Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

Abstract

This paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field. The method inherits the main advantage of isogeometric analysis, ie, preserves the original exact computer-aided design geometry (for example, given by nonuniform rational B-splines), but allows pairing it with an approximation space, which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain, and therefore without weakening the link with the computer-aided design model. We demonstrate the use of the method with different choices of geometry and field spaces and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for nonnested spaces.

What makes Data Science different? A discussion involving Statistics2.0 and Computational Sciences

“…Recourse is always made to some type of mathematical model, usually a set of partial differential equations (PDEs). The resulting problem is solved numerically using a wide variety of discretisation methods including finite element methods [22][23][24][25][26], finite differences, meshfree methods [27], isogeometric approaches [28,29], geometry independent field approximation [30,31], scaled-boundary finite elements [32][33][34][35][36], boundary element approaches [37], enriched boundary elements [38] or combinations thereof [39][40][41].…”

Isogeometric analysis of thin Reissner–Mindlin shells: locking phenomena and B-bar method

“…Note that, more recently, a generalisation of the isogeometric concept was proposed, whereby the geometry continues to be described by NURBS functions, as in the CAD, but the unknown field variables are allowed to live in different (spline) spaces. This lead to the concept of sub and super-geometric analysis, also known as Geometry Independent Field approximaTion (GIFT), described within a boundary element framework in [4] and proposed in [5,6] and later refined in [7]. Related ideas, aiming at the construction of tailored spline spaces for local refinement were proposed recently in [8].…”

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

“…Special parameterization techniques, such as variational harmonic-based methods [29,30] and analysis-aware parameterization methods for single [31] and multi-domain geometries [32], have been proposed for the computational domain. Alternatives to NURBS, such as T-splines [33,34], polynomial splines over hierarchical T-meshes (PHT-splines) [35][36][37], and Powell-Sabin splines [38], have been studied for local refinement in IGA due to the limitation of the tensor product form of NURBS in computation refinement. Methods of parameterization of the interior domain while retaining the geometry exactness from the CAD model have been devised [39,40], and isogeometric collocation method is one of the most important among these methods [39].…”