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HIGEOM Report Summary

Project ID: 616563
Funded under: FP7-IDEAS-ERC
Country: Italy

Mid-Term Report Summary - HIGEOM (Highly accurate Isogeometric Method)

Partial Differential Equations (PDEs) are widely used in science and engineering simulations, often in tight connection with Computer Aided Design (CAD). The IsoGeometric Method, or IsoGeometric Analysis (IGA), proposed in 2005 by T.J.R. Hughes et al., aims at improving the interoperability between CAD and the PDE solver. This is achieved by adopting the CAD mathematical primitives, i.e. Splines and extensions, both for geometry and unknown fields representation. The IGA has gained an incredible momentum especially in the engineering community. However, we are far from having a satisfactory mathematical understanding of the IGM and, even more importantly, from exploiting its full potential. Until now, IGA theory and practice have been deeply influenced by finite element analysis. For example, IGA is implemented resorting to a finite element standard code design, which is very inefficient for high-degree and high-smoothness NURBS.
The use of higher degree IGA for real-world applications asks for new tools allowing for the efficient construction and solution of the linear system, time integration, unstructured mesh, and so on. These questions need to be approached beyond the finite element framework.
This project is providing the crucial knowledge to make it a superior, highly accurate and stable methodology, having a significant impact in the field of numerical simulation of PDEs, particularly when accuracy is essential both in geometry and fields representation.

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