A Review of Numerous Parallel Multigrid Methods

Multigrid methods originated earlier this century, in the personnel computing era. Someone who needed to compute an approximation to the solution of a partial di erential equation during that era would ll a room with people. After using very simple mechanical calculators to compute parts of the approximation, these people would pass their parts to the other people in the room who needed them. Except for the very di erent time scales and approximate solution accuracy, this process is similar to computing on today's distributed memory parallel computers. The most basic model problem for elliptic boundary value problems in multigrid has always been, e ectively, the two dimensional Poisson equation