Isogeometric Analysis (IGA)

Isogeometric analysis (IGA) was introduced by Professor Thomas J. R. Hughes and co-workers at University of Texas at Austin in 2005 as an innovative numerical methodology for the discretization of Partial Differential Equations (PDEs). The main idea was to improve the interoperability between design, i.e., Computer Aided Design (CAD) and analysis, i.e., Finite Element Method (FEM). To achieve this, Hughes and co-workers proposed to use CAD mathematical primitives, i.e., splines and NURBS, to represent both the finite element (FE) geometry as well as the PDE unknowns.  In this manner one may represent the geometry in the FE-analysis exactly similar to the designed geometry. Furthermore, the smoothness of splines is useful in improving the accuracy per degree of freedom and solving higher order PDEs via direct approximations.