@TechReport{ it:2003-007,
author = {Henrik Brand{\'e}n and Sverker Holmgren and Per Sundqvist},
title = {Discrete Fundamental Solution Preconditioning for
Hyperbolic Systems of {PDE}},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2003},
number = {2003-007},
month = feb,
abstract = {We present a new preconditioner for the iterative solution
of linear systems of equations arising from discretizations
of systems of first order partial differential equations
(PDEs) on structured grids. Such systems occur in many
important applications, including compressible fluid flow
and electormagnetic wave propagation. The preconditioner is
a truncated convolution operator, with a kernel that is a
fundamental solution of a difference operator closely
related to the original discretization.
Analysis of a relevant scalar model problem in two spatial
dimensions shows that grid independent convergence is
obtained using a simple one-stage iterative method. As an
example of a more involved problem, we consider the steady
state solution of the non-linear Euler equations in a two
dimensional, non-axisymmetric duct. We present results from
numerical experiments, verifying that the preconditioning
technique again achieves grid independent convergence, both
for an upwind discretization and for a centered second
order discretization with fourth order artificial
viscosity. }
}