Domain decomposition using spectral expansions of Steklov-Poincaré operators II: A matrix formulation

We describe a matrix formulation of the iterative domain decomposition method in Natarajan [SIAM J. Sci. Comput., 16 (1995), pp. 470-495]. From one point of view, this method can be regarded as a preconditioning technique for the interface Schur-complement operator obtained from a decomposition into nonoverlapping subdomains. Prom another point of view, it can be viewed es a method of the Schwarz type for overlapping subdomains, but with an "overlap" between the physical space in one subdomain and the leading components of the eigenspace induced by the Steklov-Poincaré operator in the complementary domain.