Geodesic
Application of absorbing boundary conditions M-PML for numerical simulation of wave propagation in anisotropic media. Part~II: Stability
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 1, pp. 45-54

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This paper deals with studies of the detailed properties of absorbing boundary conditions M-PML (Multiaxial Perfectly Matched Layer) that arise when a computational domain is limited. These conditions are stable for any type of anisotropy with a correct choice of a stabilization parameter. In the first part of this paper [3], the authors show a linear dependence of the reflectivity on the stabilization parameter. Based on this study, the problem of finding the optimal stabilizing parameter, which provides stability and minimal reflection has been formulated. In this paper, we provide a necessary stability condition of M-PML, which allows limiting the lower value of the stabilizing parameter. It is shown that this criterion is not sufficient. 
@article{SJVM_2012_15_1_a3,
     author = {M. N. Dmitriev and V. V. Lisitsa},
     title = {Application of absorbing boundary conditions {M-PML} for numerical simulation of wave propagation in anisotropic media. {Part~II:} {Stability}},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {45--54},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_1_a3/}
}
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M. N. Dmitriev; V. V. Lisitsa. Application of absorbing boundary conditions M-PML for numerical simulation of wave propagation in anisotropic media. Part~II: Stability. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 1, pp. 45-54. http://geodesic.mathdoc.fr/item/SJVM_2012_15_1_a3/