Robust solvers for Isogeometric Analysis

Dr. Stefan Takacs

March 20, 2018, 3:30 p.m. S2 416-1

The key idea of Isogeometric Analysis (IgA), as proposed in
the year 2005 by Hughes et al., is to unite the world of computer aided
design (CAD) and the world of finite element (FEM) simulation. From a
technical point of view, IgA can be seen as a spline-based FEM approach.
It aims to converge like a high-order method, for the costs of a
low-order method. This is not obtained for free: the condition number of
the matrix resulting from discretizing a partial differential equation
(PDE) with IgA grows exponentially in the spline degree. We will still
that it is nonetheless possible to set up multigrid solvers whose
convergence rates do not deteriorate if the spline degree is increased.
Besides a sketch of the convergence theory, numerical experiments
indicating the efficiency of the proposed methods will be presented.

This talk is a preparation for the RICAM scientific advisory board meeting.