Fast Solvers for Isogeometric Analysis based on Alternating Linear Schemes for Tucker Tensors

Dr. Clemens Hofreither

March 26, 2019, 3:30 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.