An introduction to isogeometric analysis

Isogeometric analysis (IGA) is a numerical technique for the solution of partial differential equations (PDE), introduced with the goal of improving the interaction between Computer Aided Design (CAD) software and PDE solvers. IGA can be simply defined as a Galerkin method in which the computational domain is given by standard CAD functions, such as B-splines or NURBS, and the discrete solution is computed with the same kind functions. Apart from working with a CAD geometry, the main difference of IGA with respect to the standard finite element method is the higher continuity of the basis functions. This allows a direct discretization of high order PDEs, and also introduces some difficulties in the numerical analysis, because the basis functions have larger support.
In this seminar I will give an introduction to IGA, starting from the properties of B-splines and NURBS, and how they are used to generate geometries in CAD software. I will briefly present some of the most successful applications of IGA, in particular their use for the solution of Kirchhoff-Love shells, and also existing challenges and open problems.