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The Domain decomposition is a natural technique for reducing the computational cost for solving large-scale linear systems, somebody know how to do it using mathematica?

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Do you really need to do domain decomposition? LinearSolve[] is perfectly capable of handling large sparse matrices, using iterative methods. –  Guess who it is. May 29 '13 at 3:07
If LinearSolve is insufficient, would you add an example to your question that illustrates the problem? –  Michael E2 May 29 '13 at 3:44

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