Fast Solvers for Isogeometric Analysis based on Alternating Linear Schemes for Tucker Tensors
Dr. Clemens HofreitherMarch 26, 2019, 2:30 p.m. S2 416-1
In this talk, we consider the construction of fast and memory-efficient solvers for tensor product Isogeometric Analysis by means of low-rank approximation. In particular, we consider the approximation of the solution fields by means of Tucker tensors and then propose an iterative method for the approximation of the solution based on a so-called Alternating Linear Scheme. The idea is to reduce the nonlinear best tensor approximation problem in the energy norm to a series of linear approximation steps for the individual factors of the Tucker tensor. We study several numerical examples in 2D and 3D where the proposed solution method exhibits very robust performance in both the spline degree and the geometry mapping.