The Argyris isogeometric space on unstructured multi-patch planar domains
Mario Kapl, Giancarlo Sangalli, Thomas Takacs

TL;DR
This paper introduces the Argyris isogeometric space on unstructured multi-patch planar domains, providing a basis with explicit local support that achieves optimal approximation and extends Argyris finite element ideas to isogeometric analysis.
Contribution
It constructs a new $C^1$ isogeometric spline space called the Argyris space with explicit basis and dual basis on AS-$G^1$ multi-patch domains, independent of parametrization.
Findings
The Argyris space achieves optimal approximation order.
The basis has explicit, simple, and local support representations.
Numerical experiments confirm the space's effectiveness for isogeometric analysis.
Abstract
Multi-patch spline parametrizations are used in geometric design and isogeometric analysis to represent complex domains. We deal with a particular class of planar multi-patch spline parametrizations called analysis-suitable (AS-) multi-patch parametrizations (Collin, Sangalli, Takacs; CAGD, 2016). This class of parametrizations has to satisfy specific geometric continuity constraints, and is of importance since it allows to construct, on the multi-patch domain, isogeometric spaces with optimal approximation properties. It was demonstrated in (Kapl, Sangalli, Takacs; CAD, 2018) that AS- multi-patch parametrizations are suitable for modeling complex planar multi-patch domains. In this work, we construct a basis, and an associated dual basis, for a specific isogeometric spline space over a given AS- multi-patch parametrization. We…
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques
