Recent progress in Multigrid Methods for multi-patch IgA discretizations
Dr. Stefan TakacsMay 30, 2017, 2:15 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.