NEUMANN-NEUMANN ALGORITHMS FOR SPECTRAL ELEMENTS IN 3 DIMENSIONS

In recent years, domain decomposition algorithms of Neumann-Neumann ty pe have been proposed and studied for h-version finite element discret izations. The goal of this paper is to extend this family of algorithm s to spectral element discretizations of elliptic problems in three di mensions. Neumann-Neumann methods provide parallel and scalable precon ditioned iterative methods for the linear systems resulting from the s pectral discretization. In the same Schwarz framework successfully emp loyed for h-version finite elements, quasi-optimal bounds are proved f or the conditioning of the iteration operator. These bounds depend pol ylogarithmically on the spectral degree p and are independent of the n umber and size of subdomains and the jumps in the coefficients of the elliptic operator on the element interfaces.