An algebraic method to develop well-posed PML models absorbing layers, perfectly matched layers, linearized Euler equations

  • Authors:

  • Adib N. Rahmouni

  • Affiliations:

  • Department of Mathematics, LAGA, Université Paris, Paris 13, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

In 1994, Bérenger [Journal of Computational Physics 114 (1994) 185] proposed a new layer method: perfectly matched layer, PML, for electromagnetism. This new method is based on the truncation of the computational domain by a layer which absorbs waves regardless of their frequency and angle of incidence. Unfortunately, the technique proposed by Bérenger (loc. cit.) leads to a system which has lost the most important properties of the original one: strong hyperbolicity and symmetry. We present in this paper an algebraic technique leading to well-known PML model [IEEE Transactions on Antennas and Propagation 44 (1996) 1630] for the linearized Euler equations, strongly well-posed, preserving the advantages of the initial method, and retaining symmetry. The technique proposed in this paper can be extended to various hyperbolic problems.