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Craig C. Douglas and Karen M. WaltersAlgorithm 2 performs the cascadic multigrid method for an O(h 4 ) method. On thecoarsest level, we solve the problem directly using an O(h 4 ) discretization. This solutionis interpolated to the next finer level using a fourth order interpolation method due toHyman [6], which is similar to doing interpolation plus a smoothing. Next we smooth usingsymmetric Gauss-Seidel until the energy norm is less than 1/4 that of the energy normE 2 computed in Algorithm 1. This is repeated on all levels with bound E 2 /(4 (level−1) ).The initial guess on the finer grids is the fourth order interpolation of the approximationfrom the previous grid.Algorithm 2 Cascadic multigrid using O(h 4 )method1. If j =1(a) Solve directly(b) Interpolate to j = 2 using fourth order interpolation2. If j>1(a) Smooth on z until E (j) 1(a) Smooth on z until E (j)
Craig C. Douglas and Karen M. WaltersAlgorithm 4 Cascadic multigrid switching discretization at level k1. If j =1(a) Solve directly using O(h 4 )method(b) Interpolate to j =22. Else if j =2,...,k(a) Smooth until E (j)
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