Geodesic
Application of M-PML absorbing boundary conditions to the numerical simulation of wave propagation in anisotropic media. Part~I: reflectivity
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 4, pp. 333-344

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This paper presents a detailed study of the construction of reflectionless boundary conditions for anisotropic elastic problems. A Multiaxial Perfectly Matched Layer (M-PML) approach is considered. With a proper stabilization parameter, the M-PML ensures solution stability for arbitrary anisotropic media. It is proved that this M-PML modification is not perfectly matched, and the reflectivity the M-PML exceeds that of the standard PML. Moreover, the reflection coefficient linearly depends on the stabilization parameter. A problem of constructing an optimal stabilization parameter is formulated as follows: find a minimal possible parameter that ensures stability. This problem is considered in a second paper on this work. 
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     author = {M. N. Dmitriev and V. V. Lisitsa},
     title = {Application of {M-PML} absorbing boundary conditions to the numerical simulation of wave propagation in anisotropic media. {Part~I:} reflectivity},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_2011_14_4_a0/}
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M. N. Dmitriev; V. V. Lisitsa. Application of M-PML absorbing boundary conditions to the numerical simulation of wave propagation in anisotropic media. Part~I: reflectivity. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 4, pp. 333-344. http://geodesic.mathdoc.fr/item/SJVM_2011_14_4_a0/