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.