The Multigrid Workbench: Algorithm

The general multigrid algorithm for the solution of

A_hu_h = f_h

procedure MG(level,A_h,u_h,f_h) if level=coarsest then

solve coarse grid equation

else smooth A_hu_h = f_h (m₁ times) Compute residual r_h = f_h - A_hu_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_hu_h = f_h (m₂ times) endif endprocedure

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

m₁, the number of presmoothing steps
m₂, 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