Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird DI Dr. Thomas Takacs, Institut für Angewandte Geometrie, JKU, am Wed, Feb. 3, 2021 um 17:00 Uhr im ZOOM einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "Smooth Geometries for Isogeometric Analysis" halten, zu dem die Veranstalter des Symposiums,

O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, und
die ÖMG (Österreichische Mathematische Gesellschaft)

hiermit herzlich einladen.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

Smooth Geometries for Isogeometric Analysis

In this talk, we study smooth geometry representations suitable forIsogeometric Analysis (IGA). The aim of IGA is to combine geometricmodeling and numerical simulation of partial differential equations(PDEs) in a common framework. While geometric modeling often employssmooth B-spline and non-uniform rational B-spline (NURBS) representations, numerical analysis of PDEs is usually based on finite elements over triangle or quadrilateral meshes.
Thus, when performing numerical analysis on a spline based geometric model, the classical approach requires a finite element mesh to be created. This meshing process usually introduces a discretization error and is in general quite time consuming. The core idea of IGA isto use the spline based geometry representation directly for the numerical discretization, allowing an exact geometry representation preserving smoothness as well as geometric features.
We study the relation between a geometric model and its suitability for IGA. Note that this depends on the underlying PDE. We mostly considerdiscretizations suitable for second- and fourth-order boundary valueproblems. For such model problems, we develop strategies to construct suitable geometric models. We especially focus on smooth multi-patch parameterizations and spline manifolds, representing planar and surface domains.