Řešení Helmholtzovy úlohy pomocí metody FETI-H

Abstract

This thesis is concerned with the solution of the Helmholtz partial differential equation by the domain decomposition method known as FETI-H (Finite Element Tearing and Interconnecting - Helmhotlz). The method is based on decomposition of the computational domain into several non-overlaping subdomains and solving for restrictions of the final solution on individual subdomains independently. However, it is necessary to overcome a few problems that arise during the proccess. First, it is local regularization by the means of complex mass matrix on interfaces between subdomains. Unlike Laplace's equation, where the coarse space is obtained naturally, in the case of Helmhotlz equation this coarse space have to be constructed artificially.