This activity, which addresses the interoperability between CAD and analysis with the objective of improving simulation-based design tools, is one of the main research lines of IMATI, and it is actually funded by large companies (Total, Michelin, Hutchinson).
It aims at developing Isoparametric techniques based on NURBS for simulating PDEs arising in electromagnetics, fluid dynamics and elasticity. Isogeometric analysis (IGA) stands for a collection of methods that uses splines and NURBS as main mathematical primitives both for the description of the computational domain and for the unknown fields.
The Finite Element Method (FEM) is by large the most popular technique for the computer-based simulation of PDEs and hinges on the assumption that the discretized domain and field are represented both by means of piecewise polynomials. Such an isoparametric feature is at the very core of FEM. However, CAD software, used in industry for geometric modeling, typically describes physical domains by means of Non-Uniform Rational B-Splines (NURBS) and the interface of CAD output with FEM calls for expensive re-meshing methods that result in approximate representation of domains. We study discretization schemes that are compatible in the sense that the discretized models embody conservation principles of the underlying physical phenomenon (e.g., charge in electromagnetism, mass and momentum in fluid motion and elasticity). The key benefits of NURBS-based methods are: exact representation of the physical domain, direct use of the CAD output, a substantial increase of the accuracy-to-computational-effort ratio. Furthermore, from the theoretical study of isogeometric methods, this research activity also aims at increasing the spread of IGA by developing our own software, which is made available to the research community through an open source license. Two main libraries are being developed by our group: GeoPDEs, written in Octave/Matlab, and igatools, written in C++.
|Buffa Annalisa||Bressan Andrea||Garau Eduardo||Reali Alessandro|
|Antólin Pablo||Brivadís Ericka||Martinelli Massimiliano||Sangalli Giancarlo|
|Beirão da Veiga Lourenço||Durkbin Cho||Pauletti Miguel Sebastian||Vázquez Rafael|
L. Beirão da Veiga, A. Buffa, G. Sangalli, R. Vázquez.
Mathematical analysis of variational isogeometric methods. Acta Numer. 23 (2014) 157–287.
L. Beirão da Veiga, A. Buffa, C. Lovadina, M. Martinelli, G. Sangalli,
An isogeometric method for the Reissner-Mindlin plate bending problem, Comput. Methods Appl. Mech. Engrg. 209-212 (2012) 45–53.
A. Buffa, J. Rivas, G. Sangalli, R. Vázquez,
Isogeometric discrete differential forms in three dimensions, SIAM J. Numer. Anal. 49 (2) (2011) 818–844.
L. Beirão da Veiga, A. Buffa, J. Rivas, G. Sangalli,
Some estimates for h-p-k-refinement in isogeometric analysis, Numer. Math. 118 (2) (2011) 271–305.