Towards novel refinement strategies for isogeometric analysis

Hugo Verhelst (DICAR Unipv)

Abstract. Introduced in 2005 [1], the concept of Isogeometric Analysis (IGA) is to bridge the gap between Computer-Aided Design (CAD) and Finite Element Analysis (FEA) by using splines as a common basis for design and analysis. Even though, two decades later, the seamless interaction between CAD and FEA seems to be beneficial only for simple geometries, IGA has shown its benefits primarily in the context of higher-order continuity, which is useful for higher-order equations such as the Kirchhoff–Love shell model [2], or the Cahn–Hilliard equation [3]. In addition, IGA brought researchers in CAD and FEA closer together, yielding several new points of view in the world of computational mechanics.
In this talk, I will present ongoing work on the development of adaptive spline methods for IGA. On the one hand, it focuses on two crucial aspects on the geometry side: i) investigation of anisotropic spline constructions, and, ii) relocation-based adaptivity for IGA. On the other hand, I elaborate on two possible applications of the developed geometric methods: I) phase-field computations, and, II) space-time simulations. The work is a result of ongoing collaborations with the Department of Mathematics and Computer Science (DIMAI) at the University of Florence, the Department of Civil Engineering and Architecture (DiCAr) of the University of Pavia and the Delft Institute of Applied Mathematics (DIAM) at TU Delft.
[1] Hughes, Thomas JR, John A. Cottrell, and Yuri Bazilevs. “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement.” Computer methods in applied mechanics and engineering 194.39-41 (2005): 4135-4195.
[2] Kiendl, Josef, et al. “Isogeometric shell analysis with Kirchhoff–Love elements.” Computer methods in applied mechanics and engineering 198.49-52 (2009): 3902-3914.
[3] Gómez, Héctor, et al. “Isogeometric analysis of the Cahn–Hilliard phase-field model.” Computer methods in applied mechanics and engineering 197.49-50 (2008): 4333-4352.