Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis

• DOI: 10.1016/j.cma.2018.07.013
• Publication Date: 2018-07-17T18:10:13Z
• Authors: Xiaodong Wei; Yongjie Jessica Z...; Deepesh Toshniwal; Hendrik Speleers; Xin Li; Carla Manni; John A. Evans; Thomas J.R. Hughes
• Keywords: Isogeometric analysis; Quadrilateral; Partition of unity; Hexahedron; Spline (mechanical); B-spline

Abstract We present a novel blended B-spline method to construct bicubic/tricubic splines over unstructured quadrilateral and hexahedral meshes for isogeometric analysis. C 1 and (truncated) C 2 B-spline functions are used in regular elements, whereas C 0 and (truncated) C 1 B-spline functions are adopted in boundary elements and interior irregular elements around extraordinary edges/vertices. The truncation mechanism is employed for a seamless transition from irregular to regular elements. The resulting smoothness of the blended construction is C 2 -continuous everywhere except C 0 -continuous around extraordinary edges and C 1 -continuous across the interface between irregular and regular elements. The blended B-spline construction yields consistent parameterization during refinement and exhibits optimal convergence rates. Spline functions in the blended construction form a non-negative partition of unity , are linearly independent, and support Bezier extraction such that the construction can be used in existing finite element frameworks. Several examples provide numerical evidence of optimal convergence rates.