Two-Grid Algorithm Of Domain Decomposition Methods For Solving Pdes

Some methods are constructed by combining two-grid algorithm with domain decomposition methods, such as the additive Schwarz algorithm of two-level overlapping domain decomposition methods and the two-level non-overlapping domain decomposition methods of the additive Schwarz preconditioner, they are studied on theory analysis and solving ellipse equations. Then, local and parallel finite element algorithm based on two-grid discretezations is constructed, it is studied on theory analysis and is applied to solve non-linear equations. Theory analysis and numerical result indicate that the algorithms combined two-grid with domain decomposition methods have some advantage in solving partial differential equations. The two-grid algorithm is a iteration method with higher convergence speed, it solves the whole iteration with slower convergence speed of the phenomenon that is caused by low frequency components. The additive Schwarz algorithm of two-level overlapping domain decomposition methods and the two-level non-overlapping domain decomposition methods of the additive Schwarz preconditioner are more efficient to solve partial differential equations.Chapter 1 introduces the background of domain decomposition methods. In chapter 2, domain decomposition methods is simply introduced, then chapter 2 introduces domain decomposition methods for non-overlapping subdomains and domain decomposition methods for overlapping subdomains. Chapter 3 constructs the additive Schwarz method of two-level overlapping domain decomposition methods and gives convergence analysis, error estimates and numerical example. In chapter 4, the two-level non-overlapping domain decomposition methods of the additive Schwarz preconditioner is constructed, then we give convergence analysis and error estimates and numerical example. Chapter 5 introduces local and parallel finite element algorithms on two-grid discretization for solving nonlinear problems in detail. Numerical example and convergence analysis and error estimates are presented at last. Chapter 6 is conclusion of this thesis, main results are given. And the work needs to complete later areenumerated.