Využití izogeometrické analýzy při řešení 1D úloh pomocí MKP

Abstract

This thesis is focused on isogeometric analysis and its use for solving 1D boundary value problems. This is a modern variant of the finite element method. Assignment of the thesis has been extended also to 2D boundary value problems. First, the thesis is focused on the finite element method. Steps involved in the method are explained on solution of a 2D boundary value problem for the Poisson's equation with the combination of Dirichlet and Neumann boundary conditions. Next, NURBS curves and surfaces and their basis functions are described. Then, this thesis describes the isogeometric analysis, whose procedure is explained on solution of a 2D boundary value problem for the Poisson's equation with Dirichlet boundary condition. Finally, the finite element method and the isogeometric analysis are used for solving the specific examples of 1D and 2D boundary value problem for the Poisson's equation.