We present an efficient adaptive refinement procedure that preserves analysis-suitability of the T-mesh, this is, the linear independence of the T-spline blending functions. We prove analysis-suitability of the overlays and boundedness of their cardinalities, nestedness of the generated T-spline spaces, and linear computational complexity of the refinement procedure in terms of the number of marked and generated mesh elements.
@article{arxiv.1407.6175,
title = {Analysis-suitable adaptive T-mesh refinement with linear complexity},
author = {Philipp Morgenstern and Daniel Peterseim},
journal= {arXiv preprint arXiv:1407.6175},
year = {2016}
}
Comments
We now account for T-splines of arbitrary polynomial degree. We replaced the proof of Dual-Compatibility by a proof of Analysis-suitability, added a section where we address nestedness of the corresponding T-spline spaces, and removed the section on finite overlap the spline supports. 24 pages, 9 Figures