Domain Decomposition Algorithm For Compact Difference Schemes Of Heat Equation

In recent years, domain decomposition algorithm for solving partial differential equations has become one of the effective method. Domain decomposition method is used to make complex or large-scale domain divided into several overlapping or non-overlapping sub-domains, and then the problem can be solved by using various algorithm in the sub-domain. By means of do-main decomposition, the computation on the sub-domains can be paralleled. This approach on one hand allows for the different sub-regions on the sub-model features using different discrete meth-ods, which help to improve accuracy, on the other hand it can be independent of each sub-domain method to solve the issue, which greatly increases the computational speed. Domain decomposition method for solving partial differential equations numerically have been extensively studied, but on the compact difference scheme for the domain decomposition method is still relatively rare, so this paper based on the basis of previous work, mainly introduces the non-overlapping domain decom-position method and overlapping domain decomposition method for the compact difference scheme of heat equation numerically. This paper is divided into three chapters. The first chapter is an introduction, brief overview of the domain decomposition algorithms and the basic content of the discussion paper. Chapterâ…¡, it is firstly presented that Dawson and others for solving heat equation domain decomposition method and error estimates, then extend this algorithm to compact differ-ence scheme of heat equation. This algorithm is non-overlapping domain decomposition method, in which algorithm the domain over the problem is divided into sub-domains by introducing interface point. Interface values between sub-domains are found by an explicit difference formula and big space step while the interior of the sub-domains it satisfies an implicit difference formula and small step, possibly different, once interface values are calculated, sub-domain problems can be solved in parallel, and then give the corresponding a priori error estimation. Chapterâ…¢, mainly using over-lapping domain decomposition algorithm for the heat equation Compact Difference Scheme, which is an efficient parallel finite difference scheme based upon overlapping domain decomposition the algorithm is based upon the domain decomposition and the subspace correction method, the resid- ual is modified on each subspace, and the computation is completely parallel. Optimal convergent rate is proved.