An iterative domain decomposition method for problems of mathematical physics. III

Abstract

The present paper completes the cycle of papers [1, 2] dealing with the construction and inves- tigation of efficient iterative domain decomposition methods for elliptic boundary value problems. The problem of developing and improving efficient algorithms for equations of mathematical physics in complicated composite domains such that these algorithms admit convenient implementation on multiprocessor computers is quite important [3-5]. For stationary problems, such methods are mainly the Schwartz iterative method and the domain decomposition method [5, 6], which allow one to reduce the original problem to subproblems considered in subdomains. Along with the above-mentioned methods, the alternating direction method and the method of total approxima- tion (component decomposition) [7-12] are also used for the decomposition of the original problem. The first algorithm has the following disadvantage: it cannot be applied if there are three or more components, which does not allow one to use the domain decomposition idea in full extent. The component decomposition schemes are constructed on the basis of the total approximation and are not very efficient for stationary problems.