Plamen Yalamov, Marcin Paprzycki and Lubin Vulkov
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Numerical modelling and studying of stationary heat and mass transfer processes in composite materials often bring us to singularly perturbed problems in composed domains, that is, to elliptic equations with discontinuous coefficients and a small parameter e multiplying the highest derivatives. For such problems the application of numerical methods based on a domain decomposition (DD) technique seems quite reasonable; the original domain is naturally decomposed into several subdomains with smooth coefficients. Due to the presence of transition and boundary layers, standard numerical methods yield large errors. By this reason, we need for special numerical methods with errors independent of the parameter e, i.e., methods convergent e-uniformly. For the above problems considered on sufficiently simple canonical regions, we construct domain decomposition finite difference schemes that converge e-uniformly. To this end, we use classical finite difference approximations on piecewise uniform grids, which are a priori refined in the transition and boundary layers. We study parameters of the DD schemes for which the number of iterations in the iterative numerical process is independent of the perturbation parameter.
The work has been supported by the Russian Foundation for Basic Research under Grant N 98-01-00362.
Date received: February 4, 2000