Automatic Handling of C 0 - G 0 Continuous Rational Bézier Elements Produced from T-Splines Through Bézier Extraction

Christopher Provatidis () and Ioannis Dimitriou
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Christopher Provatidis: School of Mechanical Engineering, National Technical University of Athens, 15780 Zografou, Greece
Ioannis Dimitriou: Department of Mechanical Design and Control Systems, National Technical University of Athens, 15780 Zografou, Greece

Mathematics, 2025, vol. 13, issue 3, 1-29

Abstract: This paper shows that at a certain time-point in the analysis procedure, the accuracy of T-spline based isogeometric analysis (IGA) may be substantially improved by increasing the multiplicity of the inner knots up to the polynomial degree. This task can be performed by considering the Bézier extraction operator matrix elementwise, and thus an increased number of updated control points are easily received in the geometrical and computational models. Nevertheless, after the determination of the unique control points, the Bézier elements near the T-junctions may not be well shaped, and thus minor automatic interventions are required to ensure full (i.e., C 0 and G 0 ) compatibility. The improved IGA-based solution may be used as a reference to determine the a posteriori error estimations in the T-spline elements of the domain, and thus may be a useful tool for IGA adaptation. The methodology is shown in BVPs dominated by Laplace–Poisson equations in rectangular and curvilinear domains, while eigenvalues and eigenvectors were extracted in a rectangular acoustic cavity.

Keywords: isogeometric analysis; T-splines; Bézier extraction operator; C 0 - G 0 continuity; potential problems; Laplace equation; eigenvalue problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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