Additive Schwarz Domain-Decomposition method with embedded small scales for Diffusion Equation.

Juergen Geiser , Susanne Kilian

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 16 pages, figures in color and black-white

MSC 2000

80A20 Heat and mass transfer, heat flow

80M25 Other numerical methods

Abstract
We present a convergence and error bound study for domain-decomposition methods with very small domains. The idea is to apply very fast solver methods for strips with $h << \epsilon$ and to exploit optimized local smoothing properties on the interface for $h \approx \epsilon$. We apply the results in some applications for 2 dimensional domains.