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Mathematics > Numerical Analysis

arXiv:2308.09007 (math)
[Submitted on 17 Aug 2023 (v1), last revised 22 Dec 2023 (this version, v2)]

Title:A locally based construction of analysis-suitable $G^1$ multi-patch spline surfaces

Authors:Andrea Farahat, Mario Kapl, Aljaž Kosmač, Vito Vitrih
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Abstract:Analysis-suitable $G^1$ (AS-$G^1$) multi-patch spline surfaces [4] are particular $G^1$-smooth multi-patch spline surfaces, which are needed to ensure the construction of $C^1$-smooth multi-patch spline spaces with optimal polynomial reproduction properties [16]. We present a novel local approach for the design of AS-$G^1$ multi-patch spline surfaces, which is based on the use of Lagrange multipliers. The presented method is simple and generates an AS-$G^1$ multi-patch spline surface by approximating a given $G^1$-smooth but non-AS-$G^1$ multi-patch surface. Several numerical examples demonstrate the potential of the proposed technique for the construction of AS-$G^1$ multi-patch spline surfaces and show that these surfaces are especially suited for applications in isogeometric analysis by solving the biharmonic problem, a particular fourth order partial differential equation, with optimal rates of convergence over them.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2308.09007 [math.NA]
  (or arXiv:2308.09007v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2308.09007

Submission history

From: Vito Vitrih [view email]
[v1] Thu, 17 Aug 2023 14:22:36 UTC (9,334 KB)
[v2] Fri, 22 Dec 2023 15:43:11 UTC (9,870 KB)
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