Overlapping technique can make each subdomain contain more nodes, and the overlapped subdomains are nonlonger disjoint, is it taking the average value of the multiple nodes as the result.After overlapping, we will solve larger sundomins, and it will cost more time and storage, how can the benefit from taking average value of multiple nodes outperform the increse cost per iteration.Why is it necessary and usually beneficial.
why overlapping technique can accelerate the additive/multiplictive Schwarz
domain decomposition
The problem with elliptic operators is that the solution at any specific point depends on all the domain. The overlap allows to 'mix' the approximate solution between subdomains and therefore accelerates the solution of the problem. http://en.wikipedia.org/wiki/Domain_decomposition_methods