A root‐finding absorbing boundary condition (RFABC) for scalar‐wave propagation problems in infinite anisotropic media was developed. Although the phase velocity and the group velocity in isotropic media have the same sign, the sign of the latter can differ from that of the former in anisotropic media. Therefore, a RFABC for anisotropic scalar waves consistent with the group velocity of the considered media is developed, as the velocity is closely related to the direction of energy propagation. The developed boundary condition is shown to satisfy a criterion for an “enough accurate” boundary condition. The well‐posedness of the boundary condition is proven at the continuous level. Its finite‐element formulation, which ensures well‐posedness at a discrete level, is derived, after which it is demonstrated that accurate and stable solutions to the problem of antiplane shear‐wave propagation in an anisotropic elastic waveguide, an example of anisotropic scalar‐wave propagation, can be obtained using the proposed numerical approach.

中文翻译：

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无限介质中各向异性标量波的寻根吸收边界条件

建立了无限各向异性介质中标量波传播问题的寻根吸收边界条件（RFABC）。尽管各向同性介质中的相速度和群速度具有相同的符号，但在各向异性介质中，后者的符号可能与前者的符号不同。因此，由于速度与能量传播的方向密切相关，因此开发了一种与所考虑介质的群速度相一致的各向异性标量波的RFABC。所示的边界条件满足“足够准确”边界条件的标准。边界条件的适定性在连续水平上得到了证明。推导了它的有限元公式，该公式可确保离散水平上的适定性，