@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. }
}