2408797","volume":"56","author":"H Esmaeilzadeh","year":"2013","unstructured":"Esmaeilzadeh, H., Blem, E., Amant, R., Sankaralingam, K., Burger, D.: Power challenges may end the multicore era. Commun. ACM 56(2), 93\u2013102 (2013). https:\/\/doi.org\/10.1145\/2408776.2408797","journal-title":"Commun. ACM"},{"key":"2_CR15","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/0168-9274(93)90038-S","volume":"11","author":"C Gear","year":"1993","unstructured":"Gear, C.: Massive Parallelism across Space in ODEs. Appl. Numer. Math. 11, 27\u201343 (1993). https:\/\/doi.org\/10.1016\/0168-9274(93)90038-S","journal-title":"Appl. Numer. Math."},{"key":"2_CR16","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/0168-9274(93)90039-T","volume":"11","author":"C Gear","year":"1993","unstructured":"Gear, C., Xuhai, X.: Parallelism across time in ODEs. Appl. Numer. Math. 11, 45\u201368 (1993). https:\/\/doi.org\/10.1016\/0168-9274(93)90039-T","journal-title":"Appl. Numer. Math."},{"key":"2_CR17","doi-asserted-by":"publisher","unstructured":"G\u00f6ddeke, D., et al.: Energy efficiency vs. performance of the numerical solution of PDEs: an application study on a low\u2013power ARM\u2013based cluster. J. Comput. Phys. 237, 132\u2013150 (2013). https:\/\/doi.org\/10.1016\/j.jcp.2012.11.031","DOI":"10.1016\/j.jcp.2012.11.031"},{"key":"2_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1007\/978-3-319-93698-7_45","volume-title":"Computational Science \u2013 ICCS 2018","author":"A Haidar","year":"2018","unstructured":"Haidar, A., et al.: The design of fast and energy-efficient linear solvers: on the potential of half-precision arithmetic and iterative refinement techniques. In: Shi, Y., et al. (eds.) ICCS 2018. LNCS, vol. 10860, pp. 586\u2013600. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-93698-7_45"},{"issue":"6","key":"2_CR19","doi-asserted-by":"publisher","DOI":"10.1002\/cpe.4485","volume":"31","author":"A Haidar","year":"2019","unstructured":"Haidar, A., Jagode, H., Vaccaro, P., YarKhan, A., Tomov, S., Dongarra, J.: Investigating power capping toward energy-efficient scientific applications. Concurr. Comput. Pract. Exp. 31(6), e4485 (2019). https:\/\/doi.org\/10.1002\/cpe.4485","journal-title":"Concurr. Comput. Pract. Exp."},{"key":"2_CR20","doi-asserted-by":"publisher","unstructured":"Hairer, E., N\u00f8rsett, S., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems. Springer\u2013Verlag, Berlin (1993). https:\/\/doi.org\/10.1007\/978-3-540-78862-1","DOI":"10.1007\/978-3-540-78862-1"},{"key":"2_CR21","doi-asserted-by":"publisher","unstructured":"Harrison, R., Moroz, I., Tod, K.P.: A numerical study of the Schr\u00f6dinger-Newton equations. Nonlinearity 16(1), 101\u2013122 (2002). https:\/\/doi.org\/10.1088\/0951-7715\/16\/1\/307","DOI":"10.1088\/0951-7715\/16\/1\/307"},{"key":"2_CR22","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/0377-0427(90)90200-J","volume":"29","author":"P van der Houwen","year":"1990","unstructured":"van der Houwen, P., Sommeijer, B.: Parallel iteration of high-order Runge-Kutta methods with stepsize control. J. Comp. Appl. Math. 29, 111\u2013127 (1990)","journal-title":"J. Comp. Appl. Math."},{"key":"2_CR23","doi-asserted-by":"crossref","unstructured":"van\u00a0der Houwen, P., Sommeijer, P.: Parallel ODE solvers. In: Proceedings of the ACM International Conference on Supercomputing, pp. 71\u201381. ACM (1990)","DOI":"10.1145\/77726.255141"},{"key":"2_CR24","unstructured":"Intel: Intel 64 and IA-32 Architecture Software Developer\u2019s Manual, System Programming Guide (2011)"},{"key":"2_CR25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.97.083519","volume":"97","author":"P Mocz","year":"2018","unstructured":"Mocz, P., Lancaster, L., Fialkov, A., Becerra, F., Chavanis, P.: Schr\u00f6dinger-Poisson-Vlasov-Poisson correspondence. Phys. Rev. D 97, 083519 (2018). https:\/\/doi.org\/10.1103\/PhysRevD.97.083519","journal-title":"Phys. Rev. D"},{"key":"2_CR26","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/0010-4655(85)90006-2","volume":"34","author":"V Nguyen","year":"1985","unstructured":"Nguyen, V., Bertrand, P., Izrar, B., Fijalkow, E., Feix, M.: Integration of Vlasov equation by quantum mechanical formalism. Comput. Phys. Commun. 34, 295\u2013301 (1985)","journal-title":"Comput. Phys. Commun."},{"issue":"5","key":"2_CR27","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1007\/BF02105068","volume":"28","author":"R Penrose","year":"1996","unstructured":"Penrose, R.: On gravity\u2019s role in quantum state reduction. Gen. Relativ. Gravit. 28(5), 581\u2013600 (1996). https:\/\/doi.org\/10.1007\/BF02105068","journal-title":"Gen. Relativ. Gravit."},{"key":"2_CR28","doi-asserted-by":"publisher","unstructured":"Rauber, T., R\u00fcnger, G.: Iterated Runge-Kutta methods on distributed memory multiprocessors. In: Proceedings of the 3rd Euromicro Workshop on Parallel and Distributed Processing, pp. 12\u201319. IEEE Computer Society, January 1995. https:\/\/doi.org\/10.1109\/EMPDP.1995.389159","DOI":"10.1109\/EMPDP.1995.389159"},{"key":"2_CR29","doi-asserted-by":"publisher","unstructured":"Rauber, T., R\u00fcnger, G.: Energy-aware execution of fork-join-based task parallelism. In: 20th IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS 2012), pp. 231\u2013240. IEEE (2012). https:\/\/doi.org\/10.1109\/MASCOTS.2012.35","DOI":"10.1109\/MASCOTS.2012.35"},{"key":"2_CR30","doi-asserted-by":"publisher","unstructured":"Rauber, T., R\u00fcnger, G.: Modeling the effect of application-specific program transformations on energy and performance improvements of parallel ODE solvers. J. Comput. Sci. 51, 101356 (2021). https:\/\/doi.org\/10.1016\/j.jocs.2021.101356","DOI":"10.1016\/j.jocs.2021.101356"},{"issue":"2","key":"2_CR31","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1109\/MM.2012.12","volume":"32","author":"E Rotem","year":"2012","unstructured":"Rotem, E., Naveh, A., Ananthakrishnan, A., Rajwan, D., Weissmann, E.: Power-management architecture of the Intel microarchitecture code-named sandy bridge. IEEE Micro 32(2), 20\u201327 (2012). https:\/\/doi.org\/10.1109\/MM.2012.12","journal-title":"IEEE Micro"},{"key":"2_CR32","doi-asserted-by":"publisher","first-page":"1767","DOI":"10.1103\/PhysRev.187.1767","volume":"187","author":"R Ruffini","year":"1969","unstructured":"Ruffini, R., Bonazzola, S.: Systems of self-gravitating particles in general relativity and the concept of an equation of state. Phys. Rev. 187, 1767\u20131783 (1969). https:\/\/doi.org\/10.1103\/PhysRev.187.1767","journal-title":"Phys. Rev."},{"issue":"2","key":"2_CR33","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1145\/1646353.1646370","volume":"53","author":"E Saxe","year":"2010","unstructured":"Saxe, E.: Power-efficient software. Commun. ACM 53(2), 44\u201348 (2010). https:\/\/doi.org\/10.1145\/1646353.1646370","journal-title":"Commun. ACM"},{"key":"2_CR34","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1016\/j.parco.2014.09.001","volume":"40","author":"L Tan","year":"2014","unstructured":"Tan, L., Kothapalli, S., Chen, L., Hussaini, O., Bissiri, R., Chen, Z.: A survey of power and energy efficient techniques for high performance numerical linear algebra operations. Parallel Comput. 40, 559\u2013573 (2014). https:\/\/doi.org\/10.1016\/j.parco.2014.09.001","journal-title":"Parallel Comput."},{"issue":"6","key":"2_CR35","doi-asserted-by":"publisher","first-page":"1633","DOI":"10.1109\/TPDS.2015.2456020","volume":"27","author":"KM Tarplee","year":"2016","unstructured":"Tarplee, K.M., Friese, R., Maciejewski, A.A., Siegel, H.J., Chong, E.K.P.: Energy and make span tradeoffs in heterogeneous computing systems using efficient linear programming techniques. IEEE Trans. Parallel Distrib. Syst. 27(6), 1633\u20131646 (2016). https:\/\/doi.org\/10.1109\/TPDS.2015.2456020","journal-title":"IEEE Trans. Parallel Distrib. Syst."}],"container-title":["Lecture Notes in Computer Science","Parallel Processing and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-85697-6_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T05:06:48Z","timestamp":1743570408000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-85697-6_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031856969","9783031856976"],"references-count":35,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-85697-6_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"1 April 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"PPAM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Parallel Processing and Applied Mathematics","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Ostrava","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Czech Republic","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 September 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 September 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ppam2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ppam.edu.pl\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}