Year: 2008
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 2 : pp. 113–137
Abstract
The uniaxial perfectly matched layer (PML) method uses rectangular domain to define the PML problem and thus provides greater flexibility and efficiency in dealing with problems involving anisotropic scatterers. In this paper an adaptive uniaxial PML technique for solving the time harmonic Helmholtz scattering problem is developed. The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates. The adaptive finite element method based on a posteriori error estimate is proposed to solve the PML equation which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the PML absorbing layer. Numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method. In particular, it is demonstrated that the PML layer can be chosen as close to one wave-length from the scatterer and still yields good accuracy and efficiency in approximating the far fields.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-NMTMA-6044
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 2 : pp. 113–137
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Adaptivity uniaxial perfectly matched layer a posteriori error analysis acoustic scattering problems.