  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.
