# Recent progress in Multigrid Methods for multi-patch IgA discretizations

## Dr. Stefan Takacs

**May 30, 2017, 4:15 p.m. S2 059**

In classical isogeometric Analysis (IgA), the geometry of the computational

domain was represented by a global geometry function, based on (tensor-

product) B-splines or NURBS. For such a setting, we (C. Hofreither,

W. Zulehner and myself) have developed multigrid methods that are robust

both the polynomial degree and the grid size.

However, more complicated domains cannot be represented by just one such a

simple geometry representation. Instead, the whole domain is decomposed into

subdomains, typically called patches in IgA, where each of those is

represented by its own geometry function. It was shown that such a setting

can be handled with domain decomposition approaches, like IETI. We will

discuss, that such a setting can also be handled by applying multigrid

methods directly to the multi-patch setting.

As the smoother is the most expensive ingredient, additive variants of our

method could even be considered for parallelization.