• Panagiotis Karakitsios, Geomiso Company
• Vasiliki Tsotoulidi

Ιsogeometric analysis (IGA) is a powerful high-order methodology for numerical solution of partial differential equations that has come to bridge the gap between computer-aided design (CAD) and finite element analysis. It has been originally introduced by T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs in 2005, to generalize and improve finite element analysis with the goal of achieving a seamless integration of design and computer-aided analysis (CAA). Since then, it has attracted a lot of attention for solving boundary value problems, as a result of using the same shape functions, means splines, functions commonly used in CAD, for both describing the domain geometry and building the numerical approximation of the solution. IGA appears to be clearly superior to standard finite elements, while it has a wide spectrum of industrial applications (mechanical, naval, structural, and geotechnical engineering, fluid mechanics, aeronautics, cardiovascular bioengineering).

This powerful generalization of the traditional finite element analysis offers better capabilities, as it exploits the full potential of the CAD model, and achieves efficient, seamless design-through-analysis procedures. The utilization of the exact geometry mesh for analysis, not only improves the geometry modeling within analysis, but also eliminates geometric errors, significantly increases the accuracy of the numerical results of the analysis, and drastically reduces the required computational time and cost. It thus creates high added value for both engineers and their projects, while there is no need of repeating the geometry design for refinement purposes. Therefore, engineering applications and products end up being better and more optimized.

IGA encompasses all the latest and most advanced CAD tools. Popular NURBS and modern T-splines are proved the most suitable shape functions and a mighty tool for IGA. NURBS were until lately the main shape functions used in isogeometric analysis. T-splines were first introduced by Sederberg et al. in 2003, as a more efficient alternative that holds all the benefits of NURBS. As opposed to B-splines and NURBS, T-splines are not restricted to a tensor product structure, while exhibit more design capabilities, like watertightness, but also sophisticated implementation that allows better handling more complex geometries and permits local refinement ensuring higher-order continuity and smoothness across patches. New spline techniques, such as polycube splines, have been proposed. While on simple geometries splines have shown superior performance in various challenging applications such as fluid-structure interaction, electromagnetism, and shell analysis, there remain many challenging problems in utilizing complex geometries in IGA and many difficulties between the basic science research in academia and technology transfer to problem solving by industry and other end users. The solution of these difficulties is expected to boost growth for CAD and CAE international markets.

The purpose of this minisymposium is to bring together experts in isogeometric analysis to discuss the latest advancements on analysis and design with spline techniques. It seeks for presenting successful collaborations between industries, national laboratories, and academia on challenging real-world problems, as well as for showcasing underexplored problems and emerging paradigms in industry upon which IGA could have an impact. This minisymposium will feature a broad representation of industrial results and projects in IGA, including presentations from industrial researchers, academics consulting on industry projects, software vendors, tech startups, and end users. In addition to theoretical study, the minisymposium will also expose best practices and spark new ideas for effective collaboration on multidisciplinary research, while it welcomes related presentations on industrial applications and software development. Areas of interest include, but are not limited to:
• Structural statics and dynamics
• Materials and structures
• Complex geometries, multi-patch isogeometric analysis, smooth multi-patch methods
• NURBS, T-splines, manifold splines, polycube splines, subdivision surfaces, subdivision volumes, U-splines, UE-splines, CB-splines, HB-splines, NUAT splines, V-splines, Hermite splines, composed splines, Beta-splines
• Spline methods on unstructured quadrilateral and hexahedral meshes
• Analysis of trimmed NURBS
• Flexible local refinement technologies based on T-splines and hierarchical B-splines
• Volumetric parameterizations
• Mesh adaptivity
• Design optimization
• Space time variational multiscale isogeometric analysis
• Thermomechanical isogeometric analysis
• New computing platforms: cloud computing, GPU, high performance computing