Isogeometric analysis based on extended Loop's subdivision

Abstract

In this paper, we present a new approach of isogeometric analysis (IGA) based on the extended Loop's subdivision scheme. This strategy allows us to integrate geometric modeling and physical simulation. The geometries can be open and with holes. Our proposed method performs geometric modeling via the extended Loop's subdivision which allows arbitrary topological structure, treats concave/convex vertices, and has at least C1-continuity everywhere. It is capable of handling domains with arbitrary shaped boundary represented by piecewise cubic B-spline curves. We apply an efficient integration technique to the domain elements with a fast evaluation technique for closed Loop's subdivision surfaces. As an example, the Poisson equation is solved on three planar domains. We develop the approximate estimation of finite element in the limit function space of the extended Loop's subdivision. A detailed study on the convergence character is given with the comparison to the classical finite element analysis (FEA) with linear elements. Numerical experiments are consistent with our theoretical results. It shows that compared with the FEA with linear elements, the IGA scheme based on extended Loop's subdivision converges faster and behaves more robustly with respect to the mesh quality.