Unstructured spline spaces for isogeometric analysis based on spline manifolds

2015/07/30 by Sangalli, Giancarlo, Takacs, Thomas, Vázquez, Rafael
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1507.08477

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 h-refined meshes.

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