Metody rozložení oblasti urychlené multigridem v 2d

Abstract

This thesis is focused on two dimensional Domain decomposition method optimization by replacing Gauss elimination, with the quadratic complexity, by Multigrid whose complexity is linear. The introductory text deals with the finite element method, which is the most used method in numerical solution of partial differential equations. Next, the method of domain decomposition is described, which allows to divide the problem into local tasks and solve them parallel. Further text describes multigrid and the two-gird algorithm. Finally, there are compared two variants of domain decomposition method. The standart one, using Gauss elimination method, is compared to a novel one, where Gauss elimination method is replaced by two-grid method.