A Domain Decomposition Method For Solving Burgers Equation On Two-dimensional Unbounded Domains

In this thesis,by the theory of the natural boundary reduction and the key idea of domain decomposition method(DDM),a Dirichlet-Neumann(D-N)alternating algorithm and a Schwarz alternating algorithm based on the natural boundary reduction are devised for the solution of the Burgers equation in an exterior two-dimensional domains.In the first chapter,based on the Cole-Hopf transformation,the Burger-s equation is changed into a heat conduction equation,and then by the New-mark method we discredize the heat conduction equation in time,leading to a time-stepping scheme,where an exterior elliptic problem has to be solved at each time step.Secondly,we introduce a circular artificial boundary and obtain the Poisson integral formula and the natural integral equation of the problem in exterior circular domain by the principle of the natural boundary reduction(NBR).Thirdly,by means of the results of NBR,the Dirichlet-Neumann al-ternating algorithm for solving the discrete problem is proposed.We analyze the convergence of the algorithm.And D-N alternating algorithm is proved to be equivalent to preconditioned Richardson iteration.Finally,some numerical experiments are presented to illustrate the feasibility and effectiveness of the method.In the second chapter,a Schwarz alternating algorithm based on NBR for Burgers equation is proposed.we analyze the convergence of the algorithm and prove the geometric convergence in the sense of energy norm.Finally,some numerical experiments are presented to illustrate the feasibility and effectiveness of the method.