Isogeometric collocation with smooth mixed degree splines over planar multi-patch domainsKapl, Mario (Avtor) Kosmač, Aljaž (Avtor) Vitrih, Vito (Avtor) isogeometric analysiscollocationC^s-smoothnessmixed degree spline spacemulti-patch surfaceWe 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.20262026-03-05 10:46:33Članek v reviji22715UDK: 004:51ISSN pri članku: 0898-1221DOI: 10.1016/j.camwa.2026.02.017COBISS.SI-ID: 270566147sl