Application of M-PML reflectionless boundary conditions to the numerical simulation of wave propagation in anisotropic media. Part I: Reflectivity

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 of 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 minimum possible parameter that ensures stability. This problem is considered in the second part of this work.