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

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 Bezier 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 Bezier surface patches with Gk-continuity. Additionally, after subdivision, toric surface patches are compatible with CAD systems. Combining the subdivision algorithm with the classical knot insertion algorithm of nonuniform 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. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes an improved subdivision algorithm for toric surface patches that can divide an N-sided toric surface patch into rational tensor product Bézier surface patches while maintaining continuity. By combining it with the knot insertion algorithm of nonuniform rational B-splines, a novel h-refinement scheme for isogeometric analysis with planar toric parameterizations is developed.