The general multigrid algorithm for the solution of

is a linear iteration of the form

`procedure MG(level,A _{h},u_{h},f_{h})`

if level=coarsest then

- smooth
A
_{h}u_{h}= f_{h}(m_{1}times)

- Compute residual
r
_{h}= f_{h}- A_{h}u_{h}

- Restrict
f
_{H}= Rr_{h}

- Call MG(level - 1, A
_{H},v_{H}=0,f_{H}) (m_{c}times)

- interpolate
v
_{h}= Pv_{H}

- correct
u
_{h}^{new}= u_{h}+ v_{h}

- smooth
A
_{h}u_{h}= f_{h}(m_{2}times)

endprocedure

Besides the particular choice of the algorithmic components, three parameters determine the performance of the algorithm

- m
_{1}, the number of presmoothing steps - m
_{2}, the number of postsmoothing steps - m
_{c}, the cycling strategy

Ulrich Ruede , Thu Feb 2 21:06:58 MEZ 1995

Updated by Craig C. Douglas