Improved local refinement for S-splines-based isogeometric analysis

Abstract

S-splines (Simple splines) is a generalization of T-splines that solves the problem of additional control points propagation in T-spline’s local refinement algorithm. However, when applying S-splines to isogeometric analysis (IGA), the existing local refinement algorithm for S-splines can result in a matrix with an extremely large condition number. This paper provides a solution to this problem by introducing an improved local refinement algorithm. The improvement is achieved through an optimized postprocessing process for decomposing the blending functions before insertion. We also prove that the improved local refinement algorithm can preserve the linear independence of blending functions, the partition of unity, and create nested spline spaces during local refinement. Numerical experiments show that the resulting S-splines require fewer degrees of freedom than T-splines and analysis-suitable T-splines under the same error. Additionally, the condition numbers of the matrices are much smaller than those with the original S-splines local refinement algorithm.