ONE-DAY WORKSHOP ON APPLIED MATHEMATICS 2024

SPEAKER

Carlotta Giannelli (Università degli Studi di Firenze)

SCHEDULE

15:00 - 16:00

TITLE

Adaptive spline approximations for geometric data processing and isogeometric analysis

ABSTRACT

Continuously growing computing technologies demand a novel coupling of shape representation models and numerical simulation schemes able to simplify the next-generation of computational frameworks. The talk focuses on the interaction between the geometric aspects of Computer Aided Design (CAD) representations and their intrinsic application-oriented nature. In the field of numerical simulation, the framework of isogeometric analysis (IGA), which suitably exploits CAD standard B-splines and their adaptive extensions, opens new perspectives, allowing the incorporation of automatic optimization methods into the product development process. In view of the rigidity of tensor-product B-splines, however, localized mesh refinement can only be obtained by identifying a (non-standard) spline basis on different unstructured grid configurations. In this setting, the mathematical foundations of adaptive isogeometric analysis were recently established and together with related applications, they are now a rather large research area in applied mathematics. Adaptive IGA methods are of interest for the simulation of different kinds of problems which necessarily require very fine meshes. The talk will discuss recent advances in the design and analysis of adaptive spline schemes by focusing on efficient processing and approximation for CAD model (re-)construction and (iso-)geometric modeling.