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

## TL;DR

This paper introduces a generalized isogeometric analysis framework called GIFT that decouples geometry parameterization from solution approximation, enabling flexible, adaptive local refinement while maintaining exact CAD geometry.

## Contribution

It proposes a novel approach allowing different spaces for geometry and solution approximation, enhancing flexibility and local refinement without re-parameterizing the domain.

## Key findings

- Achieves optimal convergence rates with non-nested spaces.
- Maintains exact CAD geometry during analysis.
- Enables adaptive local refinement without weakening CAD link.

## Abstract

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), 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 re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces.