Scalability and FETI based algorithm for large discretized variational inequalities

The point of this paper is to review recent theoretical and experimental results related to scalability of the FETI based domain decomposition algorithm that was proposed recently by Dostál, Friedlander, Santos and Gomes for numerical solution of discretized variational inequalities. After briefly describing the basic algorithm with a “natural coarse grid” and its implementation, we review theoretical results that indicate a kind of optimality of the algorithm, namely that the number of iterations that are necessary to complete some parts of the algorithm is bounded independently of the discretization parameter. Then, we give some results of numerical experiments with parallel solution of a model problem discretized by up to more than eight million of nodal variables to give an evidence of both numerical and parallel scalability of the algorithm presented.