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

Document Type

Article

Publication Date

1-1-2009

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

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.

Publication Title

IAENG International Journal of Applied Mathematics

Volume

39

Issue

4

First Page

1

Last Page

11

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