Journal
COMPUTER AIDED GEOMETRIC DESIGN
Volume 69, Issue -, Pages 55-75Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cagd.2019.01.002
Keywords
Isogeometric analysis; C-1 isogeometric space; Geometric continuity; Analysis-suitable G(1) parametrization; Planar multi-patch domain
Funding
- European Research Council through the FP7 Ideas Consolidator Grant HIGEOM [616563]
- Italian Ministry of Education, University and Research (MIUR) through the Dipartimenti di Eccellenza Program (2018-2022) - Dept. of Mathematics, University of Pavia
- Austrian Science Fund (FWF) [P 30926-NBL]
- government of Upper Austria [P 30926-NBL]
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Multi-patch spline parametrizations are used in geometric design and isogeometric analysis to represent complex domains. Typically, quadrilateral patches are adopted in both frameworks. We consider the particular class of multi-patch parametrizations that are analysis-suitable G(1) (AS-G(1)), which is a specific geometric continuity definition which allows to construct, on the multi-patch domain, C-1 isogeometric spaces with optimal approximation properties (cf. Collin et al., 2016). It was demonstrated in Kapl et al. (2018) that AS-G(1) multi-patch parametrizations are suitable for modeling complex planar multi-patch domains. We construct a local basis, and an associated dual basis, for a specific C-1 isogeometric spline space A over a given AS-G(1) multi-patch parametrization. The space A is C-1 across interfaces and C-2 at all vertices, and is therefore a subspace of the entire C-1 isogeometric space V-1. At the same time, A allows optimal approximation of traces and normal derivatives along the interfaces and reproduces all derivatives up to second order at the vertices. In contrast to V-1, the dimension of A does not depend on the domain parametrization. This paper also contains numerical experiments which exhibit the optimal approximation order in L-2 and L-infinity of the isogeometric space A and demonstrate the applicability of our approach for isogeometric analysis. (C) 2019 Elsevier B.V. All rights reserved.
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