Isogeometric Methods

Alessandro Reali, University of Pavia
Yuri Bazilevs, University of California San Diego
David J. Benson, University of California San Diego
René De Borst, University of Glasgow
Trond Kvamsdal, Norwegian University of Science and Technology
Thomas J.R. Hughes, University of Texas at Austin
Giancarlo Sangalli, University of Pavia
Clemens V. Verhoosel, Eindhoven University of Technology
Isogeometric Analysis (IGA) has been originally introduced and developed by T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs, in 2005, to generalize and improve finite element analysis in the area of geometry modeling and representation. However, in the course of IGA development, it was found that isogeometric methods not only improve the geometry modeling within analysis, but also appear to be preferable to standard finite elements in many applications on the basis of per-degree-of-freedom accuracy. Non-Uniform Rational B-Splines (NURBS) were used as a first basis function technology within IGA. Nowadays, a well established mathematical theory and successful applications to solid, fluid, and multiphysics problems render NURBS functions a genuine analysis technology, paving the way for the application of IGA to solve a number of problems of academic and industrial interest. Further fundamental topics of research within IGA include the analysis of trimmed NURBS, as well as the development, analysis, and testing of flexible local refinement technologies based, e.g., on T-Splines, hierarchical B-Splines, or locally-refined splines. Moreover, an important issue regards the development of efficient integration strategies able to reduce assembly costs, in particular when higher-order approximations are employed. Aiming at reducing the computational cost still taking advantage of IGA geometrical flexibility and accuracy, isogeometric collocation schemes have recently attracted a good deal of attention and appear to be a viable alternative to standard Galerkin-based IGA. Another more than promising topic, deserving a special attention in the IGA context, is finally represented by structure preserving discretizations.

Along (and/or beyond) these research lines, the purpose of this symposium is to gather experts in Computational Mechanics with interest in the field of IGA with the aim of contributing to further advance its state of the art.