Unigrid for Multigrid Simulation

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Abstract
This paper develops unigrid which is an algorithm that results from interpreting multigrid as it directly affects the fine grid approximation. Unigrid is theoretically equivalent to multigrid under certain assumptions, yet has different computational characteristics. Though it is generally less efficient, unigrid is very useful as a software tool for testing the feasibility of applying multigrid to a given problem. This is illustrated with several numerical examples.

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