Isogeometric Analysis Using Basis Functions of Splines Spaces over Hierarchical T-meshes with High Level Differences

Abstract

By using the method of space mapping, basis functions of biquadratic polynomial spline spaces over the hierarchical T-meshes without limitation for level difference can be constructed. In this paper, the basis functions defined over hierarchical T-meshes with high level differences are adopted for the application in the isogeometric analysis problems with rapidly changing local features. Without subdividing redundant cells to ensure the level difference of the adjacent cells, the refinement becomes more local, and fewer cells are subdivided for each refinement of the hierarchical T-mesh. Therefore, the dimension of the biquadratic polynomial spline space over the hierarchical T-mesh can be reduced, the superfluous control points or coefficients can be avoided, and the quantity of calculations can be decreased. Numerical examples show that these basis functions can work well on physical domains with different boundaries for the application in IGA.

Keywords

Spline spaces over hierarchical T-meshes / Space mapping / Basis functions / Isogeometric analysis

Funding

national natural science foundation of china(11771420)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature