2016/06/09 by Gang Xu, Xu, Gang, Tsz-Ho Kwok +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Computer Graphics and Visualization Techniques #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1606.02959
openalex publication_date 2016/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with similar semantic features. Given a template domain, B-spline based consistent volumetric parameterization is first constructed for a set of models with similar semantic features. An efficient quadrature-free method is investigated in our framework to compute the entries of stiffness matrix by Bezier extraction and polynomial approximation. In our approach, evaluation on the stiffness matrix and imposition of the boundary conditions can be pre-computed and reused during IGA on a set of CAD models. Examples with complex geometry are presented to show the effectiveness of our methods, and efficiency similar to the computation in linear finite element analysis can be achieved for IGA taken on a set of models.