Unigrid for Multigrid Simulation

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. 1. Introduction. The subject of this paper is unigrid, a method designed primarily for solving the equations arising from discretization of partial differential boundary value problems. The method is closely related and, under certain conditions, theoretically equivalent to multigrid, although all of the unigrid computations are performed on a single grid, as the name implies. Unigrid is generally more computa- tionally costly than multigrid, yet its simplicity is reflected in its relative ease of code implementation and use with existing applications software. This enables unigrid to act effectively as a software tool to simulate the multigrid approach that requires a