Solving PDEs: challenges and innovative tools

During this talk, I will discuss the challenges for the numerical analysis of partial differential equations, with a special attention to the impact of this activity in the real world, and in particual in the product design process. This perspective open new questions in numerical analysis and computational geometry, some of them having a very theoretical flavour.

Isogeometric analysis (IGA), introduced by Hughes et al. in 2005, is a novel numerical approach that try to tackle these challenges by redesigning numerical techniques for PDEs. Within the isogeometric approach, the interaction of geometric modelers and PDE solvers is drastically simplified, and, moreover, the isogeometric numerical methods enjoys interesting properties that would be hard to obtain with classical finite elements. I will discuss our recent advances in this field.