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* '''Correction''' – Adding prolongated coarser grid solution onto the finer grid.
There are many choices of multigrid methods with varying tradeoffs between speed of solving a single iteration and the rate of convergence with said iteration. The 3 main types are V-Cycle, F-Cycle, and W-Cycle. For a discrete 2D problem, F-Cycle takes 83% more time to compute than a V-Cycle iteration while a W-Cycle iteration takes 125% more. If the problem is setup in 3D ___domain, then a F-Cycle iteration and a W-Cycle iteration take about 64% and 75% more time than a V-Cycle iteration ignoring overheads.
Any geometric multigrid cycle iteration is performed on a hierarchy of grids and hence it can be coded using recursion. Since the function calls itself with smaller sized (coarser) parameters, the coarsest grid is where the recursion stops. In cases where the system has a high condition number, the correction procedure is modified such that only a fraction of the prolongated coarser grid solution is added onto the finer grid. {| class="wikitable"
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