Iterative methods based on domain decomposition, with particular reference to problems of machining distortion (Q1083287)

We consider some iterative methods for problems of elasticity theory based on the idea of substructuring. Suppose that the given complicated domain can be decomposed into two or more simple subdomains for which solutions are available. In contrast to customary methods of substructuring, we allow subdomains to overlap, or one to be inside another. The given domain can be formed in a rather flexible way as a union, product, or relative complement (difference) of subdomains. We study several iterative schemes of patching solutions for subdomains, to give the solution of the required problem. Convergence is established by presenting the operator of an iterative procedure as a product of two or more projectors. We then apply one of the algorithms for a problem of machining distortion as a result of residual stresses.