Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 114, Issue 6, Pages 637-659Publisher
WILEY
DOI: 10.1002/nme.5759
Keywords
Bezier extraction; linear dependency; LR T-mesh; LR T-splines; partition of unity property
Funding
- ERC [664734]
- European Research Council (ERC) [664734] Funding Source: European Research Council (ERC)
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We extend Locally Refined (LR) B-splines to LR T-splines within the Bezier extraction framework. This discretization technique combines the advantages of T-splines to model the geometry of engineering objects exactly with the ability to flexibly carry out local mesh refinement. In contrast to LR B-splines, LR T-splines take a T-mesh as input instead of a tensor-product mesh. The LR T-mesh is defined, and examples are given how to construct it from an initial T-mesh by repeated meshline insertions. The properties of LR T-splines are investigated by exploiting the Bezier extraction operator, including the nested nature, linear independence, and the partition of unity property. A technique is presented to remove possible linear dependencies between LR T-splines. Like for other spline technologies, the Bezier extraction framework enables to fully use existing finite element data structures.
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