# Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Dr. Mario Kapl, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences (ÖAW), am Wed, Jan. 22, 2020 um 17:15 Uhr im HS 12 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "Smooth isogeometric spline spaces for multi-patch geometries" 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)

Series B - Mathematical Colloquium:

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

### Smooth isogeometric spline spaces for multi-patch geometries

Isogeometric Analysis (IgA) is a numerical method for solving partial differential equations(PDEs)
by using the same (rational) spline function space for representing the geometry of the physical
domain and for approximating the solution of the PDE. Many physical problems involve for the numerical
simulation high order PDEs such as the analysis of Kirchhoff-Love shells or the phase-field crystal
equation, which are 4th or 6th order problems, respectively. Solving these 4th and 6th order
PDEs via the weak form and Galerkin discretization as mostly applied in IgA, the use of $C^1$-smooth
or even $C^2$-smooth functions is required. Moreover, so-called multi-patch geometries are needed to
describe complex physical domains, which cannot be obtained from single-patch representations.

The concept of IgA provides the possibility to combine both needs by allowing the construction of globally
$C^1$/$C^2$-smooth isogeometric spline spaces over complex multi-patch geometries and to use the generated
functions to solve high order PDEs over these multi-patch geometries. In this talk, we deal now with the topic of
$C^1$-smooth and $C^2$-smooth isogeometric spline spaces for multi-patch geometries, and present our
contributions to this field of research.