# Computationally efficient Isogeometric Analysis

## Prof. Giancarlo Sangalli

**July 13, 2018, 1:45 p.m. S2 416-2**

The concept of k-refinement was proposed as one of the key features of isogeometric analysis, ”a new, more efficient, higher-order concept”, in the seminal work [1]. The idea of using high-degree and continuity splines (or NURBS, etc.) as a basis for a new high-order method appeared very promising from the beginning, and received confirmations from the next developments. The k-refinement leads to several advantages: higher accuracy per degree-of-freedom, improved spectral accuracy, the possibility of structure-preserving smooth discretizations are the most interesting features that have been studied actively in the community. At the same time, the k-refinement brings significant challenges at the computational level: using standard finite element routines, its computational cost grows with respect to the degree, making degree raising computationally expensive. However, recent ideas allow a computationally efficient k-refinement: I present in this talk the results of [2] and the more recent work-in-progress.

References

[1] T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., Vol. 194, pp. 4135-4195 (2005).

[2] G. Sangalli and M. Tani, Matrix-free isogeometric analysis: the computationally efficient k-method, arXiv preprint arXiv:1712.08565, pp. 1–21 (2017); Comput. Methods Appl. Mech. Engrg., to appear.