20.500.12556/RUP-22715 Isogeometric collocation with smooth mixed degree splines over planar multi-patch domains We present a novel isogeometric collocation method for solving the Poisson’s and the biharmonic equation over planar bilinearly parameterized multi-patch geometries. The proposed approach relies on the use of a modified construction of the Cs-smooth mixed degree isogeometric spline space [1] for s=2 and s=4 in case of the Poisson’s and the biharmonic equation, respectively. The adapted spline space possesses the minimal possible degree p=s+1 everywhere on the multi-patch domain except in a small neighborhood of the inner edges and of the vertices of patch valency greater than one where a degree p=2s+1 is required. This allows to solve the PDEs with a much lower number of degrees of freedom compared to employing the Cs-smooth spline space [2] with the same high degree p=2s+1 everywhere. To perform isogeometric collocation with the smooth mixed degree spline functions, we introduce and study two different sets of collocation points, namely first a generalization of the standard Grevile points to the set of mixed degree Greville points and second the so-called mixed degree superconvergent points. The collocation method is further extended to the class of bilinear-like Gs multi-patch parameterizations [3], which enables the modeling of multi-patch domains with curved boundaries, and is finally tested on the basis of several numerical examples. isogeometric analysis collocation C^s-smoothness mixed degree spline space multi-patch surface izogeometrična analiza kolokacija C^s-gladkost prostori zlepkov mešanih stopenj večdelne domene true false true Angleški jezik Slovenski jezik Članek v reviji 2026-03-05 10:46:33 2026-03-05 10:46:36 2026-03-07 03:05:20 0000-00-00 00:00:00 2026 0 0 str. 89-112 Vol. 210 15 May 2026 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2026-03-04 004:51 0898-1221 10.1016/j.camwa.2026.02.017 270566147 RAZ_Kapl_Mario_2026.pdf RAZ_Kapl_Mario_2026.pdf 1 10B546795BF20865F41187D5C24433B2 5534abf092a83dc86206589ad275abd2b3ffd7b8dbda7e04a89e20f431afee02 6f02a97f-1878-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33082 https://www.sciencedirect.com/science/article/pii/S0898122126000829 1 33abc870-1878-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33081 Fakulteta za matematiko, naravoslovje in informacijske tehnologije 0 0 0