GLOBALLY STRUCTURED THREE-DIMENSIONAL ANALYSIS-SUITABLE T-SPLINES: DEFINITION, LINEAR INDEPENDENCE AND m-GRADED LOCAL REFINEMENT

This paper addresses the linear independence of T-splines that correspond to refinements of three-dimensional tensor-product meshes. We give an abstract definition of analysis-suitability and prove that it is equivalent to dual-compatibility, which guarantees linear independence of the T-spline blending functions. In addition, we present a local refinement algorithm that generates analysis-suitable meshes and has linear computational complexity in terms of the number of marked and generated mesh elements.