5-2 – Geometry and Discretization
Alessandro Reali (University of Pavia), Pablo Antolin (EPFL, Lausanne)
Despite geometry can be regarded as the foundation of analysis, modern methods of computational geometry have until recently had very little impact on analysis, leading, e.g., to many problems in interfacing Computer Aided Geometric Design (CADG) and Finite Element Analysis (FEA) tools. One of the most significant issues is the difficulty of translating CAGD files into analysis-suitable FEA geometry and meshing, reputed to take up to 80% of overall analysis time for complex engineering designs. The approximate, polynomial-based geometry of FEA also creates difficulties in modeling sliding contact, flows about aerodynamic shapes, buckling of thin shells, etc. As a consequence, in the last decade, many research efforts have been made towards the construction of modern numerical approaches being as flexible as possible regarding the representation of complex geometries and/or CAD-friendly, including, among others, isogeometric analysis, virtual element methods and mimetic finite differences, as well as maximum-entropy and subdivision-based methods. In particular, isogeometric methods have attracted a good deal of attention from both the Computational Engineering and Mathematics communities, emerging as a promising analysis tool with the potential to bridge the gap between geometry representation and numerical simulation. One of the main goals of isogeometric analysis is the construction of a fully integrated design-through-analysis process, with important practical applications and possibilities, particularly in the field of solid mechanics.
The purpose of this symposium is to gather experts in Computational Mechanics with interest in the above-mentioned class of methods, to show and discuss theoretical results, novel developments and approaches, as well as advanced engineering applications.