Paralelizace řešení eliptických okrajových úloh pomocí TFETI metody rozložení oblastí

Abstract

The bachelor thesis deals with parallel implementation of the TFETI domain decomposition method, which is developed at the Department of Applied Mathematics VŠB - TU Ostrava to solve large engineering problems. It deals also with application of TFETI on the solution of elliptic boundary value problems. After finite element space discretization we decompose the domain into nonoverlapping subdomains defined by mesh elements. This leads to a system of linear equations with block-diagonal system matrix which enables its effective parallel solution. The gluing conditions and even the Dirichlet boundary conditions are enforced by the Lagrange multipliers, so the method is more effective and simpler for implementation than FETI. The effective regularization of the stiffness matrices of the subdomains is performed and the condition number of the dual problem with Lagrange multipliers is improved by using orthogonal projectors. Both numerical and parallel scalability of TFETI are tested in the numerical experiments.