Isogeometric representation is an attempt to bridge the gap between CAD and analysis and harmonize the technology and approaches of CAD and FEA.

In CAD context shapes are represented by curve structures, surface structures and volumes described by their inner and outer hulls. Curves are either represented by degree 1 and 2 analytical curves or parametric piecewise polynomials represented as NonUniform Rational B-splines (NURBS). Similarly surfaces are represented as degree 1 or 2 analytical surfaces or piecewise polynomials described by NURBS, or trimmed versions thereof. Volumes are described by their inner and outer hulls, where each hull is described by a patchwork of surfaces. Geometrically the different surfaces do not necessarily match exactly, and thus the representation is not watertight.

In FEA, the shape is represented by structures of finite elements, where each element is a trivariate parametric polynomial, typically of degrees two or lower, but higher degree elements are also used. Compared to CAD representation the outer surface quality in FEA is (in most cases) of lower shape quality, but the models are geometrically watertight (no gaps between elements).

The isogeometric shape representation is a block structured model which consists of a set of non-trimmed NURBS surfaces or volumes depending on the dimension of the problem. Thus a solid model has got a trivariate representation. The blocks meet with exact continuity, and the parametrization of each entity is adapted for the purpose of analysis.

The process contains the following steps:

• Quality control of the CAD model
• Repair the model with emphasis on quality problems that are particularily severe in a numerical analysis context
• Investigate the structure of the model to define the block structuring of the corresponding isogeometric model
• Define the geometry of each surface or volume block. The blocks meet with C⁰ continuity and the outer boundaries of the block structured model adapt to the shape described by the CAD model.

The model is now ready for adding analysis specific information like boundary conditions and properties and define the spline space of the solution as refined version of the spline space related to the geometry blocks. Furthermore, the outer boundary of the isogeometric model can be extracted and represented as a CAD model.