ABSTRACT
The primitive ideas of multigrid can be found from error smoothing by relaxation, total reduction, and nested iteration. Relaxation processes have been long known for error-smoothing properties (Southwell, 1935, 1946). Reduction methods were originally linked to calculations on coarser grids and recursive applications in the early 1950s (Schroeder, 1954). Nested iteration has been used for a number of years to obtain first approximations on finer grids from coarser grids. In 1962, Fedorenko described the first correct two-grid iteration and emphasized on the complementary roles of Jacobi iteration and coarse-grid correction. In 1964, he formulated the first multigrid algorithm and proved its typical convergence behavior. In 1966, Bakhvalov suggested a much more complex possibility of combining multigrid with nested iteration. In 1971, Astrakhantsev generalized Bakhvalov’s convergence result in order to apply it to the general boundary conditions.
