h-Refinement method for toric parameterization of planar multi-sided computational domain in isogeometric analysis

Abstract

Toric surface patches are a class of multi-sided surface patches that can represent multi-sided domains without mesh degeneration. In this paper, we propose an improved subdivision algorithm for toric surface patches, which subdivides an N-sided toric surface patch into N rational tensor product Bézier surface patches. By the proposed subdivision algorithm, a C
^k-continuous spline surface composed of piecewise toric surface patches is subdivided into a set of rational tensor product Bézier surface patches with G
^k-continuity. Additionally, after subdivision, toric surface patches are compatible with CAD systems. Combining the subdivision algorithm with the classical knot insertion algorithm of non-uniform rational B-splines, we develop a novel h-refinement scheme for isogeometric analysis with planar toric parameterizations. Several numerical examples are given to demonstrate the effectiveness and numerical stability of the presented method.