Report Number: CS-TR-72-278
Institution: Stanford University, Department of Computer Science
Title: Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations.
Author: Concus, Paul
Author: Golub, Gene H.
Date: April 1972
Abstract: We study an iterative technique for the numerical solution of strongly elliptic equations of divergence form in two dimensions with Dirichlet boundary conditions on a rectangle. The technique is based on the repeated solution by a fast direct method of a discrete Helmholtz equation on a uniform rectangular mesh. The problem is suitably scaled before iteration, and Chebyshev acceleration is applied to improve convergence. We show that convergence can be exceedingly rapid and independent of mesh size for smooth coefficients. Extensions to other boundary conditions, other equations, and irregular mesh spacings are discussed, and the performance of the technique is illustrated with numerical examples.