Considerable opportunities for advances remain regarding parallel computation that could impact computational chemistry. For example, multigrid methods solve grid-based electrostatics problems in an optimal amount of work (and storage) on sequential computers. That is, the unknown potential can be determined on a grid of n points in O(n) work and storage. However, the standard adaptation of multigrid methods to parallel computers is not optimally efficient. A significant theoretical problem is whether a solution technique exists that uses only O(n/p) work on a parallel computer with p processors.
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