BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giancarlo Sangalli (University of Pavia) DTSTART:20210309T060000Z DTEND:20210309T070000Z DTSTAMP:20260423T052641Z UID:CMWebinar/5 DESCRIPTION:Title: Isogeometric Analysis: a high-order method for PDEs\nby Giancarlo Sa ngalli (University of Pavia) as part of Australian Seminar on Computationa l Mathematics\n\n\nAbstract\nIsogeometric Analysis was proposed in the sem inal work of Hughes\, Cottrell\, and Bazilevs in 2005\, and be seen as a g eneralisation of the finite element\nmethod that replaces classical $C^0$ finite elements with smooth\nsplines. Doing so\, IGA aims to be easily co mpatible with\ncomputer-aided geometric design systems\, where smooth spl ines are used\nto create computational geometric models. In this framework \, \nthere has been a successful creation of novel\, robust\, high-order\n accurate numerical methods for solving PDEs.\n\nThe concept of k-refinemen t (or K-method) was proposed as one of\nthe key features of isogeometric analysis\, "a new\, more efficient\,\nhigher-order concept"\, in the origi nal isogeometric article by Hughes and co-workers. The idea of using high- degree\nand continuity splines (or NURBS\, etc.) as a basis for a new\nhig h-order method appeared very promising from the beginning. The\nk-refineme nt leads to several advantages: higher accuracy per\ndegree-of-freedom\, i mproved spectral accuracy\, the possibility of\nstructure-preserving smoot h discretizations are the most interesting\nfeatures that have been studie d actively in the community. At the same\ntime\, the k-refinement brings s ignificant challenges at the\ncomputational level: using standard finite e lement routines\, its\ncomputational cost grows with respect to the degree \, making degree\nraising computationally expensive. After a brief introdu ction of\nIsogeometric Analysis\, I will discuss ideas from\n[Sangalli a nd Tani\, CMAME\, 2018\, arXiv:1712.08565] and following works\, that allo w a computationally\nefficient k-refinement.\n LOCATION:https://researchseminars.org/talk/CMWebinar/5/ END:VEVENT END:VCALENDAR