Isogeometric analysis using a tensor product blending spline construction

Abstract

In this paper, we introduce a blending spline type construction into the isogeometric analysis. We consider a general algorithm for solving a number of boundary value problems, including heat equation, wave equation, linear elasticity, etc. The usage of blending spline construction in the isogeometric context mixes standard finite element and NURBS-based approaches while accumulating the benefits of both. Since the blending spline construction is locally represented, the finite element discretization can be formulated in a standard way, while the smooth representation of these splines provides an accurate approximation of the computational domain even on a coarse mesh. Besides the standard L ² -projection algorithm for the domain approximation, we demonstrate a unique scheme for domain construction based on local surfaces and subsequent hp-refinement. In the proposed paper we focus on the features of blending splines in the isogeometric analysis context, identify possible applications, and provide some numerical analysis.