Analysis-suitable adaptive T-mesh refinement with linear complexity
Philipp Morgenstern, Daniel Peterseim
TL;DR
This paper introduces an efficient adaptive T-mesh refinement method that maintains analysis-suitability, ensuring linear independence of T-spline functions with linear computational complexity, suitable for isogeometric analysis.
Contribution
It proposes a novel adaptive refinement procedure for T-meshes that guarantees analysis-suitability and linear complexity, improving computational efficiency and stability.
Findings
Analysis-suitability of overlays proven
Boundedness of overlay cardinalities established
Refinement procedure has linear computational complexity
Abstract
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.
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