Numerical solution of differential and integral equations
In this paper, we suggest an effective iterative preconditioned method to solve elliptic problems with jumps in coefficients. This algorithm is based on the Additive Schwartz Method (domain decompositions method) for two cases. In first case we consider a domain decomposition method with nonoverlapping subdomains and in second the overlapping subdomains. Here for overlapping subdomain preconditioning operators we consider an arbitrary distribution of coefficients of the problem in subdomains and consider the two cases. In the first case we investigate the situation when we have the big coefficients in subdomains with the full Sobolev norm (Theoretical and Numerical investigation) and in the second case we investigate the next situation : when we have the big coefficients in subdomains with only Sobolev seminorms (Numerical investigation). In both cases the main computational cost is a solution of Laplace operator in whole domain and in subdomains. Iterative convergence is independent of jumps in coefficients and mesh size.
Note. Abstracts are published in author's edition
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