Metody rozložení oblasti s předpodmíněním

Abstract

This work deals with primary methods of domain decomposition for solving boundary problems with the Dirichlet's boundary conditions and study of preconditioning gradient methods. The problem of solving boundary problems is converted into the system of linear equations by finite element method and this system is solved by numerical iterative methods with preconditioning. The aim is to find the fastest methods of solving such systems and right methods of domain decomposition, which allows good parallelization of computation, helps to that. This work demonstrates how to build systems of linear equations from given boundary problems in 1D and 2D and how to apply the domain decomposition method. It also analyzes the possibilities of preconditioning with aim to find the most sensible option in terms of time and memory consumption of computation and precision of the solution.