Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 24, Issue 6, Pages 1141-1164Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202513500796
Keywords
T-splines; isogeometric analysis; local refinement; analysis-suitable; approximation
Categories
Funding
- NSF of China [11031007, 60903148]
- Chinese Universities Scientific Fund, SRF for ROCS SE
- Chinese Academy of Science (Startup Scientific Research Foundation)
- ICES CAM Graduate Fellowship
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We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended T-mesh of an analysis-suitable T-spline, is contained in the corresponding analysis-suitable T-spline space. This is accomplished through the theory of perturbed analysis-suitable T-spline spaces and a simple topological dimension formula. Second, we establish the theory of analysis-suitable local refinement and describe the conditions under which two analysis-suitable T-spline spaces are nested. Last, we demonstrate that these results can be used to establish basic approximation results which are critical for analysis.
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