Non-overlapping Pseudo-spectral Domain Decomposition Method

This paper introduces the radial basis function collocation method(RBF)、pseudospectral method(PS) and several non-overlapping domain decomposition method(DDM), and gives the algorithm framework of three kinds of non-overlapping radial basis function collocation domain decomposition method(RBF-DDM) and pseudo-spectral domain decomposition method(PS-DDM). At last, the pseudo-spectral domain decomposition method is applied to solving the Bingham fluid problem in the cylindrical pipe and fourth-order obstacle problem.The main work is as follows:1. In chapter 2, the radial basis function collocation method and three kinds of nonoverlapping domain decomposition methods are introduced in detail, we put forward three kinds of non-overlapping domain decomposition methods based on the RBF collocation method. The specific steps of the method are given. In the numerical examples, we compared the effectiveness of the three methods. The effect of basis function、parameters、the number of nodes and subdomains are also discussed.2. In chapter 3, It presented in detail the mathematical description of the Bingham fluid laminar flow problem in the cylindrical pipe and pseudo-spectral method. Two kinds of non-overlapping pseudo-spectral domain decomposition method are proposed. Compared with analytical solution, it illustrates the effectiveness of this method in the numerical examples. Finally, it discussed the influence of the choice of parameters in the numerical examples.3. In chapter 4, it introduces the obstacle problem described by a kind of fourth-order elliptic variational inequality. Reformulated the original problem by the theory of duality method, it gives two kinds of pseudo-spectral methods for obstacle problem. Numerical examples are given. Compared with the finite element method, the numerical results illustrate the effectiveness of the method. It also discussed the influence of parameters, such as obstacle parameter, to the results.4. In chapter 5, the conclusion and the prospect for future work are given.