Thus, on every level, we compute an approximation to the solution of the original equation, not of an error equation. The cost of solving a problem on the coarsest grid is, of course, related to the size of the coarsest grid. If the coarsest grid is very coarse, the cost is negligible. However, numerical reasons often dictate a minimum resolution for the coarsest grid. In some instances, the performance of the computations on the coarsest grids cannot be neglected.
Many alternatives exist for smoothing.
Parallelization will be easiest with point relaxations. Hence, we shall restrict our attention to point relaxation methods. We maintain this basic structure for the concurrent and adaptive algorithms. Although the doubly linked list of grids will be replaced by a more complex structure, the basic multigrid algorithm will not be altered. While the library of grid function operations will be expanded, the fundamental operations will remain the same.