@TechReport{	  it:2012-007,
  author	= {Kenneth Duru and Gunilla Kreiss},
  title		= {Boundary Waves and Stability of the Perfectly Matched
		  Layer},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2012},
  number	= {2012-007},
  month		= apr,
  abstract	= {We study the stability of the perfectly matched layer
		  (PML) for symmetric second order hyperbolic partial
		  differential equations on the upper half plane, with
		  boundary conditions at $y = 0$. Using a mode analysis, we
		  develop a technique to analyze the stability of the
		  corresponding initial boundary value problem on the half
		  plane. We apply our technique to the PML for the elastic
		  wave equations subject to free surface and homogenous
		  Dirichlet boundary conditions, and to the PML for the
		  curl--curl Maxwell's equation subject to insulated walls
		  and perfectly conducting walls boundary conditions. The
		  conclusion is that these half--plane problems do not
		  support temporally modes.}
}