The Perfectly Matched Layer in Curvilinear Coordinates

In 1994 B erenger showed how to construct a perfectly matched absorbing layer for the Maxwell system in rectilinear coordinates. This layer absorbs waves of any wavelength and any frequency without reeection and thus can be used to artiicially terminate the domain of scattering calculations. In this paper we show how to derive and implement the B erenger layer in curvilinear coordinates (in two space dimensions). We prove that an innnite layer of this type can be used to solve time harmonic scattering problems. We also show that the truncated B erenger problem has a solution except at a discrete set of exceptional frequencies (which might be empty). Finally numerical results show that the curvilinear layer can produce accurate solutions in the time and frequency domain. Abstract In 1994 B erenger showed how to construct a perfectly matched absorbing layer for the Maxwell system in rectilinear coordinates. This layer absorbs waves of any wavelength and any frequency without reeection and thus can be used to artiicially terminate the domain of scattering calculations. In this paper we show how to derive and implement the B erenger layer in curvilinear coordinates (in two space dimensions). We prove that an innnite layer of this type can be used to solve time harmonic scattering problems. We also show that the truncated B erenger problem has a solution except at a discrete set of exceptional frequencies (which might be empty). Finally numerical results show that the curvilinear layer can produce accurate solutions in the time and frequency domain.