# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics
**DI Dr. Thomas
Takacs**, Institut für Angewandte Geometrie, JKU,
will give a public talk (followed by a discussion) on **Wed, Feb. 3, 2021**
at **16:00 o'clock** at **ZOOM**
on the topic of
"Smooth Geometries for Isogeometric Analysis"
. The organziers of the symposium,

Univ.-Prof. Dr. Gerhard Larcher

A.Univ.-Prof. Dr. Jürgen Maaß, and

die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

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 for Isogeometric Analysis (IGA). The aim of IGA is to combine geometric modeling and numerical simulation of partial differential equations (PDEs) in a common framework. While geometric modeling often employs smooth 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 is to 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 consider discretizations suitable for second- and fourth-order boundary value problems. 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.