Isogeometric Analysis on Implicit Domains: Approximation, Stability and Error Estimates

Abstract

The gap between finite element analysis and computer-aided design derives the development of isogeometric analysis (IGA), which uses the same representation in the geometry and the analysis. However, the parameterization in IGA is non-trivial. Weighted extended B-splines (WEB) method replaces grid generation and parameterization with weight function construction (R-function or distance function). By using implicit spline representation, isogeometric analysis on implicit domains (IGAID) adopts the merits of the “isoparametric” in IGA and “weight function generation” in WEB. But the theoretical properties have not been fully studied yet. In this paper, we study the theoretical aspects of IGAID using tensor-product B-splines. Both the approximation and stability properties of IGAID are considered. By setting appropriate constraints on the weight function, we can derive the optimal approximation order and stability. Numerical examples show the effectiveness of the approach and validate the theoretical results.

Keywords

Isogeometric analysis / WEB method / Implicit domain / Weight function / Error estimates

Funding

National Natural Science Foundation of China(12171453)