# Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Dr. Stefan Takacs, Institute of Computational Mathematics, JKU Linz, am Wed, Oct. 9, 2019 um 17:15 Uhr im HS 12 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "Robust multigrid solvers and related topics" 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)

A third aspect of robustness is linked to the polynomial (spline) degree, which we consider in the context of Isogeometric Analysis. The dependence of the condition number on the spline degree is particularly severe since it grows exponentially with the spline degree. This being not enough, the spline degree also affects the sparsity pattern of the stiffness matrix. The number of non-zero entries of the stiffness matrix grows like $p^d$, where $p$ is the spline degree and $d$ is the spatial dimension. This means that the computational costs per multigrid cycle are not expected to be independent of the spline degree. To be able to talk about robustness, we have to have both robust convergence behavior and a well bounded computational complexity per multigrid cycle. In this framework, we first consider single-patch domains that are parameterized by one single geometry function. Then, the results are extended to domains that are composed of numerous patches.