A Multigrid Block Krylov Subspace Spectral Method for Variable-Coefficient Elliptic PDE

Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time‐dependent variable‐coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this same approach to time‐independent PDE of the form Lu = g where L is an elliptic differential operator. Numerical results demonstrate the effectiveness of this approach, in conjunction with residual correction applied on progressively finer grids, for Poisson’s equation and the Helmholtz equation