Isogeometric analysis based on modified Loop subdivision surface with improved convergence rates

Abstract

This paper introduces a modified version of Loop subdivision, called modified Loop subdivision surface (MLSS), to improve the convergence rates in isogeometric analysis. Motivated by the control net of B-splines with non-repetitive end knots, the subdivision surface is parameterized on the non-boundary elements, where no special subdivision rules and evaluation needed for the boundaries. This idea together with the Nitsche’s method which is adopted for weakly imposing boundary conditions is used to solve the non-optimal convergence rate problem for extended Loop subdivision even without extraordinary points (EPs). For the EPs, we define a new rule with a parameter λ (0<λ<1.0), which is exactly the second maximum eigenvalue of the subdivision matrix. The MLSS is defined by combining the two ideas, which is global C2-continuous except G1 and curvature bounded around the EPs. The MLSS limit surface has comparable shape quality as Loop subdivision surface. Besides that, the numerical experiments show that MLSS can achieve the optimal convergence rate in the Poisson problem both in the L2 and H1 norm.