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Highly accurate Isogeometric Method

Objective

"Partial Differential Equations (PDEs) are widely used in science and engineering simulations, often in tight connection with Computer Aided Design (CAD). The Finite Element Method (FEM) is one of the most popular technique for the discretization of PDEs. The IsoGeometric Method (IGM), proposed in 2005 by T.J.R. Hughes et al., aims at improving the interoperability between CAD and FEMs. 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 IGM has gained an incredible momentum especially in the engineering community. The use of high-degree, highly smooth NURBS is extremely successful and the IGM outperforms the FEM in most academic benchmarks.

However, we are far from having a satisfactory mathematical understanding of the IGM and, even more importantly, from exploiting its full potential. Until now, the IGM theory and practice have been deeply influenced by finite element analysis. For example, the IGM is implemented resorting to a FEM code design, which is very inefficient for high-degree and high-smoothness NURBS. This has made possible a fast spreading of the IGM, but also limited it to quadratic or cubic NURBS in complex simulations.

The use of higher degree IGM for real-world applications asks for new tools allowing for the efficient construction and solution of the linear system, time integration, flexible local mesh refinement, and so on. These questions need to be approached beyond the FEM framework. This is possible only on solid mathematical grounds, on a new theory of splines and NURBS able to comply with the needs of the IGM.

This project will provide the crucial knowledge and will re-design the IGM 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."

Field of science

  • /natural sciences/mathematics/pure mathematics/geometry
  • /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations/partial differential equations

Call for proposal

ERC-2013-CoG
See other projects for this call

Funding Scheme

ERC-CG - ERC Consolidator Grants

Host institution

UNIVERSITA DEGLI STUDI DI PAVIA
Address
Strada Nuova 65
27100 Pavia
Italy
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 928 188
Principal investigator
Giancarlo Sangalli (Dr.)
Administrative Contact
Sofia Baggini (Dr.)

Beneficiaries (1)

UNIVERSITA DEGLI STUDI DI PAVIA
Italy
EU contribution
€ 928 188
Address
Strada Nuova 65
27100 Pavia
Activity type
Higher or Secondary Education Establishments
Principal investigator
Giancarlo Sangalli (Dr.)
Administrative Contact
Sofia Baggini (Dr.)