Finite element preconditioning for spectral multigrid methods (Q1316108)

Second-order linear elliptic equations are considered on a rectangle in the plane. The basic method is collocation by tensor products of Chebyshev polynomials. The method of solution is by a multigrid iteration, where for each iteration the defect is computed from the collocation operator and the new iterate is a line-Gauss-Seidel approximate inverse of a finite element operator. Computed examples indicate that the method is very efficient.