Isogeometric analysis: Mathematical and implementational aspects, with applications

Isogeometric analysis (IGA) is a recent and successful extension of classical finite element analysis. IGA adopts smooth splines, NURBS and generalizations to approximate problem unknowns, in order to simplify the interaction with computer aided geometric design (CAGD). The same functions are used to parametrize the geometry of interest. Important features emerge from the use of smooth approximations of the unknown fields. When a careful implementation is adopted, which exploit its full potential, IGA is a powerful and efficient high-order discretization method for the numerical solution of PDEs. We present an overview of the mathematical properties of IGA, discuss computationally efficient isogeometric algorithms, and present some significant applications.