Year: 2016
Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 3 : pp. 358–382
Abstract
The anisotropic perfectly matched layer (APML) defines a continuous vector field outside a rectangle domain and performs the complex coordinate stretching along the vector field. Inspired by [Z. Chen et al., Inverse Probl. Imag., 7, (2013):663--678] and based on the idea of the shortest distance, we propose a new approach to construct the vector field which still allows us to prove the exponential decay of the stretched Green function without the constraint on the thickness of the PML layer. Moreover, by using the reflection argument, we prove the stability of the PML problem in the PML layer and the convergence of the PML method. Numerical experiments are also included.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2016.m1505
Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 3 : pp. 358–382
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
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Finite Element and Discontinuous Galerkin Methods with Perfect Matched Layers for American Options
Song, Haiming
Zhang, Kai
Li, Yutian
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 4 P.829
https://doi.org/10.4208/nmtma.2017.0020 [Citations: 6]