20.500.12556/RUP-22589 An Isogeometric Tearing and Interconnecting (IETI) method for solving high order partial differential equations over planar multi-patch geometries 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. isogeometric analysis Galerkin method C^s-smoothness Tearing and Interconnecting multi-patch domain polyharmonic equation izogeometrična analiza Galerkinova metoda C^s-gladkost Tearing and Interconnecting večdelna domena poliharmonična enačba true false true Angleški jezik Slovenski jezik Članek v reviji 2026-02-02 08:25:02 2026-02-02 08:25:05 2026-02-03 03:05:21 0000-00-00 00:00:00 2026 0 0 str. 1-23 article 118769 Vol. 452, pt. B 15 Apr. 2026 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2026-01-27 51 0045-7825 10.1016/j.cma.2026.118769 266901251 RAZ_Kapl_Mario_2026.pdf RAZ_Kapl_Mario_2026.pdf 1 46AF442F3E0B6494E7025BFD30D857A5 de41e74f05ffd69fd7425aa47d5bf6cbb1fcd63b451f54eb1d4a6393cc6996dd 8734a497-0008-11f1-b092-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32865 https://www.sciencedirect.com/science/article/pii/S0045782526000435 1 54424e12-0008-11f1-b092-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32864 Fakulteta za matematiko, naravoslovje in informacijske tehnologije Inštitut Andrej Marušič 0 0 0