Unstructured spline spaces for isogeometric analysis based on spline manifolds
Abstract
Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces that have a tensor-product structure locally, but not globally. This includes configurations such as B-splines over multi-patch domains with extraordinary points, analysis-suitable unstructured T-splines, or more general constructions. Within this framework, we generalize the concept of dual-compatible B-splines, which was originally developed for structured T-splines. This allows us to prove the key properties that are needed for isogeometric analysis, such as linear independence and optimal approximation properties for -refined meshes.
Cite
@article{arxiv.1507.08477,
title = {Unstructured spline spaces for isogeometric analysis based on spline manifolds},
author = {Giancarlo Sangalli and Thomas Takacs and Rafael Vázquez},
journal= {arXiv preprint arXiv:1507.08477},
year = {2015}
}