{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,8]],"date-time":"2025-06-08T22:40:05Z","timestamp":1749422405932,"version":"3.41.0"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030779795"},{"type":"electronic","value":"9783030779801"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-77980-1_14","type":"book-chapter","created":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T07:17:01Z","timestamp":1623223021000},"page":"173-185","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Three-Level Linearized Time Integration Scheme for Tumor Simulations with Cahn-Hilliard Equations"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3386-0555","authenticated-orcid":false,"given":"Maciej","family":"Smo\u0142ka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5576-5671","authenticated-orcid":false,"given":"Maciej","family":"Wo\u017aniak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1669-2086","authenticated-orcid":false,"given":"Robert","family":"Schaefer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,9]]},"reference":[{"key":"14_CR1","doi-asserted-by":"publisher","first-page":"4333","DOI":"10.1016\/j.cma.2008.05.003","volume":"197","author":"H G\u00f3mez","year":"2008","unstructured":"G\u00f3mez, H., Calo, V.M., Bazileves, Y., Hughes, T.J.R.: Isogeometric analysis of the Cahn-Hilliard phase-field model. Comput. Methods Appl. Mech. Eng. 197, 4333\u20134352 (2008)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"14_CR2","doi-asserted-by":"publisher","first-page":"5310","DOI":"10.1016\/j.jcp.2011.03.033","volume":"230","author":"H G\u00f3mez","year":"2011","unstructured":"G\u00f3mez, H., Hughes, T.J.R.: Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models. J. Comput. Phys. 230, 5310\u20135327 (2011)","journal-title":"J. Comput. Phys."},{"key":"14_CR3","doi-asserted-by":"publisher","first-page":"1457","DOI":"10.1007\/s00285-012-0595-9","volume":"67","author":"A Hawkins-Daarud","year":"2012","unstructured":"Hawkins-Daarud, A., Prudhomme, S., van der Zee, K.G., Oden, J.T.: Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth. J. Math. Biol. 67, 1457\u20131485 (2012). https:\/\/doi.org\/10.1007\/s00285-012-0595-9","journal-title":"J. Math. Biol."},{"issue":"3","key":"14_CR4","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1002\/cnm.2597","volume":"30","author":"X Wu","year":"2014","unstructured":"Wu, X., van Zwieten, G.J., van der Zee, K.: Stabilized second-order convex splitting schemes for Cahn-Hilliard models with application to diffuse-interface tumor-growth models. Numer. Methods Biomech. Eng. 30(3), 180\u2013203 (2014)","journal-title":"Numer. Methods Biomech. Eng."},{"key":"14_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cma.2018.08.036","volume":"343","author":"M \u0141o\u015b","year":"2019","unstructured":"\u0141o\u015b, M., K\u0142usek, A., Hassaan, M.A., Pingali, K., Dzwinel, W., Paszy\u0144ski, M.: Parallel fast isogeometric L2 projection solver with GALOIS system for 3D tumor growth simulations. Comput. Methods Appl. Mech. Eng. 343, 1\u201322 (2019)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"16","key":"14_CR6","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1080\/10255842.2019.1661388","volume":"22","author":"V Puzyrev","year":"2019","unstructured":"Puzyrev, V., \u0141o\u015b, M., Gurgul, G., Calo, V.M., Dzwinel, W., Paszy\u0144ski, M.: Parallel splitting solvers for the isogeometric analysis of the Cahn-Hilliard equation. Comput. Methods Biomech. Biomed. Eng. 22(16), 1269\u20131281 (2019)","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"14_CR7","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1016\/j.procs.2016.05.373","volume":"80","author":"M Wo\u017aniak","year":"2016","unstructured":"Wo\u017aniak, M., Smo\u0142ka, M., Cortes, A., Paszy\u0144ski, M., Schaefer, R.: Scalability of direct solver for non-stationary Cahn-Hilliard simulations with linearized time integration scheme. Procedia Comput. Sci. 80, 834\u2013844 (2016)","journal-title":"Procedia Comput. Sci."},{"key":"14_CR8","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1137\/S0036141094267662","volume":"27","author":"CM Elliott","year":"1996","unstructured":"Elliott, C.M., Garcke, H.: On the Cahn-Hilliard equation with degenerate mobility. SIAM J. Math. Anal. 27, 404\u2013423 (1996)","journal-title":"SIAM J. Math. Anal."},{"key":"14_CR9","doi-asserted-by":"crossref","unstructured":"Demkowicz, L., Kurtz, J., Pardo, D., Paszy\u0144ski, M., Rachowicz, W., Zdunek, A.: Computing with hp Finite Elements. II. Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications. Chapman&Chall\/CRC, Taylor&Francis Group Boca Raton, London, New York (2007). ISBN-13: 978-1584886723, ISBN-10: 1584886722","DOI":"10.1201\/9781420011692"},{"key":"14_CR10","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/S0045-7825(00)00203-6","volume":"190","author":"KE Jansen","year":"2000","unstructured":"Jansen, K.E., Whiting, C.H., Hulbert, G.M.: A generalized-$$\\alpha $$ method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput. Methods Appl. Mech. Eng. 190, 305\u2013319 (2000)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"14_CR11","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1016\/j.procs.2016.05.373","volume":"80","author":"M Wo\u017aniak","year":"2016","unstructured":"Wo\u017aniak, M., Smo\u0142ka, M., Cortes, A., Paszy\u0144ski, M., Schaefer, R.: Scalability of direct solver for non-stationary Cahn-Hilliard simulations with linearized time integration scheme. Procedia Comput. Sci. 80, 834\u2013844 (2016)","journal-title":"Procedia Comput. Sci."