Final Report Summary - HIGEOM (Highly accurate Isogeometric Method)
Partial Differential Equations (PDEs) are used in science and engineering simulations, often in tight connection with Computer Aided Design (CAD). The IsoGeometric Method (IGM), a.k.a Isogeometric Analysis (see https://en.wikipedia.org/wiki/Isogeometric_analysis) proposed in 2005 by T.J.R. Hughes et al., aims at improving the interoperability between CAD and PDEs solvers. This is achieved by adopting the CAD mathematical primitives, i.e. Splines and Non-Uniform Rational B-Splines (NURBS), both for geometry and unknown fields representation. The aim of the ERC project HIGEOM has been the development of a mathematical understanding of the IGM, giving the basis for a development of new tools for the efficient construction and solution of the linear systems, time integration, flexible local mesh refinement, and so on. These tools are essential for the use of higher degree and higher accuracy IGM in real-world applications. We have been able to make IGM a superior, highly accurate and stable methodology, well suited for the numerical simulation of PDEs, when accuracy is essential both in geometry and fields representation.