{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T03:32:51Z","timestamp":1777865571618,"version":"3.51.4"},"publisher-location":"Cham","reference-count":18,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031976285","type":"print"},{"value":"9783031976292","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\/978-3-031-97629-2_17","type":"book-chapter","created":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T06:30:49Z","timestamp":1751610649000},"page":"237-248","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Using B-Spline Function Properties in\u00a0the\u00a0PIES Method to\u00a0Handle Singularities in\u00a0Boundary Value Problems"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4761-1170","authenticated-orcid":false,"given":"Agnieszka","family":"Bo\u0142tu\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6395-5096","authenticated-orcid":false,"given":"Eugeniusz","family":"Zieniuk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,7,5]]},"reference":[{"issue":"9","key":"17_CR1","doi-asserted-by":"publisher","first-page":"2301","DOI":"10.1016\/S0020-7683(03)00050-7","volume":"40","author":"E Zieniuk","year":"2003","unstructured":"Zieniuk, E.: B\u00e9zier curves in the modification of boundary integral equations (BIE) for potential boundary-values problems. Int. J. Solids Struct. 40(9), 2301\u20132320 (2003)","journal-title":"Int. J. Solids Struct."},{"issue":"3","key":"17_CR2","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1142\/S0218396X06003098","volume":"14","author":"E Zieniuk","year":"2006","unstructured":"Zieniuk, E., Boltuc, A.: B\u00e9zier curves in the modeling of boundary geometry for 2D boundary problems defined by Helmholtz equation. J. Comput. Acoust. 14(3), 353\u2013367 (2006)","journal-title":"J. Comput. Acoust."},{"issue":"25\u201326","key":"17_CR3","doi-asserted-by":"publisher","first-page":"7939","DOI":"10.1016\/j.ijsolstr.2006.04.008","volume":"43","author":"E Zieniuk","year":"2006","unstructured":"Zieniuk, E., Boltuc, A.: Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation. Int. J. Solids Struct. 43(25\u201326), 7939\u20137958 (2006)","journal-title":"Int. J. Solids Struct."},{"key":"17_CR4","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.enganabound.2016.04.009","volume":"69","author":"A Bo\u0142tu\u0107","year":"2016","unstructured":"Bo\u0142tu\u0107, A.: Parametric integral equation system (PIES) for 2D elastoplastic analysis. Eng. Anal. Boundary Elem. 69, 21\u201331 (2016)","journal-title":"Eng. Anal. Boundary Elem."},{"key":"17_CR5","volume-title":"The Finite Element Methods","author":"OC Zienkiewicz","year":"1977","unstructured":"Zienkiewicz, O.C.: The Finite Element Methods. McGraw-Hill, London (1977)"},{"key":"17_CR6","volume-title":"The Finite Element Method: A Practical Course","author":"GR Liu","year":"2003","unstructured":"Liu, G.R., Quek, S.S.: The Finite Element Method: A Practical Course. Butterworth Heinemann, Oxford (2003)"},{"key":"17_CR7","volume-title":"Computational elasticity","author":"M Ameen","year":"2005","unstructured":"Ameen, M.: Computational elasticity. Alpha Science International Ltd, Harrow (2005)"},{"key":"17_CR8","unstructured":"Aliabadi, M.H.: The Boundary Element Method, vol. 2. Applications in Solids and Structures. Wiley, Chichester (2002)"},{"key":"17_CR9","volume-title":"Boundary Element Programming in Mechanics","author":"XW Gao","year":"2002","unstructured":"Gao, X.W., Davies, T.G.: Boundary Element Programming in Mechanics. Cambridge University Press, Cambridge (2002)"},{"key":"17_CR10","volume-title":"Curves and surfaces for CAGD: A practical Guide","author":"G Farin","year":"2002","unstructured":"Farin, G.: Curves and surfaces for CAGD: A practical Guide. Morgan Kaufmann Publishers, San Francisco (2002)"},{"key":"17_CR11","volume-title":"Curves and Surfaces for Computer Graphics","author":"D Salomon","year":"2006","unstructured":"Salomon, D.: Curves and Surfaces for Computer Graphics. Springer, New York (2006)"},{"key":"17_CR12","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.matcom.2018.11.002","volume":"164","author":"H Idais","year":"2019","unstructured":"Idais, H., Yasin, M., Pasadas, M., Gonz\u00e1lez, P.: Optimal knots allocation in the cubic and bicubic spline interpolation problems. Math. Comput. Simul. 164, 131\u2013145 (2019)","journal-title":"Math. Comput. Simul."},{"key":"17_CR13","doi-asserted-by":"publisher","DOI":"10.1002\/9780470749081","volume-title":"Isogeometric Analysis: Toward Integration of CAD and FEA","author":"JA Cottrell","year":"2009","unstructured":"Cottrell, J.A., Hughes, T., Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Hoboken (2009)"},{"key":"17_CR14","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.cma.2011.08.008","volume":"209\u2013212","author":"RN Simpson","year":"2012","unstructured":"Simpson, R.N., Bordas, S., Trevelyan, J., Rabczuk, T.: A two-dimensional isogeometric boundary element method for elastostatic analysis. Comput. Methods Appl. Mech. Eng. 209\u2013212, 87\u2013100 (2012)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"17_CR15","doi-asserted-by":"publisher","DOI":"10.1201\/9781420082104","volume-title":"Meshfree Methods: Moving Beyond The Finite Element Method","author":"GR Liu","year":"2009","unstructured":"Liu, G.R.: Meshfree Methods: Moving Beyond The Finite Element Method. CRC Press, Boca Raton (2009)"},{"key":"17_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59223-2","volume-title":"The NURBS Book","author":"L Piegl","year":"1997","unstructured":"Piegl, L., Tiller, W.: The NURBS Book. Springer, Germany (1997)"},{"key":"17_CR17","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970425","volume-title":"Numerical Analysis of Spectral Methods","author":"D Gottlieb","year":"1977","unstructured":"Gottlieb, D., Orszag, S.A.: Numerical Analysis of Spectral Methods. SIAM, Philadelphia (1977)"},{"key":"17_CR18","volume-title":"Theory of Elasticity","author":"SP Timoshenko","year":"1970","unstructured":"Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity. McGraw-Hill, Tokyo (1970)"}],"container-title":["Lecture Notes in Computer Science","Computational Science \u2013 ICCS 2025"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-97629-2_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T06:53:23Z","timestamp":1777532003000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-97629-2_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031976285","9783031976292"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-97629-2_17","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":"5 July 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"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":"Singapore","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Singapore","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 July 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 July 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iccs-computsci2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.iccs-meeting.org\/iccs2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}