Technological applications nowadays require more and more efficient and accurate computations supporting them. This need cannot be satisfied just by improving the raw power of computers, but it calls for innovative solvers that integrate in a natural way flexible tools for geometric design and numerical simulation. The school aims at a presentation of numerical methods that effectively combine Computer Aided Design (CAD) and efficient solvers for systems of Partial Differential Equations (PDEs). The focus is on Isogeometric Analysis, whose basic idea is to merge the two above standards by using spline spaces both for the modeling of geometries and for the discretization of PDEs of interest.

The school will cover the mathematical foundations of Isogeometric analysis as well as its applications and future perspectives. The main features of splines basis will be analyzed, including recent results on their approximation properties. Another topic that will be discussed in the school is the design of locally refinable spaces. Structure-preserving isogeometric discretizations will be presented.  Space-time isogeometric methods and low-rank isogeometric methods will also be introduced. Finally, applications will be presented, ranging from civil and mechanical to biomedical engineering, including, e.g., simulation of shells, laminates and fluid-structure interaction.