Petr Vaněk¹, Roman Kužel¹, Ivana Pultarová², Milan Hanuš¹, Pavla Fraňková¹, and Zbyněk Vastl¹
¹ Západočeská univerzita v Plzni
² ČVUT v Praze

Multi-level methods with evolving coarse-space for solving linear and nonlinear problems
We propose a new non-linear multigrid that is a kind of exact approximation scheme. To solve non-linear problems, we add the current approximation vector as a column of the prolongator. This construction guarantees that the current approximation is present in the coarse-space. Thus, in the limit, the coarse-space contains the exact solution. We apply our method to the generalized eigenvalue problem and show very promising numerical results. We discuss shortly the issue of convergence theory that is currently in progress.