# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics Dr. Mario Kapl, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences (ÖAW), will give a public talk (followed by a discussion) on Wed, Jan. 22, 2020 at 16:15 o'clock at HS 12 on the topic of "Smooth isogeometric spline spaces for multi-patch geometries" . The organziers of the symposium,

O.Univ.-Prof. Dr. Ulrich Langer,
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 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.