},{"key":"14_CR12","doi-asserted-by":"crossref","unstructured":"Austin Cottrell, J., Hughes, T.J.R., Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Hoboken (2009)","DOI":"10.1002\/9780470749081"},{"key":"14_CR13","unstructured":"Balay, S. et al.: PETSc (2014). http:\/\/www.mcs.anl.gov\/petsc"},{"key":"14_CR14","unstructured":"Balay, S., et al.: PETSc User Manual, Argonne National Laboratory ANL-95\/11 - Revision 3.4 (2013)"},{"key":"14_CR15","doi-asserted-by":"publisher","unstructured":"Balay, S., Gropp, W.D., Curfman McInnes, L., Smith, B.F.: Efficient management of parallelism in Object Oriented Numerical Software Libraries. In: Arge, E., Bruaset, A.M., Langtangen, H.P. (eds.) Modern Software Tools in Scientific Computing. Birkh\u00e4user, Boston (1997). https:\/\/doi.org\/10.1007\/978-1-4612-1986-6_8","DOI":"10.1007\/978-1-4612-1986-6_8"},{"key":"14_CR16","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1016\/S0045-7825(99)00242-X","volume":"184","author":"PR Amestoy","year":"2000","unstructured":"Amestoy, P.R., Duff, I.S.: Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput. Methods Appl. Mech. Eng. 184, 501\u2013520 (2000)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"23","key":"14_CR17","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1137\/S0895479899358194","volume":"1","author":"PR Amestoy","year":"2001","unstructured":"Amestoy, P.R., Duff, I.S., Koster, J., L\u2019Excellent, J.Y.: A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 1(23), 15\u201341 (2001)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"32","key":"14_CR18","first-page":"136","volume":"2","author":"PR Amestoy","year":"2001","unstructured":"Amestoy, P.R., Guermouche, A., L\u2019Excellent, J.-Y., Pralet, S.: Hybrid scheduling for the parallel solution of linear systems. Comput. Methods Appl. Mech. Eng. 2(32), 136\u2013156 (2001)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"14_CR19","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1145\/1089014.1089017","volume":"31","author":"XS Li","year":"2005","unstructured":"Li, X.S.: An overview of SuperLU: algorithms, implementation, and user interface. TOMS Trans. Math. Softw. 31(3), 302\u2013325 (2005)","journal-title":"TOMS Trans. Math. Softw."},{"key":"14_CR20","doi-asserted-by":"crossref","unstructured":"Li, X.S., Demmel, J.W., Gilbert, J.R., Grigori, L., Shao, M., Yamazaki, I.: SuperLU Users\u2019 Guide, Lawrence Berkeley National Laboratory, LBNL-44289 (1999). http:\/\/crd.lbl.gov\/ xiaoye\/SuperLU\/","DOI":"10.2172\/751785"},{"issue":"2","key":"14_CR21","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/S0167-8191(01)00141-7","volume":"28","author":"P H\u00e9non","year":"2002","unstructured":"H\u00e9non, P., Ramet, P., Roman, J.: PaStiX: a high-performance parallel direct solver for sparse symmetric definite systems. Parallel Comput. 28(2), 301\u2013321 (2002)","journal-title":"Parallel Comput."},{"key":"14_CR22","unstructured":"Collier, N., Dalcin, L., Calo, V.M.: PetIGA: high-performance isogeometric analysis. arxiv:1305.4452 (2013)"},{"key":"14_CR23","doi-asserted-by":"publisher","first-page":"1832","DOI":"10.1016\/j.procs.2017.05.013","volume":"108C","author":"W Dzwinel","year":"2017","unstructured":"Dzwinel, W., K\u0142usek, A., Paszy\u0144ski, M.: A concept of a prognostic system for personalized anti-tumor therapy based on supermodeling. Procedia Comput. Sci. 108C, 1832\u20131841 (2017)","journal-title":"Procedia Comput. Sci."},{"key":"14_CR24","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1016\/j.procs.2016.05.396","volume":"80","author":"W Dzwinel","year":"2016","unstructured":"Dzwinel, W., K\u0142usek, A., Vasilyev, O.V.: Supermodeling in simulation of melanoma progression. Procedia Comput. Sci. 80, 999\u20131010 (2016)","journal-title":"Procedia Comput. Sci."},{"key":"14_CR25","unstructured":"Siwik, L., \u0141o\u015b, M., K\u0142usek, A., Dzwinel, W., Paszy\u0144ski, M., Pingali, K.: Supermodeling of tumor dynamics with parallel isogeometric analysis solver. arXiv:1912.12836"},{"key":"14_CR26","unstructured":"Schaefer, R., S\u0229dziwy, S.: Filtration in cohesive soils. Part II - Numerical approach, Computer Assisted Mechanics and Engineering Sciences (CAMES), vol. 6, pp. 15\u201326 (1999)"},{"key":"14_CR27","unstructured":"Schaefer, R., S\u0229dziwy, S.: Filtration in cohesive soils. Part I - The mathematical model, Computer Assisted Mechanics and Engineering Sciences (CAMES), vol. 6, pp. 1\u201313 (1999)"}],"container-title":["Lecture Notes in Computer Science","Computational Science \u2013 ICCS 2021"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-77980-1_14","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,8]],"date-time":"2025-06-08T22:03:07Z","timestamp":1749420187000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-77980-1_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030779795","9783030779801"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-77980-1_14","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"9 June 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Science","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Krakow","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 June 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 June 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iccs-computsci2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.iccs-meeting.org\/iccs2021\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"156","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"48","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"14","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"31% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.8","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.9","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"212 full and 43 short papers were selected from 479 submissions to the workshops\/ thematic tracks. The conference was held virtually.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}