The Heat Conduction Equation Finite Difference Domain Decomposition Algorithm

The domain decomposition is a natural way to develop methods for numerically approximating solutions to partial differential equations on parallel computers. It is to divide the domain over which the problem is defined into subdomains, and solve th submain problem in parallel.The developments of the parallel algorithm of the heat equation have been introduced in Chapter 1, in which main work of this paper is also described. In Chapter 2, When the interface points decompose (0,1) with equal distance into multi-subdomains, there is given that a new error estimate result on the difference solution of the domain decomposition algorithm developed by C.N.Dawson and others [13] for solving the heat equation. In Chapter 3, a new decomposition algorithm for the heat equation is also developed by using Saul'yev's asymmetric schemes at the interface points, and the prior error estimates of the approximate solution is obtained. The results of the new algorithm is compared with that of the algorithm in [13]. Numerical experiments on the accuracy of the algorithms are also presentsd. In Chapter 4, we present some new techniques in designing finite difference domain decomposition algorithm for the heat equation. The basic procedure is to define the finite difference schemes at the interface grid points with smaller time step by explicit schemes, and the prior error estimates for the numerical solutions are obtained. Numerical experiments on accuracy are also presented. In Chapter 5, we extent the results of the finite difference domain decomposition algorithm of paper [13] for two dimensional heat equation and give some numerical results. The conclusions for the research work of this paper are surveyed in the last chapter.