The multigrid methodology is reviewed. By integrating numerical processes at
all scales of a problem, it seeks to perform various computational tasks at a
cost that rises as slowly as possible as a function of n, the number of
degrees of freedom in the problem. Current and potential benefits for lattice
field computations are outlined. They include: O(n) solution of Dirac
equations; just O(1) operations in updating the solution (upon any local
change of data, including the gauge field); similar efficiency in gauge fixing
and updating; O(1) operations in updating the inverse matrix and in
calculating the change in the logarithm of its determinant; O(n) operations
per producing each independent configuration in statistical simulations
(eliminating CSD), and, more important, effectively just O(1) operations per
each independent measurement (eliminating the volume factor as well). These
potential capabilities have been demonstrated on simple model problems.
Extensions to real life are explored.Comment: 4