Locally Refined T‐splines

Abstract

SummaryWe extend Locally Refined (LR) B‐splines to LR T‐splines within the Bézier 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 Bézier 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 Bézier extraction framework enables to fully use existing finite element data structures.