Isogeometric Discretization Techniques

Isogeometric analysis (IGA) was proposed by Hughes and coworkers in 2005. Its main original purpose was to bridge the gap between computer aided design and finite element analysis, thus simplifying the cost-intensive mesh generation process required for standard finite elements and leading to a tighter integration of design and analysis tools. In the IGA framework, the same smooth and higher-order basis functions, e.g., non-uniform rational B-splines (NURBS) or T-splines, are used for the representation of the exact design geometry and for the approximation of the finite element solution fields. In addition to the achievement of the original goal, IGA soon turned out to exhibit increased accuracy and robustness on a per-degree-of-freedom basis in comparison to standard finite element methods and to possess a number of additional attractive features in several areas of computational mechanics.