| Title: | An Isogeometric Tearing and Interconnecting (IETI) method for solving high order partial differential equations over planar multi-patch geometries |
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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 (6,42 MB)
MD5: 46AF442F3E0B6494E7025BFD30D857A5
 https://www.sciencedirect.com/science/article/pii/S0045782526000435
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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
IAM - Andrej Marušič Institute
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| Abstract: | We present a novel method for solving high-order partial differential equations (PDEs) over planar multi-patch geometries with
possibly extraordinary vertices demonstrated on the basis of the polyharmonic equation of order m, m ≥ 1, which is a particular linear elliptic PDE of order 2m. Our approach is based on the concept of Isogeometric Tearing and Interconnecting (IETI) and allows to couple the numerical solution of the PDE with Cs-smoothness, , across the edges of the multi-patch geometry. The proposed technique relies on the use of a particular class of multi-patch geometries, called bilinear-like Gs multi-patch parameterizations, to represent the multi-patch domain. The coupling between the neighboring patches is done via the use of Lagrange multipliers and leads to a saddle point problem, which can be solved first by a small dual problem for a subset of the Lagrange multipliers followed by local, parallelizable problems on the single patches for the coefficients of the numerical solution. Several numerical examples for the polyharmonic equation of order m = 1, m = 2 and m = 3, i.e. for the Poisson’s, the biharmonic and the triharmonic equation, respectively, are shown to demonstrate the potential of our IETI method for solving high-order problems over planar multi-patch geometries with possibly extraordinary vertices.
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| Keywords: | isogeometric analysis, Galerkin method, C^s-smoothness, Tearing and Interconnecting, multi-patch domain, polyharmonic equation |
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| Publication version: | Version of Record |
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| Publication date: | 27.01.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 1-23 |
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| Numbering: | Vol. 452, pt. B, article 118769 |
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| PID: | 20.500.12556/RUP-22589  |
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| UDC: | 51 |
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| ISSN on article: | 0045-7825 |
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| DOI: | 10.1016/j.cma.2026.118769 |
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| COBISS.SI-ID: | 266901251 |
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| Publication date in RUP: | 02.02.2026 |
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| Views: | 46 |
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| Downloads: | 4 |
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