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.