@TechReport{ it:2003-034,
author = {Per L{\"o}tstedt and Alison Ramage and von Sydow, Lina and
Stefan S{\"o}derberg},
title = {Preconditioned Implicit Solution of Linear Hyperbolic
Equations with Adaptivity},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2003},
number = {2003-034},
month = may,
abstract = {This paper describes a method for solving hyperbolic
partial differential equations using an adaptive grid: the
spatial derivatives are discretised with a finite volume
method on a grid which is structured and partitioned into
blocks which may be refined and derefined as the solution
evolves. The solution is advanced in time via a backward
differentiation formula. The discretisation used is second
order accurate and stable on Cartesian grids. The resulting
system of linear equations is solved by GMRES at every
time-step with the convergence of the iteration being
accelerated by a semi-Toeplitz preconditioner. The
efficiency of this preconditioning technique is analysed
and numerical experiments are presented which illustrate
the behaviour of the method on a parallel computer. }
}