Isogeometric Analysis: high-order numerical solution of PDEs and computational challenges

Abstract: 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.
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).

numerical analysis

Audience: researchers in the topic

Seminars on Numerics and Applications