Highly accurate Isogeometric Method

HIgeoM - ERC Consolidator Grant n.616563

Project information

  • Principal Investigator: Giancarlo Sangalli
  • Project start: June 2014
  • Project duration: 60 months

Available positions

Project summary

Models in many areas of scientific and technological interest (such as solid mechanics, fluid mechanics, fluid-structure interaction, electromagnetism, ...) are written in the language of Partial Differential Equations (PDEs). These equations have rich mathematical structure and their exact solution is impractical or impossible, for real world problems. Therefore, so-called numerical methods are studied in order to approximate the PDE solution by means of a computer algorithm. The ERC HIgeoM project ("Highly accurate Isogeometric Method") is aimed at developing one recent and very promising numerical method, named IsoGeometric Method (IGM). IGM addresses the interoperability between Computer Aided Design (CAD) and numerical simulation of PDEs. CAD softwares, used in industry for geometric modeling, typically describe the geometry of physical domains by mathematical functions named Non-Uniform Rational B-Splines (NURBS), and the interface between CAD output and classical numerical schemes (relying on a different class of functions) calls for expensive re-meshing methods that result in approximate representation of domains. IGMs are NURBS-based schemes for solving PDEs whose benefits go beyond the improved interaction with CAD. Indeed, they provide a substantial increase of the accuracy-to-computational-effort ratio and, thanks to the use of high-degree smooth NURBS within the numerical scheme, they outperform classical numerical schemes in most academic benchmarks. However, the mathematical understanding of the IGM is still incomplete and likely we are far from exploiting its full potential. 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. The HIgeoM research activity is aimed at providing the crucial knowledge to further develop the IGM into a highly accurate and stable numerical methodology, having an impact in many fields of numerical simulation, particularly when accuracy is essential both in geometry and solution representation. The HIgeoM project is carried on in Pavia at the Mathematics Department and in close cooperation with IMATI-CNR (Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, CNR), involving a large group of PhDs and Post-docs, and spans from very theoretical research to implementation and testing for complex applications close to industrial benchmarks.


Above: isogeometric simulation of the bukling of a shell represented by 32 NURBS patches (by P. Antolin)

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