On page 1332 of the above article the statement "For example, in DelPhi, one may only employ cubical meshes with 63 mesh lines in each direction" is no longer accurate; more recent versions of DelPhi have been extended to allow for the use of larger cubical meshes.
This paper concerns the iterative solution of the linear system arising from the Chebyshev-collocation approximation of second-order elliptic equations and presents an optimal multigrid preconditioner based on alternating line Gauss-Seidel smoothers for the corresponding stiffness matrix of bilinear finite elements on the Chebyshev-Gauss-Lobatto grid.
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