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Excerpt from Domain Decomposition Algorithms for Indefinite Elliptic Problems
Domain decomposition techniques are powerful iterative methods for solving lin ear systems oi equations that arise from finite element problems. In each iteration step, a coarse mesh finite element problem and a number of smaller linear sys tems, which correspond to the restriction of the original problem to subregions, are solved instead of the large original system. These algorithms can be regarded as divide and conquer methods. The number of subproblems can be large and these methods are therefore promising for parallel computation. The central mathematical question is to obtain estimates on the rate of convergence of the iteration by deriving bounds on the spectrum of the iteration operator. We are able to establish quite satisfactory bounds if the coarse mesh is fine enough.
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