| Title: | Isogeometric collocation with smooth mixed degree splines over planar multi-patch domains |
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| Authors: | ID Kapl, Mario (Author)
ID Kosmač, Aljaž (Author)
ID Vitrih, Vito (Author) |
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| Files: |  RAZ_Kapl_Mario_2026.pdf (4,88 MB)
MD5: 10B546795BF20865F41187D5C24433B2
 https://www.sciencedirect.com/science/article/pii/S0898122126000829
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
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| Abstract: | 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. |
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| Keywords: | isogeometric analysis, collocation, C^s-smoothness, mixed degree spline space, multi-patch surface |
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| Publication version: | Version of Record |
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| Publication date: | 04.03.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 89-112 |
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| Numbering: | Vol. 210 |
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| PID: | 20.500.12556/RUP-22715  |
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| UDC: | 004:51 |
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| ISSN on article: | 0898-1221 |
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| DOI: | 10.1016/j.camwa.2026.02.017 |
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| COBISS.SI-ID: | 270566147 |
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| Publication date in RUP: | 05.03.2026 |
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| Views: | 69 |
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| Downloads: | 2 |
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