Primární metody rozložení oblasti a hraniční prvky

Abstract

This work deals with primal domain decomposition methods for a 2-dimensional Poisson equation with homogenous Dirichlet's boundary conditions and jumping coefficients. The computational domain is decomposed into subdomains, that align the coefficients jumps. The problem is discretized by finite element method and converted into system of linear equations, which are solved by inexact three-step method acting as a preconditioner. Parallel preconditioner, comprised of three parts, is introduced. These parts are local problems on subdomains, local problems for all edges between the subdomains and a global coarse problem. The global coarse problem may be diskretized by finite element method and also by boundary element method using Steklov-Poincare operator. The boudary element approach gives us the possibility to solve this problem for more complicated shapes of subdomains. This approach is being introduced and tested in this thesis.