Globally structured 3D Analysis-suitable T-splines: definition, linear independence and m-graded local refinement

Abstract

This paper addresses the linear independence of T-splines that correspond to refinements of three-dimensional tensor-product meshes. We give an abstract definition of analysis-suitability, and prove that it is equivalent to dual-compatibility, wich guarantees linear independence of the T-spline blending functions. In addition, we present a local refinement algorithm that generates analysis-suitable meshes and has linear computational complexity in terms of the number of marked and generated mesh elements.

24 pages, 14 figures. Minor typos corrected and title changed. arXiv admin note: text overlap with arXiv:1407.6175

References in corpus (3)

• Axioms of Adaptivity
• Hierarchical analysis-suitable T-splines: Formulation, Bézier extraction, and application as an adaptive basis for isogeometric analysis
• Analysis-suitable adaptive T-mesh refinement with linear complexity

Cited by in corpus (6)

• Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison
• Mathematical foundations of adaptive isogeometric analysis
• Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
• BPX preconditioners for isogeometric analysis using analysis-suitable T-splines
• Optimal convergence rates for goal-oriented FEM with quadratic goal functional
• Adaptive IGAFEM with optimal convergence rates: T-splines